Handbook of Hydraulic Resistance - Coeficientes de Resistência Hidráulica

7 t 9EClr 4 a 4 C 11c ý i Ct Q LE ldelchik HANDBOOK OF HYDRAULIC RESISTANCE Coefficients of Local Resistance and of Friction C C LEEAR IN G H 0 U S E FOR FEDERAL SCIENTIFIC AND TECHNICAL INFORMATION HardopMicrofiche OU9E 3PP Novi 4 I Translated from Russian Published for the US Atomic Energy Commission and the National Science Foundation Washington DC by the Israel Program for Scientific Translations Reproduced by NATIONAL TECHNICAL INFORMATION SERVICE Springfield Va 22151 T IE IDELCCHIK HANDBOOK OF HYDRAULIC RESISTANCE I Coefficients of Local Resistance and of Friction Spravochnik po gidravlicheskim soprotivleniyam Koeffitsienty rnestnykh soprotivlenii i soprotivleniya treniya Gosudarstvennoe Energeticheskoe Izdatelstvo MoskvaLeningrad 1960 Translated from Russian 0 Israel Program for Scientific Translations Jerusalem 1966 i AECtr 6630 Published Pursuant to an Agreement with THE U S ATOMIC ENERGY COMMISSION and THE NATIONAL SCIENCE FOUNDATION WASHINGTON DC Copyright 0 1966 Israel Program for Scientific Translations Ltd IPST Cat No 1505 Translated by A Barouch M Sc Edited by D Grunaer P E and IPST Staff Printed in Jerusalem by S Monson Price 828 Available from the US DEPARTMENT OF COMMERCE Clearinghouse for Federal Scientific and Technical Information Springfield Va 22151 xS Table of Contents FOREWORD Sect ion One GENERAL INFORMATION AND RECOMMENDATIONS FOR USING THE HANDBOOK vii 1 11 List of general symbols used througl 12 General directions 13 Properties of fluids a Specific gravity b Viscosity 14 Equilibrium of fluids 15 Motion of fluids a Discharge and mean stream ve b Equation of continuity of a strea c Bernoulli equation Head loss 16 The flow of fluids through an orific a Flow of an incompressible fluid b Discharge of a compressible gas 17 Fluidflow states 18 Fluid resistance hout the book 1 o o o ocity am it e I e 19 Work of a compressor in systems 110 Examples of the calculations of the fluid resistance of systems 2 3 3 4 12 14 14 15 16 21 21 25 26 29 32 35 53 53 53 62 65 66 So 80 81 91 92 Section Two STREAM FLOW THROUGH STRAIGHT PIPES AND CHANNELS FRICTION COEFFICIENTS AND ROUGHNESS 21 List of sym bols 22 Explanations and practical recommendations 23 Roughness of pips and channels 24 List of the diagrams of friction coefficients of section II 25 Diagrams of friction coefficients Section Three STREAM INTAKE IN PIPES AND CHANNELS RESISTANCE COEFFICIENTS OF INLET SECTIONS 31 List of sym bols 32 Explanations and recommendations 33 List of the diagrams of resistance coefficients of section III 34 Diagrams ofresistance coefficients Section Four SUDDEN VARIATION OF VELOCITY IN STREAM PASSAGE THROUGH AN ORIFICE RESISTANCE COEFFICIENTS OF STRETCHES WITH SUDDEN EXPANSION ORIFICE PLATES APERTURES ETC 41 List of sym bols 42 Explanations and practical recommendations 43 List of diagrams of resistance coefficients of section IV 44 Diagrams of resistance coefficients Section Five SMOOTH VELOCITY VARIATION RESISTANCE COEFFICIENTS OF DIFFUSERS 51 List of sym bols 52 Explanations and recommendations 2 112 112 112 127 128 151 151 151 iii 53 List of the diagrams of resistance coefficients of section V 165 54 Diagrams of resistance coefficients 166 Section Six VARIATION OF THE STREAM DIRECTION RESISTANCE COEFFICIENT OF CURVES STRETCHESBRANCHES ELBOWS ETC 189 61 List of symbols 189 62 Explanations and recommendations 190 63 List of the diagrams of resistance coefficients of section VI 204 64 Diagrams of resistance coefffcients 206 Section Seven STREAM JUNCTIONS AND DIVISIONS RESISTANCE COEFFICIENTS OF WYES TEES AND CROSSES 247 71 List of symbols 247 72 Explanations and recommendations 247 73 List of diagrams for resistance coefficients of section VII 258 74 Diagrams of resistance coefficients 260 Section Eight FLOW PAST OBSTRUCTIONS UNIFORMLY DISTRIBUTED OVER CONDUIT CROSS SECTIONS RESISTANCE COEFFICIENTS OF GRIDS SCREENS PIPE BUNDLES PACKINGS ETC 305 81 List of sym bols 305 82 Explanations and recommendations 306 83 List of the diagrams of resistance coefficients of section VIII 319 84 Diagrams of resistance coefficients 321 Section Nine STREAM FLOW THROUGH PIPE FITTINGS AND LABYRINTH SEALS RESISTANCE COEFFICIENTS OF THROTTLES VALVES LABYRINTHS ETC 350 91 List of symbols 350 92 Explanations and recommendations 350 93 List of the diagrams of resistance coefficients of section IX 358 94 Diagrams of resistance coefficients 359 Section Ten FLOW PAST OBSTRUCTIONS IN A CONDUIT RESISTANCE COEFFIC1ENTS OF STRETCHES WITH PROJECTIONS TRUSSES GIRDERS AND OTHER OBSTRUCTIONS 379 101 List of symbols 379 102 Explanations and recommendations 379 103 List of the diagrams of resistance coefficients of section X 387 104 Diagrams of resistance coefficients 388 Section Eleven STREAM DISCHARGE FROM PIPES AND CHANNELS RESISTANCE COEFFICIENTS OF EXIT STRETCHES 400 111 List of symbols 400 112 Explanations and recommendations 400 113 List of the diagrams of resistance coefficients of section XI 414 114 Diagrams of resistance coefficients 416 Section Twelve STREAM FLOW THROUGH VARIOUS APPARATUS RESISTANCE COEFFICIENTS OF APPARATUS AND OTHER DEVICES 442 121 List of symbols I 442 122 Explanations and recommendations 442 123 List of the diagrams of resistance coefficients or resistance magnitudes of section XII 456 124 Diagrams of resistance coefficients 458 BIBLIOGRAPHY 492 INDEX 509 iv a This handbook contains data on the friction coefficients of straight pipes and channels and the coefficients of fluid resistance of fittings throttles obstructions elements of hydraulic or gasair lines and several devices used in industrial systems for gas purification heat exct ange and ventilation The handbook is divided into twelve sections The first section contains general informationon hydraulics and mechanics of fluids The other sections are each devoted to a definite group of fittings or other elements of pipes and obstructions with similar conditions of fluid motion and contain data on their fluid resistances Each of these sections is divided into descriptive material and separate diagrams for practical calculations each of which corresponds to a certain element of the pipe or obstruction In most instances these diagrams contain formulas for calculating the resistance coefficient of the element as a function of its main characteristics a graphical representation of this functional relationship and tables of the values of the resistance coefficients This handbook is intended for a wide range of specialists scientists designing and operating engineers of all branches of hydroengineering and students of universities and technical institutes A V V FOREWORD There is almost no branch of engineering which is not somehow concerned with the necessity of moving fluids through pipes conduits or machinery The degree of com plexity of a hydraulic or gasair line can be quite varied In some cases these are large scale systems of pipes gas mains water conduits steam pipes air ducts etc while in other cases these are pipelines of relatively small length but having a large number of fittings and branches various obstructions such as throttles and adjusting devices grids protruding parts etc The network through which a fluid moves usually represents a single unit such as boilers furnaces heat exchangers motors scrubbers chemical instruments and wind tunnels The correct calculation of the fluid resistance of these systems is necessary in all cases and a special handbook on the friction coefficients and the coefficients of local resistances should be available for this Until recently only restricted data were available on the subject and these were scattered among various textbooks on hydraulics and aerodynamics and in scientific papers In many cases these data are contradictory or dated and deal with only a limited number of local resistances Furthermore the coefficients of local resistances generally were given only for special geometric and physical characteristics In order to fill this gap in 1954 the author published a book Gidravlicheskie sopro tivleniya Fluid Resistances Gosenergoizdat 1954 on the general problems of fluid resistances based on the processing collating and classification of materials obtained from our studies and those of others We present here in the same spirit this special handbook on the local fluid and friction resistances The writing of this handbook presented considerable difficulties mainly due to the range of local resistances their geometric boundaries and the states of flow in them which are much narrower than required by practice Furthermore much of the data obtained is insufficiently accurate and reliable this is particularly true of the coefficients of local resistances Therefore it would have been better to delay the publication of this handbook until all coefficients of local resistances could have been checked and refined experimentally by some standard method based on the contemporary level of metrology Unfortunately it seems unlikely that such a series of experiments would be completed in the near future A different approach was also possible to include in the handbook only such data as can be considered reliable The amount of such data is however very small and this approach would result in a book which does not fulfill our object to present the necessary material for the hydraulic calculation of gasair and hydraulic lines Taking into account the great need of even tentative data for assessing the resistance of conduits made of stretches of quite varied configurations we decided to include vii PRECEDNG PAGEBLANK in this handbook not only data checked satisfactorily by laboratory studies but also data obtained by crude experiments and those obtained theoretically or by approximate calculations etc We feel that such an approach is justified since the accuracy with which conduits and components are manufactured and installed under industrial conditions can differ considerably from installation to installation and also from the laboratory conditions under which most coefficients of fluid resistances were obtained We have found it necessary to add to the basic material in the handbook some general principles of hydraulics and mechanics of fluids with descriptions of the contents of each section as well as additional explanations and recommendations for calculating and selecting hydraulic components The coefficient of local resistance is usually a function of many parameters and is therefore represented by an expression with many terms In order to obtain the numerical value of such a coefficient it is therefore necessary to use several curves or tables The different formulas for calculating the resistance coefficients frequently contain similar terms The curves representing these terms are not repeated each time but are given once and for all in one of the diagrams the number of this diagram is then indicated in the other diagrams This arrangement naturally complicates the use of the handbook it is however dictated by the necessity of reducing the volume of the book as much as possible These shortcomings are probably not the only ones Nevertheless it is our hope that this handbook will be of use to specialists in the calculation of the fluid resistances of various conduits The author will be grateful for any suggestions for correcting the mistakes that are found The author acknowledges the help of A D Altshul ASGinevskii IS Mochan L A Rikhter Candidates of Engineering Sciences and of Engineer L E Medovar in reading the MS and ýgiving many valuable suggestions The Author 4 viii Section One GENERAL INFORMATION AND RECOMMENDATIONS FOR USING THE HANDBOOK 11 LIST OF GENERAL SYMBOLS USED THROUGHOUT THE BOOK F crosssection area m 2 Do crosssection diameter m Dh dh hydraulic diameters 4X hydraulic radius m II crosssection perimeter m T crosssection coefficient 1 length of the stretch m h height m R r radii of cross sections or curvature respectively m A mean height of roughness peaks m A relative roughness Dh n area ratio or number of elements a angle of divergence or convergence of the conduit or angle of attack of the stream w stream velocity msec p pressure absolute kgm 2 H gage pressure kgm 2 A pressure loss or resistance kgm 2 AE energy loss kg msec Q volume flow rate m 3 sec G mass flow rate kgsec specific gravity of the flowing medium kgm 3 P density of the flowing medium kgsec 2 m 2 g g gravitational acceleration msec2 q dynamic viscosity v kinematic viscosity To absolute temperature of the medium OK to temperature of the medium C c c mean specific heats at p const and v const respectively kcalkgdegree P specificheat ratio C coefficient of fluid resistance Z friction coefficient of unit relative length length in sectiondiameter units of the stretch calculated C coefficient of drag velocity coefficient e coefficient of jet contraction p discharge coefficient Re Reynolds number I 12 GENERAL DIRECTIONS 1 The basic reference data given here are the friction coefficients cf in straight pipes and channels and the coefficients of local fluid resistance CI of pipe fittings thtottles obstructions and industrial instruments 2 When using this handbook it is assumed that all magnitudes in the wellknown formula for calculating the resistance cf 166 Atur sur 2gsum g T kgm2 11 except the total coefficient of fluid resistance sum rC and all geometric parameters of the system element being considered are given The only unknowns are Csum or simply C and its components Cfr and C P 3 The coefficient of local resistance can be considered equal to the total coefficient C in all diagrams for elements of conduits of relatively short length since the values of Cft in such elements can be neglected compared with the values of CP 4 Diagrams referring to elements of relatively long pipes and channels give the values of both the coefficients of local resistance C and the friction coefficients Cfr The values of resistance coefficients appearing in diagrams giving tentative data are to be considered as total coefficients 4 accordingly the frictional losses in these fittings are not to be added separately when summing all losses in the lines 5 The values of C I given in this handbook include the local pressure losses in the immediate proximity of a variation in the system configuration and also the pressure losses associated with the subsequent equalization of velocities over the straight exit section Since however local losses are arbitrarily determined as the difference between the total and frictional lpsses in the exit section the frictional losses have to be taken into account 6 In the case of a stream discharged from a fitting or some other element into a large volume such as the atmosphere the given coefficients of local resistance take into account the losses of dynarric pressure e at the exit Wex velocity at outlet section 2g 7 All values of local resistance coefficients given in the handbook with certain exceptions are given for conditions of uniform velocity distribution in the inlet section of the element considered as a rule such conditions prevail behind a smooth inlet 8 The influence on the local resistance of an element due to fittings obstructions or lengthy straight stretches located downstream is not allowed for by the values given fr C in the handbook except as noted In certain cases this influence causes an increase in the value of C of the element considered and7in other cases a decrease As yet there is no general method of allowing for this 9 The dependence of the coefficients of local resistance on the Reynolds number Re is onlygiven in those cases where the influence of the latter is known or can be estimated In practice Re has an influence on the local resistance in the range Re 10 52Xl10 At Re 105 2 X 105 ittcan almost alwaysbe assumed that the coefficients of local resistance are independent of Re At smaller values of Re it is necessary to allow for itsl influence on the basis of the data given in the handbook In what follows the subscript sum in the symbols for the total resistance coefficient r and the total resistance AH will be omitted 2 If there is no indication of the values of Re for which the values given for C were obtained it can be assumed in the case of turbulent flow Re 103 that the resistance coefficient is practically independent of the value of Re In the case of laminar flow Rel 03 the data given in the handbook can be used only for a rough estimate of the resistance 10 All values of the resistance coefficients given in this handbook except as noted w were obtained for Mach numbers M 03 In practice however the values given for t CI and tfr are correct even for higher subsonic velocities roughly up to M 0708 In some cases the relationship between C and MI is given 11 Most of the data on the coefficients of local resistance were obtained for smooth channel walls the influence of roughness on the local resistance has not been extensively studied Therefore unless otherwise specified the walls of the stretches given here should be considered smooth In practice the influence of the roughness for Reynolds numbers Re 4X 104 can be approximated by introducing into the coefficient C a factor of the order of 11 to 12 higher at large roughness 12 The shape of the cross section of fittings is indicated in the handbook when it has a bearing on the value of the resistance coefficient or when the values of this coefficient were obtained for specific cross sections In all cases where the cross section is not indicated or when no additional data on the resistance of elements of noncircular section are given the value of the resistance coefficient for a polygonal or rectangular section of a0 side ratio 0617 is to be considered equal to the value for a circular section 13 The curves and tables of resistance coefficients given are based either on calcula tions or empirical data In the latter case the values of C given by approximate formulas can differ somewhat from the data of the curves and tables These formulas can be used for tentative calculations only 14 Since the coefficients of fluid resistance are independent of the medium flowing through a system and are determined chiefly by the geometric characteristics of the given element or in some cases by the flow conditions the Reynolds or Mach numbers the data given in the handbook are suitable for calculating resistances of purely hydraulic lines as well as gas air and other lines and elements 15 A complete calculation of the fluid resistance of the entire network can be performed by means of the proposed tables cf examples of hydraulic calculation Table 110 etc 16 This handbook gives the values of the resistance coefficients for various shapes and parameters of pipe and channel elements The minimum values of can be easily established on the basis of the curves and tables of resistance given in the diagram and on the basis of the recommendations given in the explanatory part of each section of the handbook 1 7 The list of diagrams of resistance coefficients given at the beginning of each section indicates both the source and the method experimental theoretical or tentative by which these coefficients were obtainedso that it is possible to form some opinion on their reliability 13 PROPERTIES OF FLUIDS a Specific gravity 1 The specific gravity y is defined as the ratio of the weight of a given body to its 3 volume weight of a unit volume In technical units it is usually measured in kgmr o Where the medium is homogeneous 3 2 The values of the specific gravity of water are given in Table 11 The specific gravity of some other liquids at different temperatures is given in Table 12 The values of the specific gravity of some gases at standard conditions 00C 760 mmmer cury 100 dry and of their weight relative to air whose specific gravity is taken as unity are given in Table 13 TABLE 11 Specific gravity of water 121 I C 0 10 20 30 40 50 1 60 70 SO j 90 100 120 140 160 T kgmr3 99987 99973 99823 99567 99224 98807 98324 97781 j 971S3 96534 9583S 9434 j 9264 9075 3 For multicomponent gases blastfurnace gas coke gas the specific gravity of the mixture is determined by the formula Tm Ot IL2V YRP Y kg m d ry 100 where YI T2 are the specific gravities of the mixture components at 0C and7 60 mm mercury cfTable 13 kgmi3 dry v V v are the volume percentages of the mixtures components according to data obtained from a gas analysis b Viscosity 1 Viscosity is a property of all fluids and manifests itself as internal friction during motion There is a difference between 1 the absolute or dynamic viscosity T defined as the ratio between the shearing stress and the velocity gradient 7u 12 dy dw where is the shearing stress Tis the velocity gradient in the direction of the nornmal y 2 the kinematic viscosity v defined as the ratio between the dynamic viscosity of the fluid and its density 2 The dynamic viscosity is measured in the CGS system in poises ps the correlspond ing units of measurement of the shearing stress and the velocity gradient are dynicm 2 and cmsecXcm rspectively 1 po Iise 1dyn X sec g cdnse 1 cm X sec The centipoise cps which is 102 times smaller or the micropoise Fips which is 106 times smaller aremore generally used dyn X sec CM2 1 ps 100 cps 106 IPs 4 TABLE 12 Specific gravity of various liquid s at a pressure of 1 atm 111 18 Type of liquid C kgrn3 9 Ammonia Aniline I Acetone Gasoline Benzene Brom ine Butane normal W ater Sea water Glycerine anhydrous Coal tar Dichloroethane Nitrogen dioxide Sulfur dioxide Kerosene Lignite oil Wood oil Castor oil Coconut oil Linseed oil boiled Light machine oil 34 15 15 15 15 60 15 05 see Table 11 15 15 18 20 15 15 32 10 15 20 15 15 15 15 10 20 50 10 20 50 15 15 18 15 15 15 5 15 15 15 18 20 15 1518 15 0 0 684 1004 790 680740 900 882 3190 601 10201030 1270 1260 1250 1200 11751200 1484 1472 790820 970 920 970 930 940 809 898 895 Soo 898 895 890 960 920 925 870 930 700900 537 1290 1800 1890 870 13546 810 790 2 964 1469 954 Medium machine oil Mineral lubricating oil O live oil Paraffin oil Turpentine oil Cotton oil Natural mineral oil Liquefied ozone Carbon bisulfide Sulfuric acid 87 Sulfuric acid fuming Turpentine M ercury Methyl alcohol methanol Ethyl alcohol ethanol Tetrabromoethane Chlorine Methyl chloride Ethyl chloride Chloroform Hydrogen Ethyl ether 0 1518 0 1518 919 1480 715 740 5 Specific gravity of dry gas at 0C and 1 TABLE 13 atm and specific heats at 20C of 1 kg dry gas 18 Specific Weight Type of gas Chemical formula gravity T relative e 1 ev kgim to air C Nitrogen N 2 12507 09612 0250 018 140 Ammonia NH3 07710 05962 0530 0400 129 ArgonA 17820 13781 0127 0077 166 Acetylene C2H2 11710 09056 0402 0323 125 Benzene C6 H6 34840 26950 0299 0272 110 Butane C 4H1 0 26730 20672 0458 0414 111 Isobutane C4H10 26680 20633 0390 Air 12930 10000 0241 0172 140 Hydrogen H 2 00899 06450 3410 2420 141 Water vapor H2 08040 06218 Helium He 01785 01380 1260 0760 166 Nitrous oxide NO 19780 15297 0210 0164 128 Oxygen 02 14290 11051 0218 0156 140 Krypton Kr 37080 28677 0060 0036 167 Xenon Xe 58510 45252 0038 0023 170 Methane CH4 07170 05545 0531 0405 131 Neon Ne 09002 06962 0248 0148 168 Ozone 0 22200 17169 129 Nitric oxide NO 13400 10363 0233 0166 138 Carbon oxide CO 12500 09667 0250 0180 140 Propane C3 118 20200 15622 0445 0394 113 Propylene C3H6 19140 14802 0390 0343 117 Hydrogen sulfide H2S 15390 11902 0253 0192 130 Carbon oxysulfide COS 27210 21044 Sulfur dioxide SO2 29270 22637 0151 0120 125 Carbon dioxide C 02 19760 15282 0200 0156 130 Chlorine C1 2 32170 24880 0115 0085 136 Methyle chloride CH 3C1 23080 17772 0177 0139 128 Ethane C2H6 13570 10486 0413 0345 120 Ethylene C 2H 4 12610 09752 0365 0292 125 In industry the unit i kg is the unit of mass of measurement of the dynamic viscosity is kg X sec or where kg is the unit of force m kg where mXhour The unit of measurement of kinematic viscosity in the CGS systen is the stoke st CM2 or2 the ceinok ct m cm or the enistoke est mm which is 102 smaller its unit of measurement in see m2 see industry is s see 3 Conversion factors for the different systems are given in Table 14 for the dynamic viscosity q and in Table 15 for the kinematic viscosity 4 Exampies of conversion of the viscosity units of measurement a Given the value of the dynamic viscosit of a gas n poises ps 180 9 10c g It is required to convert tto the industrial system of units jl6 kgx secm 2 ý6 04 TABLE 14 According to Table 14 the conversion factor is equal to 102x 10 2 Then S7lS1210ips 10210 X 180 910 8510 kgxsecm 2 b Given the value of the dynamic viscosity of water in the footpoundsecond system of units qffps 692x10 6 1bft xsec It is required to convert it to the CGS system kgx secm 2 According to Table 14 the conversion factor is equal to 152X 10 I Then l s 15210169210 i05102 kgxsecm 2 c Given the value of the kinematic viscosity of air in centistokes vcst 150 It is required to convert itto industrial units IS m2sec 6 According to Table 15 the conversion factor is equal to 10 Then I S 10 Vcst 150106 msec d Given the value of the kinematic viscosity of water in the footpound hour system of units ft 2hour fh 578101 It is required to convert it to CGS units stokes According to Table 15 the conversion factor is equal to 260x10 Then Sst2 2 6 vfh 60057810 15010 cm 5 When the kinematic viscosity is determined as the ratio dynamic viscosity speci fic gravity care should be taken to use consistent units of measurement in numerator and denominator In order to obtain the value of the kinematic viscosity V in stokes st the dyna mic viscosity 71 must be in ps and the specific gravity in gcm3 the result is cm 2sec ie st in order to obtain v inm 2 sec istakeninkgXsecm 2 and is divided by the density 7 y n kgXsec 2 pm in inorder toobtain v in m 2hour q istakeninkgmXhourandis divided kg by the specific gravity y in 6 The dynamic and kinematic viscosities depend on the characteristics of the medium The dynamic viscosity of fluids is a function of the temperature only and for perfect gases is independent of the pressure The viscosity of vapors and gases increases with the increase of the temperature while that of liquids decreases The kidnematic viscosity of liquids and gases is a function of both temperature and pressure TABLE 15 Conversion factors for kinematic viscosity v Unit of measurement Cent istoke Stoke 2 2 ft2 2 c m m 2 sec cm 2 sec converttoro sec hour sec hour given cst st Centistoke mmm2 sec cst 1 102 106 360X10 107 x 10 385x 10 Stoke cm 2 sec st 102 1 104 360X 10 107 x 103 385 m 2 6 4 4 10 10 1 360x10 107x10 385x10 sec 278x102 278 278x10 4 1 298x10s 107x10 hour ft2 935 x10 935x 102 935 x 1 02 36 X 10 1360 x 10 sec ft 260X10 260x 10 260X 105 935 102 278X10 1 hour 7 The relationship between the viscosity of gases and the temperature can be expressed approximately by Sutherlands formula 273 C T 21a 13 where 71 is the dynamic viscosity of the gas at 0C Tis the absolute temperature OK C is a constant depending on the igas The values of tHe dynamic viscosity qin micropoises for various gases as a function of the ternperature and the values of the constant C and the maximum temperature at which the value ofrthis constant ýhas been corroborated experimentally are given in Table 16 The values of the kinematic viscosity v in cst for the same gases as a function of the temperature at a pressure of 1 atm are given in Table 17 The values of vffor air in m 2 sec are also given in Figure 11 8 The kinematic viscosity ofa gasý mixture can be determined by Manns approximate formula 100 14 V 02 Vn where v V are the dynamic viscosities of the components v0 v v are the percentage weights of themixture components 8 0 0 0 6 4 TABLE 16 Dynamic viscosity of gases v ILps at a pressure of 1 atm as a function of the temperature and the values of the constant C in the Sutherland formula 17 18 11921 Gas Formula Temperature Temperature Ga s2 015 C range C Nitrogen i57 5 1660 1748 1835 1925 2000 2082 2290 2460 2810 3110 3660 4130 104 25280 Ammonia NH 2 860 930 1005 1078 1145 1215 1280 1460 503 20300 Argon A 2120 2220 2710 3210 3670 4100 4870 5540 142 20827 Acetylene C2 H2 902 960 1021 1082 1145 1202 1260 215 Benzene CH6 620 686 735 790 840 895 950 1080 1210 1470 448 130313 Butane C 4H10 690 740 950 358 Hydrogen H2 804 840 880 918 959 996 1030 1130 1210 1390 1540 1830 2100 710 20100 Water vapor HO 820 893 967 1040 1113 1187 1260 1604 2000 2390 3145 3865 961 20406 Air M620 1712 1809 1904 1998 2089 2190 2602 2972 3301 3906 4430 111 16825 Helium He 1750 1860 1955 2040 2135 2205 2290 2700 3070 3420 4070 4650 0 21100 Sulfur dioxide SO 2 1160 1260 1630 2070 2460 306 300825 Nitrous oxide N2 0 1370 1460 1830 2250 2650 260 25280 Oxygen 02 1815 1920 2025 2130 2235 2340 2440 2900 3310 3690 4350 4930 125 20280 Krypton Kr 2330 2460 3060 188 Xenon Xe 2110 2260 2870 252 Methane CHA 955 1020 1080 1150 1214 1270 1330 1470 1610 1860 164 20250 Nitric oxide NO 1790 1880 2270 2680 128 20250 Carbon monoxide CO 1595 1680 1768 1855 19j5 2024 2102 2290 2470 2790 100 Ao 130 Pentanep CsH 12 6U0 1000 1030 383 Propane C3 Hs 700 750 800 854 905 958 1001 1130 1250 1440 278 20250 Propylene C3 H6 780 835 1070 1410 487 Hydrogen sulfide H2 S 1160 1240 1590 331 Carbon dioxide CO 1280 1380 1470 1570 1670 1755 1845 2260 2640 2990 3620 4135 254 Chlorine Cl 1145 1230 1320 1410 1500 1590 1680 1890 2100 2500 350 100250 Methyl chloride CH 3C1 980 1060 1360 1750 454 Ethyl chloride C2H 5Cl 940 1050 1430 411 Hydrogen cyanide HCN 740 901 Ethane C 2 H 860 920 1150 1280 1420 252 20250 Ethylene CH 4 885 945 1010 107 0 1120 1185 1240 1400 1540 225 10250 TABLE 17 Kinematic viscosity v cst at a pressure of 1 atm as a function of temperature 17 18 119121 0S Gag FormTemperature C Ga Formula o 1 1 I io hl20 ojo6 1 20 0 20o 40 o 60 60 o 1 100 1 15 1 200 1 0 M 0 0 Nitrogen N2 1167 1330 500 1685 18806 2065 2230 2830 3410 4720 6140 9350 13000 Ammonia NH 3 681 1200 1400 1600 1810 2035 2270 2930 3600 Argon A A 1190 1330 2070 3120 4330 5650 8750 12300 Acetylene C2 H2 473 820 935 1060 1194 1325 1470 Benzene C6 H6 i66 1195 226 260 294 333 373 480 602 885 Butane C 4HI 0 25806 2970 4850 Hydrogen H2 8400 9350 10500 11730 13000 14300 15660 19500 23300 32400 42300 65100 91800 Water vapor H2 0 950 1112 1290 1484 1690 1866 2150 Air 1166 1320 1500 1698 1885 2089 2300 30 3490 4820 6320 9650 13400 Helium He 912 1040 1174 1312 1455 1597 1750 2620 3610 4730 7280 10250 Sulfur dioxide S02 400 460 760 1220 1760 Nitrous oxide N20 682 793 1270 1970 2820 Oxygen 02 1104 1340 1536 1713 1905 2116 2340 3520 4870 6380 9750 13570 Krypton Kr 62 713 1370 Xenon Xe 359 415 670 Methane CH4 1257 1420 1650 1844 2007 2290 2540 318 3900 5450 Nitric oxide NO 1330 1510 2320 3054 Carbon monoxide CO 1186 1350 1516 1700 1896 2100 2270 284 3430 4685 Propane C 3H 8 304 370 426 490 552 618 E76 870 1084 1510 Propylene C 3H6 408 470 770 114 Hydrogen sulfide H2 S 762 870 1410 1980 2800 3730 6520 8200 Carbon dioxide CO2 562 700 802 905 1030 1210 1280 Chlorie Cl2 309 380 436 502 566 636 715 910 1150 1625 Methyl chloride CH 3C1 428 490 805 1310 Ethane C2H6 635 728 1160 1470 1810 Ethylene C 2H4 680 750 866 973 1085 1215 1340 1730 2120 4 1 m 2 sec 450 W 00 Iff 40 o 0a JI 20 7W0 205 250 221 W0 40 44 V18 FIGURE 11 Kinematic viscosity of air as a function of its temperature at p 10 atm viscosity of the mixture can be determined by the approximate formula The dynamic 100 O II 1O 1 5 where 71 12 ij are the dynamic viscosities of the components 0 2 Gn are the percentage weights of the mixture components 9 The dependence of the dynamic kgXsec and kinematic m 2see viscosities of water on the temperature and pressure is given in Table 18 The dependence of v 2fof werinsec water on the temperature at 1 atm is given in Figure 12 M FIGURE 12 Kinematic viscosity o1 water as a function of its temperature II TABLE 18 Dynamic and kinematic viscosities of water as functions of temperature and pressure 121 C 0 10 20 30 40 1 501601 70 so W 1100 1 1201 130 p kgcm 2 10 10 10 10 10 10 10 10 10 10 103 146 202 275 1kgxsec 823 1331 1024 817 666 560 479 414 362 321 288 264 242 225 n12 m 2 Sx10 1792 1306 006 0805 0659 0556 0478 0415 0365 0326 0295 0272 0252 0233 Sec C 140 150 160 70 I 80 I 190 M00 210 220 Z0 NO 25 0 270 p kgcm2 368 485 630 808 1023 1280 1586 1946 2346 2853 3414 4056 4787 5614 qxl06 kgxsec 205 190 177 166 156 147 139 133 127 122 117 112 108 104 6m I 06 018 1 0 0217 0203 0191 0181 0173 0165 0158 0153 0148 0145 0141 0137 0135 0133 sec r s C 290 1 300 310 320 330 340 350 360 370 p kgcm 2 6546 7592 8761 10064 11512 13118 14996 16863 19042 21468 6 kgxsec 100 960 930 900 870 830 790 740 680 5801 6 M1 2 VXlO 6 m 0131 0129 0128 0128 0128 0127 0127 0126 0126 0126 14 EQUILIBRIUM OF FLUIDS 1 ý A fluid is intequilibrium if the resultant of all the forces acting on any part of it is equal to zero 2 The equation of equilibrium of a fluid in one and the same volume at constant specific gravity can be written in the form Z 16 where z and z2 are the coordinates of two fluid particles in the given Volume relative to the reference plane Figurel 3 p and P are the absolute static pressures at the levels of these particles kgm 2 y is the specific gravity of the fluid kgim IThe expression one andthe same volume is to be understood as meaning a volume such that any two points of it can be connected by a line contained inside the volume The volumes of liquids filling communicating vessels are one and the same volume in this sense I U 12 a b FIGURE 13 Determination of the pressure at aln arbitrary point of a fluid from the pressure at a given point ai b T C ia rYa specific gravity of air 3 The pressure at an arbitrary point of the fluid volume can be determined if the pressure at some other point of the same volume is given and the difference in depth hzazi of one point relative to the other one is known Figure 13 P2 p T z z pA 1h 17 PP2 T zzPtth j It follows that the pressure on the wall of a vessel filled with a stationary burning gas TTat a level hzgz above the surface of separation of the gas and the surrounding air Figure 14 is lower on both sides of the wall Pg the gas pressure and ph the air pressure at level h than the pressure Pa at the surface of separation Pg PS tgT 18 and pl p Th 19 where Tg specific gravity of the gas average value over the height h T specific gravity of surrounding air averaged over height h kg s z Ph FIGURE 14 Determination of the excess pressure of a burning gas in a vessel at an arbitrary height over the atmospheric pressure at the same level 13 4 The excess pressure Hg of a stationary burning gas in a vessel at level hzgZ over the atmospheric pressure of air at the same height h will be on the strength of 18 and 19 Hg pgphhTaTg 110 15 MOTION OF FLUIDS a Discharge and mean flow velocity 1 The amount of fluid flowing across a given cross section of a pipe per unit of time is called the fluid discharge It is measured in industrial units either as weight rate of flow Gkgsec or as volume rate of flow Qm 3sec 2 At any flowvelocity distribution over the section the volume discharge is represented in a general form by the formula QdQ wdF 111 where w is velocity at the given point of the conduit section msec F is the area of the conduit cross section m 2 The weight discharge is connected with the volume discharge by the formula G Q 112 3 The distribution of the velocities over the conduit section is practically never uniform The analysis of problems is simplified by the introduction of the mean flow velocity w dF WmJ F Q 113 whence QwmF 114 4 The volume discharge and also the flow velocity of a gas is a function of its temperature pressure and humidity Designate the volume discharge at normal conditions 0C 760 mm mercury dry gas by Qn m3 sec and the corresponding mean velocity by wnmsec the corresponding magnitudes at operating conditions will be op UO m 3secJ 115 We consider the case of a perfect gas satisfying the equation p0RT and for which the internal energy is a function of the temperature only here v specific volume R gas constant 14 a Pn1 m mrsec 116 and orn2 Pop where T is the absolute temperature of the gas 0 K m is the content of water vapor in the gas kgm 3 dry gas at normal conditions m 0804 pop is the absolute pressure of the gas considered in the given section F kgm 2 pn is the absolute pressure of the gas at normal conditions Pn 10330 kgm 2 The volume discharge and the flow velocity at operating conditions for a dry gas at atmospheric pressure ppn will be t 3 Qo Qn dc 117 and op n273secJ 5 The specific gravity of a gas at operating conditions is equal to or T Mm7 I Pop kgl 119 op i L0 3 where Tn is the specific gravity of the dry gas at normal conditions kgmi In the case of a dry gas at atmospheric pressure 273 Yn 120 b Equation of continuity of a stream 1 The equation of continuity is a result of the application of the law of mass conserva tion to a moving medium fluid The equation of continuity can be represented in the following general form at any distribution of the velocities for two conduit sections II and IHI Figure 15 STlwdF TwdF 121 In the case of an incompressible homogeneous medium the specific gravity over the section is always constant and therefore Ti wdF wdF 121 where F and F2 are the areas of sections II and IIII respectively m 2 w is the flow velocity at the given point msec y and T are the specific gravities of the moving medium at sections II and II respectively kgm 3 15 t A FIGURE 15 Application of the equation of continuity the energy equation and the Bernoulli equa tion to two conduit sections 2 On the strength of expressions 112 to 114 the equation of continuity equation of discharge for a uniform compressible flow and for an arbitrary incompressible flow can be written in theform TiwiFi1 F T WA TwF 122 YQ 1 aa QA where w and w are the mean velocities over sections II and IIII respectively msec If the specific grayvity of the moving medium does not vary along the conduit i e the equation of continuity discharge reduces to wF wF wF 123 or QQ c Bernoulli equation Head loss 1 The law of energy conservation when applied to a medium moving through a conduit states that the energy of the flow per unit time across section II Figure 15 is equal to the energy of the flow per unit time across section IIII plus the heat and mechanical energy dissipated along the stretch between these sections 2 In the general case of flow of an inelastic liquid or a gas with nonuniform velocity and pressure distributions over the section the corresponding energy equation will be TwdF p l T j dF Eto 124 where z is the geometric height of the centroid of the corresponding section m M2 p is the absolute hydrostatic pressure at the point of the corresponding section kgir 2 A is the mechanical equivalent of heat 1 kcalzwd stegaittoa oeta 1zkcw dF is the gravitational potential A i th mchaicl euialet f hat427 kgm 16 energy of the flow per unit time across the corresponding section kgXmsec I pwdFis the potential pressure energy of the flow per unit time across the corresponding section kgXmsec 12wdF is the kinetic energy of the flow per F unit time across the corresponding section kgXmsec UcT is the specific internal energy of the gas kcalkg p U ywdF is the internal thermal energy of the flow per unit time across the corresponding section kgXmsec AE is the energy thermal and mechanical lost in the stretch between section II and III kgXmsec c is the mean specific heat of the gas at constant volume kcalkgXdeg 3 The static pressure p is in most cases constant over the section even with a considerably nonuniform velocity distribution The variation of specific gravity over the section due to a variation of velocities can be neglected in practice Equation 124 can therefore be replaced by the equation TizjpwF 7W3dF ULTwaF 7z tp wF dF ytWF A Substituting 3 dF 1 125 the last equation can now be written ftz p wF 2g uxW1 rw Tz1 F 1F1F Ti pin wF r N21242 wF U 1wF Ao or A QAE 126 where N and N are the kineticenergy coefficients for sections II and IIII respectively they characterize the degrees of nonuniformity of both kineticenergy distribution and velocity distribution 4 If the flow energy per second is divided by the weight or volume discharge we obtain the generalized Bernoulii equation corresponding to a real fluid and allowing for specific losses in the stretch considered p N E2 A a 127 7 or r1zpN1 YUTZa PN 2 t1 128 5 In the case of an incompressible liquid or a gas at low flow velocities 6p to w 150 to 200 msec and low pressure drop up to 1000kgmr2 UU and 1aTa the Bernoulli equation then reduces to zA N PijI 2 AN 2H 129 7 2g 7 2g or TZapaN Tz p N y2 AH 130 6 All terms in 129 have the dimension of length and they are accordingly all called heads z and z potential head m T P pressure head m All 2 Velocity head m H total head loss m 7 All the terms in 130 have the dimension of pressure kgmr2 or mm wat6r column and are called zz1 sFpecific energy of position kgm 2 p p specific pressure energy or static pressure kgm 2 NTr N Y specific kinetic energy or dynamic pressure kgm 2 AH lost pressure spent on overcoming the total resistance of the tretch between sections II and IlII kgmr2 8 In the particular case of a uniform velocity field NN8 1 Bernoullis 6quation reduces to z2 131 or Tz p Tz pj A 132 9 The addition and subtraction of P to the lefthand side of 130 and of P toits right 41 hand side gives fz pPptN P z ppN 2 A 133 18 where p is the atmospheric pressure at height z kgm 2 p2 is the atmospheric pressure at height ze kgrM2 On the basis of 19 P P TA 5 134 P Pa Tazi where p is the atmospheric pressure in the reference plane Figure 16 kgM 2 y is the mean specific gravity of atmospheric air over height z in the given case the specific 3 gravity is considered as equal at the two heights z and z kgmr Equation 133 can therefore be replaced by T T Z pA p N 4 T yT z p p No 135 10 The resistance of the stretch between sections II and IIII is equal on the basis of 135 to All p i p p pN No 7 N To Y zV Z 136 or All H H2 jd H 1 1 Hi 1 1itot H2totHl 137 where lldN 2p is the dynamic pressure at the given stream section always a positive magnitude kgrm2Hst P P is the excess hydrostatic pressure ie the difference between the absolute pressure p in the stream section at height z and the atmospheric pressure p at the same height kgm 2 this pressure can be either positive or negativeHfot HdllsHis the total pressure in the given stream section kgmr2 HL is is the excess potential head kgm 2 Ht za zJ T 7 138 11 The excess potential head is caused by the tendency of the fluid to go up or down depending on the medium in which it is located This head can be positive or negative depending on whether it promotes or hinders the flow If at yy8 the flow is directed upward Figure 16a and at Tj downward Figure 16b the excess head H1 zzyT 8 1 is negative and hinders the flow If the flow is directed downward at g Figure 16c and upward at y Figure 16d the excess head HLz 2zjTy is positive and contributes to the flow 12 When the specific gravities of a flowing medium T and the surrounding atmosphere are equal or when the conduit is horizontal the geometric head equals zero and equation 137 simplifies to AHftot HtoH 2tot kgm 2j 139 13 In those cases when both the static pressure and the velocity are nonuniform over the section and this nonuniformity cannot be neglected the resistance of the stretch must 19 be determined as the difference between total specific energies plus or minus the excess head if the latter is not equal to zero All LHstHd F SH t Hd w dF If Q 5 wd I 140 where LHst HdwdF is the total specific energy of the flow through the F given section F kgm 2 HslHd is the total pressure at the point of the section k gm 2 I IiP Paz F t4 p1 A 19 a y y FIGURE 176 Determination of sign of the head t 20 16 THE FLOW OF FLUIDS THROUGH AN ORIFICE a Flow of an incompressible fluid 1 The discharge velocity of fluid from a vessel or reservoir through an orifice in the bottom or wall Figure 17 is determined by the formula 7zl i z Np0 WC 141 VFN C or WC tp V 2 gtf djs 142 where wc and w are the velocities of flow in the vena contracta of the jet and in the vessel respectively in mjsec is the velocity coetficient Htdi 1 1 T 2 FPPc N 143 144 is the total discharge pressure kgm 2 p and p are the static pre ssures absolute in the vena contracta and the vessel respectively kgm 2 z is the height of the liquid level above the centroid of the exit section of the orifice m I is the vertical distance from the exit orifice to the reference plane Figure 17 or nozzle depth m N and N are the kinetic energy coefficients in the vena contracta and the vessel respectively C is the resistance coefficient of the orifice referred to the velocity in the vena contracta of the jet it is determined from the same data as for any stretch of pipe plane w FIGURE 17 Discharge from a vessel through an ori fice in the bottom or wall The magnitudes 2 and I are neglected in the case of a gas 21 2 In the general case the jet issuing from an orifice contracts somewhat just below the orifice so that Fe F 145 where F and F are the areas of the contracted section the vena contracta and the orifice respectively Figure18 m2 8L is the coefficientofjet contraction which depends mainly on the shape of the inlet edge of the orifice on the ratio F area of the vessel cross section and on the Reynolds number Using 145 and the continuity equation formula 141 can be reduced to V2g TZIPsIp We T r PO 1 Lca VI N 146 where Hdisy zlPsP I is the discharge pressure kgm2 aI b i a b c d L f h e g FIGURE 18 Discharge frtom a vessel through various nozzles 3 If the crosssectionalareaofthe orifice can be neglected compared with the area of the vessel cross section 146simplifies to 4 wc V iz 1 P P j1 V 2 dis 147 22 4 The volume discharge of a fluid through an orifice is given by the formula Q w 148 V7 P where Ly is the discharge coefficient of the orifice At Fe 4 Q pF V2i 149 5 The discharge coefficient p of the orifice is a function of the shape of its inlet edge and of the area ratio and also of the Reynolds number due to the dependence F of t oC on these parameters 6 The dependence of the coefficients 4pit onthe Reynolds number Re where w V Tz pipc is the theoretical velocity of discharge through an orifice in a thin wall in the vena contracta D is the orifice diameter v is the kinematic viscosity F coefficient of the liquid or gas can be determined at 0 on the basis of the curves of Figure 18 proposed by Altshul 12 7 At Re104 the values of p for the case considered can be determined approximately by the following formulas 1 circular orifice 55 Po 059 55 Altshul formula 12 2 rectangular orifice 059 89 Frenkel formula 124 3 square orifice 8 89 p3 058ge Re Frenkel formula 124 8 The values of p at Re 104 for different types of nozzles Figure 18 can be determined approximately as a function of the area ratio A by the formulas given in Table 19 9 The velocity and quantity of a liquid discharged from a submerged orifice Figure 110 are determined by the same formulas 141 to 149 as for a nonsub merged orifice the different symbols are understood in this case as follows Authors data 23 zzA immersion depth of the centroid of the exit section relative to the free liquid level in the reservoir A m PPA pressure at the free surface in the reservoir A kgm 2 P Pa Tza pressure inthe venacontracta of the jet where P8 is the pressure at the free surface of reservoir B kgm 2 Z is the immersion depth of the center of gravity of the orifice relative to the free level in reservoir B m TABLE 19 Values of pf Shape of the nozzle different 4 I 5sL Orifice in a thin wall bottom Figure 18a 1 0 10707 Vo 059 i External cylindrical nozzle Figure 18a andb 13D 082 I Internal cylindrical nozzle Figure 18 c 13D 071 Conical converging nozzle Figure 18 e a 13 094 I O 1297 Rounded approach nozzle Figure 180 1072 007 097 Diverging nozzleVenturi tube with rounded entrance 24 Figure 18h a68 2 7 l IR I 711 Z l 1 A Ae l I 7 Ti J4 P IL A 2 a III LIIIE EE111 EIEEE1 1 MI M1 1 11 11II I I I II1111 1 1 111111 1 1 1 1 III 1 1 1 I 1 1 1IIII Z f 1125 AR A W 119 AN0 Ills 4619 55212Mi 11llWlS I P FIGURE 1 9 Curves of the velocity coefficient T tie contraction coefficient c and the discharge coefficientp for a sharpedged orifice as a function of Re 24 Introduce the designation Hy RzAzTz then at 10 and WC 7 Hf PA PB and Q0 3 H PAPS Q pFo 2 150 151 10 If PA and p are equal to the atmospheric pressure opening then for a relatively small and y PY 2g WC Q tFe 2g ff 153 The same values are used for 9 and p as above FIGURE 110 Discharge from a submerged orifice b Discharge of a compressible gas 1 Whenagasis discharged at high pressure to the atmosphere a sharp variation occurs in its volume In this case it is necessary to take its compressibility into account Neglecting the nozzle losses Figure 18f for a perfect gas and the influence of the gas weight the velocity of the adiabatic discharge can be determined by the SaintVenant and Wantzel formula P1 Imsee 154 2 g 7 or RT g P j tmsec we I P Ip 1 155 25 where a is the velocity of the gas jet in the nozzle throat msec p and p are the inlet and back pressures respectively kgrM2 T is the absolute temperature of the gas before the nozzle throat OK y is the specific gravity of the gas at pressure p and temperature T kgmr R is the gas constant x CVis the specificheats ratio cf Table 13 c c are the mean specific heats of the gas at constantpressure and constant volume respectively kg al 2 When p0 decreases the discharge velocity w increases until p becomes equal to the critical pressure Pcr 2 1 156 When p Pcr the velocity in the nozzle throat F0 is equal to the speed of sound in the given medium The subsequent decrease of p has no influence on the velocity at the throat which remains equal to the speed of sound but leads to the expansion of the jet at the exit Thus when the pressure is reduced below its critical value the mass discharge of gas remains constant and equal to 2 jp 157 Formula 1 54 or 155 can therefore be used for calculating the Velocity and di scharge at p0Pcronly Formula 157 is to be used atpopcr 17 FLUIDFLOW STATES 1 The state offlow of a fluid can be laminar or turbulent In the first case the flow is stable the fluidlayers move without mixing with each other and flow smoothly past the obstacles in their way The second state of flow is characterized by a random motion of finite masses offluid mixing strongly with each other 2 The state offlow of a fluidis a function of the ratio between the inertial forces and the viscosity forces in the stream This ratio is characterized by the dimensionless Reynolds number R 158 where w0 is the determiningflow vlocity i e the mean velocity over the pipe section msec D0 is the determining linear dimension of the flow the pipe diameter m 3 For each installation there exists a certain range of critical values of R eynolds number at which the passage from laminar to turbulent flow takes place The lower limit of the critical Reynolds number for a circular pipe is about 2300 The upper limit of Re depends strongly on the inlet conditions the state of the wall surface and other factors 26 4 When a viscous fluid flows between solid boundaries the layer contiguous to the solid surface adheres to it leading to a transverse velocity gradient the velocity increases in the region near the solid surface from zero to the velocity w of the undisturbed stream Figure 111 The region in which this variation of the velocity takes place is called the boundary layer b FIGURE 111 Velocity distributions over the pipe cross section astream deformation in the initial zone Ilaminar flow 2turbulent flow bvelocity profile in the stabilized zone 5 A distinction is made in the case of flow in straight conduits between the initial zone of flow and the zone of stabilized flow Figure 111a The initial zone is the stretch along which the uniform velocity profile observed at the inlet is gradually transformed into the normal profile corresponding to stabilized flow 6 The stabilized velocity profile is parabolic for laminar flow Figure 111b 1 and roughly logarithmic or exponential for turbulent flow Figure 1I 1b 2 7 The length of the initial stretch ie the distance from the inlet section to the section in which the velocity differs from the velocity of the stabilized stream byonly 1 of a circular or rectangular pipe with a side ratio of between 07 and 15 can be determined in the case of laminar flow byShillers formula 125 Lin L029 Re D h 159 where Lin is the length of the initial stretch m Dh is the hydraulic diameter of the pipe m Reis the Reynolds number 8 In the case of turbulent flow the length of the initial stretch of an annular pipe with smooth walls can be determined by the SolodkinGinevskii formula 118 b 1 a D blg Re a 43b 160 27 where d Dnand b f are determined from the corresponding curves of Figure 112 Din and Dout are diameters of the inner and outer pipes respectively The annular pipe is transformed in the limiting case Di 0Din0 into a circular pipe for which formula 160 reduces to out Lin 788 ig Re 435 ph 161 Din In the limiting case ut 10 the annular pipe is transformed into a plane one for which formula 160 reduces to in 328 Ig Re 495 Dh 162 FIGURE 112 Curves of the coefficients a and bV as a function of the ratio of diameters of an annular pipe FIGURE 113 Flow separation and formation of eddies in a diffuser 28 9 The thickness of the boundary layer at a given distance from the initial section of a straight conduit can increase or decrease depending upon whether the medium moves in a decelerating motion or an accelerating motion A too sudden expansion can lead to the phenomenon of flow separation from the wall accompanied by the formation of eddies Figure 113 18 FLUID RESISTANCE 1 The fluid losses in the course of the motion of a fluid are due to the irreversible transformation of mechanical energy into heat This energy transformation is due to the molecular and turbulent viscosity of the moving medium 2 There exist two different types of fluid losses 1 the frictional losses AIfr 2 the local lossesAHi1 3 The frictional losses are due to the viscosity molecular and turbulent of the fluids which manifests itself during their motion and is a result of the exchange of momentum between molecules at laminar flow and between individual particles of adjacent fluid layers moving at different velocities at turbulent flow These losses take place along the entire length of the pipe 4 The local losses appear at a disturbance of the normal flow of the stream such as its separation from the wall and the formation of eddies at places of alteration of the pipe configuration or at obstacles in the pipe The losses of dynamic pressure occurring with the discharge of the stream from a pipe into a large volume must also be classed as local losses 5 The phenomenon of flow separation and eddy formation is linked with the difference between the flow velocities in the cross section and with a positive pressure gradient along the stream which appears when the motion is slowed down in an expanding channel in accordance with Bernoulli s equation The difference between the velocities in the cross section at a negative pressure gradient does not lead to flow separation The flow in smoothly converging stretches is even more stable than in stretches of constant section 6 All kinds of local pressure losses except the dynamicpressure losses at the exit of a pipe occur along a more or less extended stretch of the pipe and cannot be separated from the frictional losses For ease of calculation they are however arbitrarily assumed to be concentrated in one section it is also assumed that they do not include friction losses The summing is conducted according to the principle of superposition of losses according to which the total loss is equal to the arithmetic sum of the friction and local losses AHlsum AHfr AH1 kgm 2 163 In practice it is necessary to take AHfr into account only for relatively long fittings or when its value is commensurable with hf 1 7 Hydraulic calculations use the dimensionless coefficient of fluid resistance which has the same value in dynamically similar streams i e streams having geometrically similar stretches equal values of Re and equal values of other similitude criteria in dependent of the nature of the fluid This is especially true of the flow velocity and the dimensions of the stretches being calculated 29 8 The fluidresistance coefficient represents the ratio of the pressure loss AI to the dynamic pressure in the section F considered C 164 The numerical value of C is thus a function of the dynamic pressure and therefore of the cross section The passage from the value of the resistance coefficient in section F to its value in section P0 is realized by means of the formula C C 2w C To FN2 165 or at 9 The total fluid resistance of any element of the pipe is determined by the formula AHsum Csum 2g or lf C To0oP T 2kg M2 1 166 sum sum 2g sum r In accordance with the principle of superposition of losses rsum Cfr c 167 where fr is the friction coefficient in the given element of the pipe C1 is the 2g 26 coefficient of local resistance of the given element of the pipe Wop is the mean flow velocity at section Fatoperating conditions msec cf 116 orl18 Qop is thevolume rate of flow of the fluid m 3sec cf 115 117 yop is the specific gravity of the fluid kgmr3 cf 119 120 F is the crosssectional area of the element con sidered mi2 10 The friction coefficient of the entire element is expressed through the friction coefficient per unit ýrelative length by 168 where is the friction coefficient of unit relative length of the pipe element considered I is the length of the element considered m Dh is the hydraulic diameter four times the hydraulic radius of the element section adopted m 11 is the perimeter of the section m 30 I 11 The friction coefficient 2 and hence Cfr at constant is a function of two factors the Reynolds number Re and the roughness of the channel walls 12 The coefficient of local resistance C is mainly a function of the geometric parameters of the system element considered and also of several general factors of motion including a the velocity profile at the inlet of the element This in turn is a function of the state of flow the inlet shape the shape and distance of the various fittings or obstacles located ahead of the element the length of the preceding straight stretch etc b the Reynolds number Re c the Mach number M where a is the speed of sound a 13 The principle of superposition of losses is used not only with respect to a separate element of the conduit but also in the hydraulic calculation of the entire system This means that the losses found for separate elements of the system are summed arithmetically which gives the total resistance of the entire system AHsys 14 The principle of superposition of losses can be applied by two methods 1 by summing the absolute values of the hydraulic resistance of the separate elements of the system AHIYs AHf 169 where i is the number of the system element n is the total number of system elements Aflfis the total resistance of the Lth element of the system determined by a formula similar to 166 AH C 170 I 2g 2g F b by summing the resistance coefficients of the separate elements expressed in terms of the same velocity w and then expressing the total resistance of the system in terms of this summed resistance coefficient e Ss 171 where r1i L F72 is the total resistance coefficient of the given ith element of the system expressed in terms of the velocity w0 in the section F0 is the total resistance coefficient of the given ith element of the system expressed in terms of the velocity wi in section F Hence YH CQ I 0 L Qo 73 S E Ci L Q173 SYs CSYS 2g 2g y Fj 2g iF 31 or n A0 F 2F yooQao2 and at T TO F 2 oo qo oh 1 73 AH Sys C Aj 2 1 The first method is more convenient when a considerable variation of temperature and pressure takes place in the line roughly at t 1000C and H 5001000kgmi2 In this case the line is split in separate successive stretches for each of which the mean values of y and w are used The second method is more convenient in the absence of a substantial variation of the temperature and pressure along the line 19 WORK OF A COMPRESSOR IN A SYSTEM 1 In order to start motion of a fluid in a system it is necessary to give it a suitable head H this head iscreated by a compressor or pump fan supercharger etc 2 The head created by a compressor is used in the most general sense a to over come the difference between the pressures of the intake and discharge volumes b to overcome the excess physical head i e to raise a heavierthanair fluid by height z from the initial Sebtion of the system to its final section c to create a dynamiec head at the exit of the flow from the pipe Figure 114 i e HHI HdiSzHLAhdjsAHin kg 174 where His the total head developed by the compressor kgmi2 Hinis the excess pressure in the intake volume kgm 2 Hdisis the excess pressure in the discharge volume kgm 2 HLis the excess potentialhead lift AHinis the pressure losses along the intake Mtretch of the pipe kgm 2 AHdi is the pressure losses in the discharge stretch kgm 2 Wex is the outlet velocity rnsec 3 In the case where the pressures of the intake and the discharge volumes are equal Hin Hdis this formula reduces to AHin 11HHdis 2g t HL sys HL 175 where AHsys is calculated for the entire system as a sum of the losses in the intake and discharge stretches bf the system including the losses of dynamic pressure at thl exit of the system by formula 169 or 173 HL is calculated by formula 138 4 Since at HL b the sum of all the losses in the system is equal to the difference For pumpsHis given in meers of the displaced liquid column 32 between the total pressures before and after the compressor then A e st Htotd ýHtoti 17E where Htot in and 14totdis are the excess total pressure before and after the compressor kgM 2 HstiriandHstdisare the excess static pressure before and after the compressor kgm 2 winand Wdis are the mean stream velocity before and after the compressor msec Odis Adis FIGURE 114 Work of a compressor in a system 5 The value of His positive at normal operating conditions of the compressor ie Htot distot in At the same time either the static or the dynamic pressure can be smaller after the compressor than before it 6 Where the intake and discharge orifices have the same cross section wdis tin 2g 2g and therefore the total head of the compressor will be H fst dis H stin 177 i e the total head of the compressor is equal to the difference between the static pressures immediately before and after the compressor 7 The power on the compressor shaft is determined by the formula N QopH kw N3 600 102qov or 178 qopi h p j 3 600 756ov 33 where Qop is the volume rate of flow of the medium being displaced at operating conditions compressor m 3hr H is the compressor head at operating conditions kgm2 lov is the overall efficiency of the compressor 8 The compressor output is usually specified The head of the compressor is calculated by 174 to 177 for the specified conditions of the lines ie for a given difference between the pressures in the intake and discharge volumes Hdis H 1 excess potentialhead IfL and shape and dimensions of all the elements of the system These latter determine the magnitude of the resistance coefficients Cfr and r1 the flow velocity in each element and therefore the magnitude of Ays 9 In order to determine whether the compressor satisfies the specified values of Qcp and H it is necessary first to convert these magnitudes to the conditions for which the compressor characteristic is given If the rate of flow of the medium beingdisplaced is given in m 3hr it may be converted to operating conditions by formulasI 15 or 117 The head of the compressor is calculated by the formula Ych 2 73 10p Pch Hn 7 c raph 179 H Y J h273tch Pop where Hch is the design value of the compressor head kgme ch is the specific gravity of the medium for which the characteristic was obtained under standard conditions 0C B 760mm column of mercury kgrm3 T is the specific gravity of the medium forwhich the compressor is used at standard conditions kgm 3 t op is the operating tempEqrature of the displaced medium in the compressor C tch is the temperature at which the compressor characteristic was obtained C Pop is the absolute operating pressure of the displaced medium in the compressor kgm 2 Pch is the absolute pressure of the medium at which the compressor characteristic was determined in the case of fans Pc 10 330 kgm 2 10 In the case of high head the value used for the specific gravity of the medium being displaced is related to the mean pressure on the rotor In that case Pop in 179 is replaced by the mean absolute pressure on the rotor PmPOp AHcom05AHsys kgrM2 1 where AHcom is the pressure loss in the compressor kgm 2 Hsyý is the total pressure loss in the whole line kgm 2 11 The rated power consumption of the compressor is determined by the formula QopHch Q2 n 273 tfc Pop lvch 3 6001027j ov 3600102iov h X 273to ch N 273 TXch 273 topX Pch 180 where Nhr1 is the power output of the compressor according to the manufacturers rating kw nth kg In the case of pumps Qo the weight rate of flow of the fluid being displaced Lr and H the head in meters of the displaced liquid column lh 34 110 EXAMPLES OF THE CALCULATIONS OF THE FLUID RESISTANCE OF SYSTEMS Example 11 Forced ventilation system A ventilationsystem network is shown schematically in Figure 115 12 1 S 8 H t 17 Fan So FIGURE 115 Schematic layout of a ventilationsystem network Given 1 the output of the blower Q3200m 3 hour 2 discharge through each of the four lateral branches QI 800m 3hour 3 temperature of the external atmospheric air t 20TC 4 air temperature at the heater outlet t 20C 5 material from which the ducts are made sheet steel oil coated roughness A o 0 15mm cf Table 21 group A Since the gas temperature varies in the ducts due to the heater the first method of summing the losses will be used summing the absolute losses in the separate elements of the ducts The calculation of the resistance is given in Table 110 The following values are obtained according to this table for selecting the fan Q op 0955 m 3sec and H AHsys 23 kgmz The power on the fan rotor at a fan efficiency qov 06 is equal to QwH 0 955 2 3 036kw 4 1 I02Tov ý 020 0k6 Example 12 Installation for the scrubbing of sintering gases The installation layout is shown in Figure 116 Given 1 total flow rate of the gas under standard conditions t 0C and B 760mm mercury Q 1 0 m3hour 278m 3sec 2 specific gravity of the gas under standard conditions T 13 kgmn3 3 kinematic viscosity of the gas under standard conditions v 13 x 10 5n sec 4 internal coating of thegas mains sheet steel its roughness same as seamless corroded steel pipes equal to A 10mm cf Table 21 A 5 the gas cleaning is done in a wet scrubbing tower the rate of sprayingAS50m3hour x m2 Figure 117 I tihe example the gas temperature varies through the conduits due to cooling the first method of summing the losses will therefore be used i c summlation of the absolute losses in the separate elements of the main The calculation of the resistance is given in Table 111 35 The draft created by the exhaust pipe is equal to HLH p Ta Tg whereHp 62m height of the pipe Ty specific gravity of atmospheric air kgm 3 Tgspecific gravity of the gas at the inlet to the exhaust pipe kgfm3 The specific gravity ofatmospheric air at temperature a 0C is y 129kgM 3 The specific gravity of the gas at temperature tg 40C is g3 g 113 kgm F t00 b FIGURE 1 16 Planof an installation for scrubbing sintering gases aplan view bside view 36 Therefore HL 6 2 1 2 9 113 10 kgm 2 This is a positive head which contributes to the stream motion and therefore has to be subtracted from the total losses cf Table 111 a FIGURE 117 Wet scrubbing tower cf the plan Figure 116 and Table 111 1sprinkler tank 2distributing nozzles 3gas outlet 4louvers 5main nozzles 6spray nozzles 7diffuser for gas inlet 8scrubber bunker a front view b side view 37 No of the system element Type of the main element Diagram and dimensions of the system elements Geometric parameters of the system elements Qa m3sec t C w kgm3 v m3sec 1 Supply vent hD0 06 0825 20 140 117105 2 Straight stretch vertical lD0 80 Δ ΔD0 00003 0825 20 140 117 105 3 Bend β 90 rD0 02 Δ 00003 0825 20 140 117105 4 Straight stretch horizontal lD0 20 Δ 00003 0825 20 140 117105 5 Air heater with 3 rows of smooth pipes Imw 40 kgm2 sec 382 Various expansion joints Section IX Diagram 921 Type View Resistance coefficient ζ Stuffing box ζ 02 Bellows D0 mm 50 100 200 300 400 500 ζ 17 16 16 18 21 23 Lyreshaped smooth R0da rd5 D0 mm 50 100 200 300 400 500 ζ 17 18 20 22 24 26 Lyreshaped with grooves R0d6 rd6 D0 mm 80 100 200 300 400 500 ζ 20 22 25 28 31 35 Lyreshaped with corrugated tube R0d5 rd30 D0 mm 50 100 200 300 400 500 ζ 30 33 37 42 46 50 Πshaped D0 mm 50 100 200 300 400 500 ζ 20 21 23 25 27 29 TABLE 110 resistance of the conduits E DO Basis for the determination E ofI Crfrec to diagram So rfr 4II 427 427 427 427 130 130 130 130 18O01 18010 5 1 8010 5 180 105 030 044 0018 0018 0018 0144 0024 0036 030 0144 0464 0036 0390 0187 0605 0047 1100 316 23 69 23 1230 39 O2 E Diagram and dimensions of the Seometric parameters of system elements the system elements 0 U 7 A 6 1 Sudden sharp contraction 2 2 Vf S m m B110 m mm POJ7fm 2 7 9 10 11 Horizontal straight stretch Pyramidal diffuser behind the fan working in the mains Horizontal straight stretch Flowdivider Horizontal straight stretch Wmm am m MMM 05 I o 20 A 00003 F no 225 6r1 107 A 00004 F 0 o5 PC Ws 05 10 1I5 o188 A 000056 0955 0955 0955 0955 0478 0478 20 20 201 120 195107 120 120 1510 1510s A I 20 1 1201 1510s UWE sCb f de5 P 07J IIIT II f0111n 2 e704FIT 20 120o 1510 4 425JInIi 201 1201 1510 40 TABLE 110contd Basis for the 00 determination E of 91 reference to diagram B 495 495 195 86 86 86 150 150 233 454 454 454 16410 16410 32510 21510 1510 5 151 o5 025 019 00185 0018 0019 0037 0193 036 025 0037 019 0193 036 0374 0056 440 0875 0 1630 39 23 516 24 723 as a supply tee 23 0 41 d E Z Type of the main element Diagram and dimensions of the Geometric parameters of system elements the system elements o 12 Symmetrical smooth tee 13 1 Horizontal straight stretch A IS5 mm li 1mm 14 1 900 curve b 15 Horizontal straight stretch L01Smm r Wm 2 t4WVmm Ls gmm A 7Aff mm A 105mm A0 m mm Q6 Q 0 5 F6 F 0 50 R De 15 C 205 A 000077 a 900 R 20 A 000077 205 A 000077 a 5 20 D 020 1 0 00077 0239 2C 02391 20 1 120 15lOs 02391 20 0239 16 1 Throttle valve 02391 20 120 1510s 20 120 115105 120 129 120 1510 1510 1510 5 02391 20 17 Intake nozzle at exit from the bend W I I 42 TABLE 110contd Basis for the 2 E determination of tg reference to diagram E 80 80 80 80 80 80 39 39 39 39 39 39 104 105 104105 104105 104105 104105 025 015 025 170 0019 002 002 002 002 005 041 0065 041 030 041 0215 041 028 176 1170 1600 0840 1600 0980 6870 730 23 62 24 94 1120 006 AH sy 22764 23O0 k grn 2 43 Resistance of pipelines and fittings of the unit for 1 x m t 2JW m 5503J F 1 2500 1 a AA fO 0002 430 2 J4ZWmm 4MU0Amm Jhm 56 430 3 IN we g WO we 1 60000 45 A 10 A 7I4 0 430 4 thedistributing header Fe 24 10 QtI Qu4 161 OSI00 5 Throttle valveat 10 closing Ss5c 6Wet scrubber F0 945 100 cf Figure 1417 F 32dn at the inlet I i20C at the exit t 50C wetting intensity A 5o mmsI r Exitstretch of the scrubbersym metric tee ulZLrý sID54 S J Xx7JI2WO 4JnI F 42 ýo 5 44 TABLE 111 the scrubbing of sintering gases Figure 116 v 45 0 Type of Plan and basic dimensions of the element Geometric parameters of the 6O element element m2sec 11 8 9 10 11 12 13 14 Horizontal straight stretch Inlet to the stack First straight stretch of the stack Transition passage Second straight stretch of the stack Exit from the stack Draft in the entire stack La2S2 CAZ JUaut4LoM 2 f4tv 4a AV 2 L F ISmam 1dF i Mya L iJAAmm 1050066 10 A 16 00006 F 42 1 222000 i450 0 002 1i 2 400 10 T0000033 1 41 500 10 L 0 0 0oM 24080 24080 80 27340 775 27350 27340 80 775 27350 8Y273407 80 i4 775 27350 8 0 fl40 7 7 5 27350 A J 46 TABLE 1I Icontd It oc I Basis for the determi nation of C refer ence to diagram 50 242 23 1070 41 sudden expansion 010 23 045 37 140 23 700 111 100 Formula 138 HLZ7lg where 7al29 at t0 C Affsys i5513 z 155 kgm 2 47 Resistance of a wind Type of element Plan and dimensions of element Geometric parameters of the element z E I Circular open throat Its 8000 DO K O 2 First diffuser 3 Adapter from an an nular section to a square tin ton tinrAW mm dinN mm OeA mm SO mm b a Wi e mm 4 lElbow No 1 with reduced number of guide vanes F 000 2 a 79nEPgB 2 ýa12 ka5I8hAM0004 D D2r F3 F3 8000w FinOPFin 1 02 i801 5 max 11x k b r 1i0 0003 I t6 000 075 b4 r w02 5 6 Cylindrical stretch Elbow No 2 guide vanes as for elbow No1 caaa mm ItV mm t xmm 4ZJAmm 48 TABLE 112 tunnel Figure 118 Area ratio 1i DI k I 9frl Ia A Area Cr1 ci2 Basis for the determination Pi j b msec l W I of c reference to diagram 1 0 5000 2 30 0875 5000 Fn 1 075800f 052 4 S50002 0 306 8 00P2 0306 0306 10 60 20 107 013 077 1525 19107 005 1 001 0016 027 31 0096 1 18 1810 7 107 107 10 7 019 1 00111 001 013 0066 020 0195 0008 0165 018 1 0011 0130 0015 0008 0015 0051 0054 0019 0001 0016 427 52 51 632 1 is increased by 12 in order to allow for the influence of the dif fuser placed before it 23 632 0096 1 18 0011 0096 1 18 015 1 0011 L A I L J L 49 Sype of element Plan and dimensions of element Geometric parameters of the element 7 ISecond diffuser 8 9 10 Elbow No 3 same condi tions as elbow No 1 Elbow No 4 same condi tions as elbow No 3 but the number of guide vanes is normal Honeycomb coated sheet iron arAMO mm p1gf mmM wD 0 4 45 F d7 5 F09 20000 12 000 x 7 35 F112 000 X2 a iLS 5 n 1 25 aD 11 INozzle 4fX In m 50 TABLE 112contd Are rat i xIf tasis for the determination Fnsec t Cfrtl I reference todiagram FOY I I P I 0306 5 000 iTfo 0 o3 7 0137 0137 0 052 0096 18 001811 82 107 65106 65106 12103 2 107 0046 020 021 011 0011 0011 0057 0215 0006 0004 0011 1 0015 001811 82 0011 0060 0015 045 0225 1 0004 51 632 632 iexCfr Cinol diagram 31 Cex 11p diagram 41 tfr X 37 r 0301 eoO 30 0 0232 54 91 60 056 1 0013 0008 1 0003 0003 0003 i1 51 Example 13 Lowvelocity closedcircuit wind tunnel with an open throat A plan of the wind tunnel is shown in Figure 118 Given 1 diameter of the exit section of the nozzle outlet Do u 500m 2 length of the test section Its 800m 3 flow velocity in the test section nozzle outlet w 60 msec 4 air temperature t6 20C 5 kinematic viscosity A 15x10s m2sec 6 tunnel concrete state of the internal surface average roughness of surface A 25 mm cf Table 21 B At low stream velocities the variation of the pressure and temperature along the tunnel can be neglected in hydraulic calculation Therefore it is convenient here to use the second method of summing the losses summation of the reduced resistance coefficients of the separate elements cfA 18 The calculation of tunnel resistance is given in Table 112 According to this table the total resistance is 71 04 03 122 A0sys 6P 6 b70 kgm The rate of flow of air through the nozzle is QwF 60196 1 175 m3sec The power on the fan rotorvat a fan efficiency q ov07 is equal to QAHsYs l 1I61 100 Kw N 10ov i 0205kw The concept of quality of the tunnel is used in aerodynamic calculations The tunnel quality ALtun is defined as thl inverse of the losses in it In the given case Xtun ji 0A33 C4 I tunin 1 FIGURE 118 Plan of a closedcircuit openthroat wind tunnel dimen sions in meters DO500 D1535 D3 O fI50 lt00 1d1fO din 400 bs800 b800 b 800 tin 2 ft L 500 1t 4W 601 5 4aW0 bm1200 bj 1m110 b 1200 11220 1150 1 1 3 5 0 r160 7 52 Section Two STREAM FLOW THROUGH STRAIGHT PIPES AND CHANNELS Friction coefficients and roughness 2 1 LIST OF SYMBOLS FP area of conduit cross section m 2 S friction surface m 2 U perimeter of the conduit cross section m D diameter of the conduit cross section m Dh hydraulic diameter of the conduit cross section 4X hydraulic radius Din Dout inner and outer diameters of an annular pipe m a b sides of the rectangular cross section of a conduit m I length m A mean height of the roughness peaks of the conduit walls m A relative roughness of the walls w mean flow velocity over the conduit cross section msec AH pressure losses kgrnm AHfr frictional pressure losses kgm 2 friction coefficient of referred length 1Dia of conduit friction coefficient of conduit length considered Re Reynolds number 22 EXPLANATIONS AND PRACTICAL RECOMMENDATIONS 1 The friction losses through a straight conduit of constant cross section are calculated by the DarcyWeisbach formula Afr kSOTO 21 A4F2g II or rTU4 22 where DhD for a circular section 23 Dh2 o0 The engineering unit of measurement of Hfr for water is meters Afr Z m 2g 53 for a rectangular section and Dh Dor Din 23 contd for an annular section 2 The resistance to fluid motion at laminar flow is due to the viscosity forces which occur during the motion of one layer of a fluid relative to an adjacent one Viscosity forces are proportional to the stream velocity Due to the predominance of these forces at laminar flow even the flow past protuberances of a rough surface is smooth As a result a small amount of roughness has no effect on the magnitude of the resistance and the friction coefficient at laminar flow is a function of the Reynolds number only Re 3 An increase in the value of Re is accompanied by an increase in the inertia forces which are proportional to the square of the velocity At a certain value of Re the flow becomes turbulent This flow condition is characterized by the appearance of cross current velocities and by the resulting mixing of the fluid in the whole stream In turbulent flow the resistance to motion caused by an exchange of momentum between fluid masses moving in a random motion is much greater than in laminar flow In the case of a rough wall surface the flow past the protuberances is accompanied by jet separation and the friction coefficient becomes a function not only of Re but also of the relative roughness A Dh 4 Conduits can be either smooth or rough and the roughness can be either uniform or nonuniform The two types of roughness differ in the shape of the protuberances dimensions spacing etc Most industrial pipes are nonuniformly rough 5 The mean height A of the roughness protuberances is called the absolute geometric roughness The ratio of the mean height of the protuberances to the pipe diameter i e X is called the relative roughness Since the geometric characteristics of the Dh roughness cannot uniquely define the pipe resistance we introduce the concept of hydraulic or equivalent roughness which is determined by measuring the resistance 6 The equivalent roughness is a function of a the material and method of manufacture of a pipe Thus castiron pipes manufactured by centrifugal casting are smoother than those cast by conventional methods seamless steel pipes are less rough than welded ones etc Pipes manufactured by the same method have as a rule the same equivalent roughness independent of their diameter b the properties of the medium flowing through a pipe The influence of the fluid on the inner surface of a pipe can result in corrosion of the walls the formation of protu berances and the deposition of scale c the length of time the pipe has been in use At the same time since the friction coefficient I is always determined as the ratio of the loss of pressure to the dynamic pressure 0 the magnitude of will be larger at laminar flow than turbulent flow when Afffr is directly proportional to the velocity 54 b the zone in which the curves obtained for pipes with different roughness coincide with the Blasius curve 257 for smooth pipes 03164 25 ReP25 The accuracy of this expression decreases with an increase of the relative roughness c the zone in which the resistance curves diverge from each other and from the straight line 25 for pipes of different roughness The values of friction coefficients in certain ranges of Re increase with an increase in relative roughness The third regime of flow is called squarelaw flow flow at completely rough walls or turbulent flow and is characterized by friction coefficients independent of Re and constant for a given roughness 8 The same three regimes of flow are also observed in the frictioncoefficient curves IfRe Z for nonuniform roughness industrial pipes however the trough in the transi tion region of the curves correspondingto uniform roughness is lacking since here the frictioncoefficient curves drop gradually and smoothly reaching the lowest position at turbulent flow 9 It follows from Nikuradzes resistance formulas 266 for rough pipes and FilonenkoAltshus resistance formula 28 248 for smooth pipes that pipes with uniform roughnesso can be considered as hydraulically smooth if AAIims where A h 181ggRe 164 26 lir lir Re From this it follows by using Blasiuss formula that for Re 10ý Wlim m 1785 ReOm 26 For the case of nonuniform roughness the following formula will give results which are accurate within 3 to 4 Altshul 214 and Lyatkher 231 Mi2m 27 Alim It follows that the limiting Reynolds numbers at which the influence of roughness begins to be felt are for uniformzroughness Re c UPr Rem 28 The increase of A ceasesvin these ranges of Re 56 for nonuniform roughness Reim 29 10 The limiting value of Reynolds number at which the square law of resistance starts to apply is determined at uniform roughness by the formula Relim 2176 38221gA i 210 which follows from Nikuradzes formulas 266 for the transition and squarelaw regions For the case of nonuniform roughness the following formula will give results which are accurate within 3 to 4 Althsul 214 and Lyatkher 231 eim560 Re l 2li 11 At laminar flow Re a 2000 the friction coefficient A is independent of the wall roughness and for a circular pipe is determined by formula 24 or by curve a of diagram 2 1 For rectangular pipes with sides ratio 0 1 0 the friction coefficient is given by the formula I r k 212 where 3 r friction coefficient for conduits of rectangular section I friction coefficient for conduits of circular section k coefficient allowing for the influence of the value of the sides ratio a 242 For annular pipes made from two concentric cylinders pipe within a pipe of diameters Din and Dour respectively the friction coefficient is determined by Ian k2 213 where Ian friction coefficient of an annular pipe I friction coefficient of a circular pipe kA coefficient allowing for the influence of the diameter ratio in 242 12 The friction coefficient I for circular conduits with hydraulically smooth walls in the critical region 2000 Re 4000 can be determined from the curve IfRe of diagram 22 13 The friction coefficient 3 for circular conduits with hydraulically smooth walls at Re 4000 turbulent flow can be determined from the curve IfRe of diagram 22 or from FilolenkoAltshuls formula 28 and 248 rlhis formula is almost the same as the formulas obtained by Konakov 229 Murin 232 and Yakimov 256 57 1 214 18lg Re 6 14 The friction coefficient of circular pipes with uniform roughness in the transition region i e within the limits 269 217 6 382 4 Ig A is determined from the curve XReI of diagram 23 or from Nikuradzes formnula 266 1 abIgReVTi 1 IgIY 215 where at 36aReVXl10 a08 b20 cO smooth walls 10ZReI20 a0068 bs113 e 087 20RetI40 a1538 bO e 20 40Re V1912 as2471 b 0588 e 2588 iRe V 1912 a I 138 b 0 20 square law 15 With the exception of special pipes for which the values of I are given separately the friction coefficient I of all commercial pipes can be determined in the transition region from the curves of diagram 24 plotted on the basis of the ColebrookWhite formula 258 u 2g2 151 2 16 or in the range 000008 00125 by the simplified formula of Altshul 211 101 I46A1 2 17 The ColebrockWhite curves are 2 to 4 higher than the similar curves obtained by Murin 232 and therefore give a U certain factor of safety in the calculations Similar formulas were obtained by Adamov 25 Altshul 215Filonenko 249 and Frenkel 252 A formula similar to 217 was also obtained by Adamov 26 27 The error introduced by the assumption that the coefficients are actually constant 252 can be neglected in practical calculations 58 A simple convenient formula for the determination of I in the transition region within the limits 00001 001 was proposed by Lobaev 230 I 142 218 16 With the exception of special pipes for which the value of 3 is given separately the friction coefficient 3 of all circular pipes can be determined in the squarelaw region that is roughly at Re for any type of roughness uniform or nonuniform from the curve of diagram 25 plotted on the basis of the PrandtlNikuradze formula 240and 266 31 219 17 At turbulent flow the friction coefficient of rectangular pipes with small sides Co ratio 05 a 20 can be determined in the same way as for circular pipes The friction coefficient of annular pipes can be determined by the formula Ian k 2 1 220 where k is determined from the data of Ginevskii and Solodkin 221 given in curve c of diagram 21 as a function of the diameter ratio and Re Din Atbt 10 the annular pipe becomes a plane pipe and therefore the friction coefficient of a plane pipe is determined by the same formula220 with k determined Din for Diu 10 18 When the friction coefficients are determined as under points 14 to 17 the values of the pipe roughness A to be used are those given in Table 2 1 These values of A apply to formula 219 19 The resistance of steel pipes with welded joints which lead to the formation of metal burrs is higher than the resistance of seamless pipes 252 The additional resistance of welded pipes when the joints are located at a distance Lj 30 from each other can be roughly considered equal to the resistance of a restrictor td In the rangeL 30 the influence of the joints decreases with the decrease of the relative distance between them so that tj kt 221 The error introduced by the assumption that the coefficients are actually constant 252 can be neglected in practical calculations New experiments for more accurate determination of the influence of joints on pipe resistance are being conducted 59 Li where k 4 is the correction factor determined as a function of 5 from curve a of dia gram 26 Cd is determined as a function of ý from curve b of diagram 26 The total resistance of a pipe section with joints is equal to CZ f 222 where z is the number of joints in the pipe section to be calculated C is the resistance coefficient of the joint 20 In practice the resistance of steel pipes with coupled joints can be considered equal to the resistance of welded pipes 252 When pipes made from cast iron are being calculated the additional resistance caused by the presence of bellandspigot joints can be neglected 21 Shevelevs formula 252 can be used to calculate the increase in the coefficient of friction of steel and castiron water pipes through their service life 1 in the transition region defined by the condition Re 5D 9210D 20 03 Re 223 2 in the squarelaw region defined by the condition Re 9210D0 1 0021 224 DOO3 9 where D is in meters 22 The friction coefficient I of reinforced rubber sleeves whose characteristics are given in diagram 28 is independent of the Reynolds number for Re 4000 due to the considerable roughness of these sleeves The value of A increases with the increase of the sleeve diameter since this increase is accompanied by an increase in theheight of the internal seams Toltsman and Shevelev 246 When the pressure losses are determined by 22 the diameter to be used is not the nominal sleeve diameter dnom but the diameter dca1 calculated according to curve b of diagram 2 8 as a function of the mean internal pressure 23 The friction coefficient I of smooth rubber sleeves whose characteristics are given in diagram 29 can be determined by the ToltsmanShevelev formula 246 S A i225 Re 0o where for 5000 Re 120000 A varies from 038 to 052 depending on the quality of the rubber sleeve When the pressure losses are being determined by 22 the value of the calculated diameter is to be determined on the basis of the mean internal pressure from curve b of diagram 29 60 24 The friction coefficient I of smooth reinforced rubber sleeves is determined from the curves of I as a function of Re given in diagram 210 for different values of the mean internal pressure and dnom When the pressure loss is being determined by 22 the diameter to be used is not the nominal sleeve diameter but the calculated diameter and the sleeve length is to be multiplied by a correction coefficient k given in curves b and c of diagram 2 10 as a function of the mean internal pressure 25 The total resistance of largediameter pipes 300 to 500 mm of rubberized material used for mine ventilation usually with connections made by means of wire rings closed at the ends by pipe sockets Figure 22 is equal to the sum of the frictional resistance and the resistance of the connections Cf Z aDiO cc 226 2g where z is the number of connections I friction coefficient of unit relative length of the pipe determined as a function of the Reynolds number Re for different degrees of tension small with large wrinkles and fractures medium with small wrinkles and large without wrinkles cf diagram 211 1j distance between joints m D pipe diameter m C resistance coefficient of one connection determined as a function of the Reynolds number cf diagram 2 11 rings FIGURE 22 Circular pipe from tar paulintype rubberized material with a ring connection 26 The friction coefficients I of plywood pipes made from birch plywood with the grain running lengthwise are determined on the basis of the data of Adamov and Idelchik 23 given in diagram 212 27 All the values of I recommended above apply to Mach numbers M not a larger than 075 to 080 28 When determining the relative roughness of the walls of a section the data given in Table 21 can be used 61 23 ROUGHNESS OF PIPES AND CHANNELS TABLE 21 SType of pipe I Group and materials State of pipe surface and conditions of use a mm Reference A Metal pipes I Seamless pipes Commercially smooth made from 00015 brass copper 00100 261265 lead or aluminum The same 0015006 II Seamless steel 1 New unused 0020100 222 pipes 253263 commercial 268 2 Cleaned after many years of use Up to 004 265 3 Bituminized Up to 004 265 4 Superheatedsteam pipes of heating systems and water pipes of 010 233 heating systems with deaeration and chemical treatment of running water 5 After one year of use in gas pipelines 012 222 6 After several years of use as tubings in gas wells under various 004020 27 conditions 7 After several years of use as casings in gas wells under various 0060022 27 conditions 8 Saturatedsteam pipes and water pipes of heating systems with 020 233 inIsignificant water leakages up to 05 and deaeration of water added for making up leakage losses 9 Heatingsystem water pipes independent of their feed source 020 218 10 Oil pipelines for medium conditions of operation 020 233 11 Slightly corroded 04 268 12 Small depositions of scale z04 268 13 Steam pipes in intermittent operation and condensate pipes in 05 233 an open condensate system 14 Compressedair ducts from piston compressors and turbocompressors 08 233 15 After several years of use under various other conditions ie 01510 27 corroded or with small scale deposits 2 47 265 16 Condensate pipes working intermittently and waterheating pipes 10 233 in the absence of deaeration and chemical treatment of the water with large leakage up to 153 17 Water pipelines in operation 1215 253 18 Large depositions of scale z 30 265 19 Pipe surface in poor state Nonuniform overlapping of pipe joints 50 260 III Welded 1 New or old pipes in satisfactory state welded or riveted pipe joints 004010 261 and steel pipes 268 2 New bituminized pipes 015 264 3 Used pipes corroded bitumen partially dissolved 010 268 4 Used pipes uniform corrosion Z015 268 5 Without noticeable unevenness at the joints lacquered on the inside 0304 262 layer thickness about 10mmm satisfactory state of surface 6 Gas main after many years use 05 268 7 With simple or double transverse riveted joints inside lacquered 0607 261 layer thickness 10mm or without lacquer but not corroded as 4 62 a TABLE 21 contd Group Type of pipe State of pipe surface and conditions of use A mm Reference and materials 111 Welded 8 Lacquer coated on the inside but not rust free soiled in the process of 09510 261 steel pipes carrying water but not corroded 9 Layer deposits gas mains after 20 years use 11 1268 10 With double transverse riveted joints not corroded soiled by 1215 268 passage of water 253 11 Small deposits 15 268 12 With double transverse riveted joint heavily corroded 20 261 13 Considerable deposits 2040 268 14 25 years use in municipal gas mains uneven depositions 24 268 of resin and naphthalene 15 Pipe surface in poor state uneven overlap of joints 50 261 IV Riveted steel 1 Riveted along and across with one line of rivets lacquered on 0304 261 pipes the inside layer thickness 10 mm satisfactory state of the surface 2 With double longitudinal riveted joints and simple transverse 0607 261 riveted joints lacquered on the inside layer thickness 10 mm or without lacquer but not corroded 3 With simple transverse and double longitudinal riveted joints 1213 261 coated on the inside with tar or lacquer layer thickness 1Oto 20 mm 4 With four to six longitudinal rows of rivets long period of use 20 261 5 With four transverse and six longitudinal rows of rivets joints 40 261 overlapped on the inside 6 Pipe surface in very poor state uneven overlap of the joints 50 261 V Roofing steel 1 Not oiled 002004 243 sheets 2 Oiled 010015 243 Vl Galvanized 1 Bright galvanization new pipes 007010 268 steel pipes 2 Ordinary galvanization 01015 268 VlI Galvanized 1 New pipes 015 263 sheet steel 2 Used in water pipelines 018 258 VIIl Castiron 1 New ones 02510 258 pipes 2 New bituminized 010015 268 3 Asphaltcoated 012030 263 4 Used water pipes 14 253 5 Used and corroded pipes 1015 268 6 With deposits 1015 263 and 268 7 Considerable deposits 2040 265 and 268 8 Cleaned after many years of use 0315 268 9 Strongly corroded Up to 30 B Conduits made from concrete cement or other materials Concrete 1 Good surface plaster finish 0308 268 pipes 2 Average conditions 25 268 3 Coarse rough surface 39 268 11 Reinforced 25 1247 concrete pipes 63 TABLE 21 c6ntd Group Type of pipe State of pipe surface and conditionsofuse A mm Reference and materials IlI Asbestos 1 New 005010 247 cement pipes 2 Average 060 247 IV Cement pipes 1 Smoothed surfaces 0308 2 65 2 Nonsmoothed surfaces 1020 247 and 2 5 3 Mortar in the joints not smoothed 1964 2 61 V Channel with 1 Good plaster from purecement with smoothed connections all 005022 261 a cemernt unevennesses removed mortar plaster 2 With steeltroweling 05 247 VI Plaster over 1015 218 a metallic grid VII Ceramic salt 14 1247 glazed channels slagconcrete 1 2t8 Vill tiles 15 218 Ix Slag and Carefully finished plates 1015 218and alabaster j 258 filling tiles C Wood plywood and glass pipes Wooden 1 Very thoroughly dressed boards 0 0151 1 pipes 2 Dressed boards 030 Tentatively 3 Wellfitted undressed boards 0701 4 Undressed boards 10 268 5 Woodstave pipes 06 247 I1 Plywood 1 From goodquality birch plywood with transverse grain 012 23 pipes 2 From goodquality birch plywood with longitudinal grain 003005 23 Ill Glass pipes Plain glass 000150010 263 S 5 S 64 24 LIST OF THE DIAGRAMS OF FRICTION COEFFICIENTS OF SECTION II V Name of diagram Source TNmej Nt Conduit Friction coefficient at laminar flow Re 2000 Conduit with smooth walls Friction coefficient at Re 2000 Conduit with uniform wall roughness Friction coefficient at Re 2000 Conduit with nonuniform wall roughness commercial pipes Friction coefficient at Re 2000 Conduit with rough walls Friction coefficient Flow conditions according to square law of resistance Relim 5 Welded pipe with joints Friction coefficient Steel and castiron water pipes with allowance for the in crease in resistance with use Friction coefficient Steelreinforced rubber hose Friction coefficient Smooth rubber hose Friction coefficient Smooth steelreinforced rubber hose Friction coefficient Pipe from tarpaulintype rubberized material Friction coefficient Plywood pipe birch with longitudinal grain Friction coefficient at turbulent flow Hagen Poiseuille formula 259 and 267 Altshul 2 8 Blasius 257 Karman 227 Konakov2 29 Murin 232 Nikuradze 234 Prandtl 240 Filonenko 248 Yakimov 2 56 Nikuradze 266 Adamov 25 Altshul 211 Colebrock 258 Lobaev 230 Murin 232 Filonenko 248 Frenkel 251 Prandtl 240 Nikuradze 266 Shevelev 252 The same Toltsman and Shevelev 246 Adamov A damov and Idelchik 23 21 22 Maximum difference of JL according to the various formulas is 34 Extrapolation of experimen tal data Maximum difference of A according to the various formulas is 34 23 24 25 26 27 28 29 210 212 According to a calculating formula Experimental data To be used until refined by new experiments Experimental data 65 25 DIAGRAMS OF FRICTION COEFFICIENTS Section II Conduit Friction coefficient at laminar flow Re 2000 Diagram 2 1 4IF D h 110 U perimeter 1 Circular section k is determined by curve a 2 Rectangular section of side ratio aelbo o10 where k is determined from curve Ahr Re 100 200 300 400 500 600 700 800 900 1000 1 0640 0320 0213 0160 0128 0107 0092 0080 0071 j 0064 Re 1 I 12001 1300 1400 1500 1600W 1700I 1800 I 900m 2000 1 0058 0053 0049 0046 0043 0040 0038 0036 0034 0032 lei 0 z 01 7 1 7 1 10 3 Annular section Din inner cylinder diameter Dout outer cylinder diameter k an kX where k is determined from curve c Re is taken according to 13 b 1 imi kdHI 4i1HV a 0 101 o02 04 06 081 10 k 150 134 1 120 1 102 0o94 0 90 1 089 0 101 I 02 o3I o04 I 05 06 107 08 J0 i4 102 kI 1 0 1140114511 4711481 11491 1 1so I 41 00 as as Wi b k2 tU Re 104 k 1 10 I1031104110511051106l11061107jI107110Q7 Re 10 k I 10 110211031104 110511051106110611061106 Re 10 4 k 1 10 11021103 1104110411051105110511051106 Re 101 k I O10II011 10211031103110411041 10411051105 C 66 Section II Conduit with smooth walls Friction coefficient at Re 2000 Diagram 22 Dh 1E 119 perimeter 1 Circular and rectangular sections 0 GI5o 1 2000Re4000 IL is determined from curve a 2 4006Re100000 II Afl 03164 W T is determined from curve a 3 any Re 4000 AHI yar I V81g Re 164 is determined from curves a and b 2 Annular section kan AaA where kz is determined from curve c of diagram 21 Re fýh v is taken according to 13b Re 20 25103 3103 010 61051O8 610 10 I0 11012100 310 4 0 1 1 0 61 0 18104 I 0052 0046 0045 0041 0038 0036 0033 0032 0028 0026 0024 1 0022 0021 0020 0019 Re 101 5101 210 3 10 4 10 510 610 810 11510 210f 31P I C I5 81 1 00181 0017 0016 0015 0014 001 0013 001I 0012 0011 0011 1 0010 1 00101 0009 0009 Re 11 2101 3107 107 8107 108 008 0008 0 08 0007 000 006 0006di e 0 OWN ON a ij7 111 I Q IIj J I J b 67 Conduit with uniform wall roughness Section II Friction coefficient at Re 2000 Diagram 23 4P Dh Tlo perimeter 1Circular adrectangular sections a0 0 o a AH T WO I 29 Dh a b I Re Y T cjIg Zia is determined from curve a and Table 22 p 69 the values of a b and c are given below I Re ak J b Ca 3610 080 2000 0 1020 0068 1130 0870 2040 1538 0000 2000 401912 2471 0588 2588 1912 1138 0 2000 II V uw Apoal till 1I I IW ylV 0040 kan k where k is determined from curve c of diagram 21 Re WoDh A A mean height of roughness protuberances according to Table 21 v is taken according to 13b At AAlimDh is determined according to diagram 22 where alim 1785 Re 0 8 7 5 z0Vj f O0 O I IfVI 7T ONDJ I MrM6W UwAqý r I1 1 I 1 0000 S I A fljA 4 sp I IhH 00 IJJ LL L AI 2 j4JFI Zi z 7 seJigA z2 J6 s Age 2 J Jr6 SV z J 4 Ji6 I a 68 Conduit with uniform wall roughness Friction coefficient Section II at Re 2000 continuation of diagram 23 Table 22 Values of X Re 210 410 610 10 2101 410 6104 to 2105 005 0056 0060 0063 0069 0072 0072 0072 0072 0072 004 0053 0053 0055 0060 0065 0065 0065 0065 0065 003 0048 0046 0046 0050 0056 0057 0057 0057 0057 002 0048 0042 0041 0042 0044 0048 0049 0049 0049 0015 0048 0042 0038 0037 0039 0042 0044 0044 0044 0010 0048 0042 0038 ý0033 0032 0035 0036 0038 0038 0008 0048 0042 0038 0033 0030 0032 0033 0035 0035 0006 0048 0042 0038 0033 0048 0028 0 029 0030 0032 0004 0048 0042 0038 0033 0027 0025 0025 0026 0028 0002 0048 0042 0038 0033 0027 0023 0021 0021 0021 0001 0048 0042 0038 0033 0027 0023 0021 0018 0017 00008 0048 0042 0038 0033 0027 0023 0021 0018 0016 00006 0048 0042 0038 0033 0027 0023 0021 0018 0016 00004 0048 0042 0038 0033 0027 0023 0021 0018 0016 00002 0048 0042 0038 0033 0027 0023 0021 0018 0016 00001 0048 0042 0038 0033 0027 0023 0021 0018 0016 000005 0048 0042 0038 0033 0027 0023 0021 0018 0016 Values of X 4105 6105 106 2106 4106 6106 to0 210 108 DhA 005 0072 0072 0072 0072 0072 0072 0072 0072 0072 004 0065 0065 0065 0065 0065 0065 0065 0065 0065 003 0057 0057 0057 0057 0057 0057 0057 0057 0057 002 0049 0049 0049 0049 0049 0049 0049 0049 0049 0015 0044 0044 0044 0044 0044 0044 0044 0044 0044 0010 0038 0038 0038 0038 0038 0038 0038 0038 0038 0008 0035 0035 0035 0035 0035 0035 0035 0035 0035 0006 0032 0032 0032 0032 0032 0032 0032 0032 0032 0004 0028 0028 0028 0028 0028 0028 0028 0028 0028 0002 0022 0023 0023 0023 0023 0023 0023 0023 0023 0001 0018 0018 0020 0020 0020 0020 0020 0020 0020 00008 0016 0017 0018 0019 0019 0019 0019 0019 0019 00006 0015 0016 0017 0017 0017 0017 0017 0017 0017 00004 0014 0014 0014 0015 0016 0016 0016 0016 0016 00002 0014 0013 0012 0012 0013 0014 0014 0014 0014 00001 0014 0013 0012 0011 0011 0011 0012 0012 0012 000005 0014 0013 0012 0011 0010 0010 0010 0010 0011 69 Conduit with nonuniform wall roughness commercial pipes Section 11 Friction coefficient at Re 2000 Diagram 24 I iara 4 Dh 0 17 perimeter 1 Circular and rectangular sections bo0 0540 AH TX 1 251 f or within the limits 0 0000810012 I o 01 141 oo We is determined from curve a or Table 23 p 71 2 Annular section an h k It b I I a I LL I where k is determined from curve c of diagramS21 WDh A Re y A L A mean height of roughpess protuberances taken according to Table 21 v is taken according to 13 b AtAAlim Dh is determined from diagram 22 Alim is determined from curve b of diagram 24 4 a i i I I I 1ý ZI MW m 7 ý 00 II I III I AIII r fe a ýM A V A At I I II 1 ltA 70i EQý j 0 r S 4 100 z i f St VJ z a V s F I ZW 3 41 01 j 3 x fir g 70 Conduit with nonuniform wall roughness commercial pipes I Section II Friction coefficient at Re 2000 Table 23 Values of P 3103 4103 6103 104 2104 410 610 105 2105 005 0077 0076 0074 0073 0072 0072 0072 0072 0072 004 0072 0071 0068 0067 0065 0065 0065 0065 0065 003 0065 0064 0062 0061 0059 0057 0057 0057 0057 002 0059 0067 0054 0052 0051 0050 0049 0049 0049 0015 0055 0053 0050 0048 0046 0045 0044 0044 0044 0010 0052 0049 0 046 0043 0041 0040 0039 0038 0038 0008 0050 0047 0044 0041 0038 0037 0036 0035 0035 0006 0049 0046 0042 0039 0036 0034 0033 0033 0032 0004 0048 0044 0040 0036 0033 0031 0030 0030 0028 0002 0045 0042 0038 0034 0030 0027 0026 0026 0024 0001 0044 0042 0037 0032 0028 0025 0024 0023 0021 00008 0043 0040 0036 0032 0027 0024 0023 0022 0020 00006 0040 0040 0036 0032 0027 0023 0022 0021 0018 00004 0036 0040 0036 0032 0027 0023 0022 0020 0018 00002 0036 0040 0036 0032 0027 0022 0021 0019 0017 00001 0036 0040 0036 0032 0027 0022 0021 0019 0017 000005 0036 0040 0036 0032 0027 0022 0021 0019 0016 000001 0036 0040 0036 0032 0027 0022 0021 0019 0016 0000005 0036 0040 0036 0032 0027 0022 0021 0019 0016 Values of X Re 4105 630 106 2106 4106 6106 10 2107 30 A a 005 0072 0072 0072 0072 0072 0072 0072 0072 0072 004 0065 0 0065 0065 0065 0065 0065 0065 0065 003 0057 0057 0057 0057 0057 0057 0057 0057 0057 002 0049 0049 0049 0049 0049 0049 0049 0049 0049 0015 0044 0044 0044 0044 0044 0044 0044 0044 0044 0010 0038 0038 0038 0038 0038 0038 0038 0038 0038 0008 0035 0035 0035 0035 0035 0035 0035 0035 0035 0006 0032 0032 0032 0032 0032 0032 0032 0032 0032 0004 0028 0028 0028 0028 0028 0028 0028 0028 0028 0002 0024 0023 0023 0023 0023 0023 0023 0023 0023 0001 0021 0020 0020 0020 0020 0020 0020 0020 0020 00008 0020 0019 0019 0019 0019 0019 0019 0019 0019 00006 0018 0018 0017 0017 0017 0017 0017 0017 0017 00004 0017 0017 0016 0016 0016 0016 0016 0016 0016 00002 0016 0015 0015 0014 0014 0014 0014 0014 0014 00001 0015 0014 0013 0013 0012 0012 0012 0012 0012 000005 0014 0013 0013 0012 0011 0011 0011 0011 0031 000001 0014 0013 0012 0011 0030 0009 0009 0009 0009 0000005 0014 0013 0012 0013 0009 0009 0009 0008 0008 71 Conduit with rough walls Friction coefficient Section 11 Flow conditions according to square law of resistance Relim W Diagram 25 4F 1 Circular and rectangular sections Dh go o perimeter 05 020 702 3 is determined from the curve AIA 2 Annular section Aan k3k wherek 3 is determined from curve c of diagram 21 A A mean height of the roughness protuberances according to Table 21 v is taken according to 13b 0100005 00001 0oo 2 0001 3 00 004 0001 5 0010o016 0017 00018 0019 0021 0002 0026 0010 0001 0000 0000 0000 0051 00017 0010 0008 0009 0020 0003 0003 A 0004 0005 10006 0008 0010 0015 10020 0025 0030 0035 0040 0045 0050 I A 0028 0031 j0032 0035 0038 0044 1004q 0053 0057 j0061 0065 0068 0072 400oi AA 4 00za o 4 oo V OW AM 4 l 01o0 OV o e OoVZ 4M o4XZ ooa o 4M 0o 40M 4 t 72 Section II Welded pipes with joints Friction coefficient Diagram 26 Ij zLY z Ib Cj where z ý number of joints in the pipeline X friction coefficient determined from diagrams 22 to 25 as a function of Re wVD and 161D C resistancu coefficient of one joint 1 at 30 Cj 1 h4d Dg where k4 is determined from curve a as a function cf Ij d is determined from curve b as a function of d 2 at tj All Zb 30 V4 0 J V 0 I Lv a b 73 Steel and cast iron water pipes with allowance for the increase in Section iI resistance with use Friction coefficientI Diagram 27 7 1 Re 92Z10Do Do j is determined from the curves I mRe Dj 2 Re 19261Do 0 021 A is determined from the curves ILJe D D is in meters v is taken from I 13b Values of I Re mm 310 4 103 6 103 8103 104 2 104 4104 6104 8104 105 2105 4 10 6105 8105 10 2 10 10 1101 0094 0088 0086 0084 0084 0084 0084 0084 0084 0084 0084 0084 0084 0084 0084 25 0081 0076 0072 0065 0064 0064 0064 0064 0064 0064 0064 0064 0064 0064 50 0072 0068 0059 0053 0052 0052 0052 0052 0052 0052 0052 0052 0052 100 0055 0048 0045 0042 0042 0042 0042 0042 0042 0042 0042 200 0045 0041 0038 0037 0034 0034 0034 0034 0034 0034 400 0039 0036 0035 0030 0028 0028 0028 0028 0028 800 0033 0028 0023 0023 0023 0023 0023 1400 0027 0023 0021 0021 0020 0019 I 4 74 Steelreinforced rubber hose Friction coefficient Section II Re wdcal 410 Diagram 28 W where A is determined from curve a as a function of the nominal diameter dnom dcal calculated diameter determined as a function of the internal pressurePatm from curve b for different values ofdnom v is taken according to 13b Hose dimensions Nominal internal diameterdnom mm 25 32 38 50 65 Spiralwire diameter mm 28 28 28 30 34 Pitch mm 156 156 176 200 208 Fabric insert 11 mm thick nos 1 1 1 1 1 Rubber layer mrm 15 15 20 20 20 Cottonthread spiralthread diameter mm 18 18 18 18 18 Rubber layer mm 15 15 15 15 15 Cloth insert 11 mm thick nos 2 2 2 2 3 d ca m m m dnom 25 32 38 50 65 O e mm A 1051 0053 0072 0083 0085 0057 0066 0090 0094 0100 E SE A9 a mm DW aM om tr 1 M1 X V mm 1 61 tf 21 Iatn mJP a 75 Section 11 Smooth rubber hose Friction coefficient DiagrýLm 29 A Ir a Hose dimensions Nominal internal diameter dnom mm 25 32 38 50 65 Rubber layer internal mm 2 2 2 22 22 Fabric insert thickness 11mmnos 2 2 2 3 3 Rubber layer externalmm 09 09 09 12 12 AHI A where X Re is determined from the curve ktRe on graph a A 038 to 052 within the limits WedcaI Re v 5 5 1 000 and depending upon the sleeve quality dcal calculated diameter determined as a function of the internal pressure Patm from curve b v is taken according to 13b Re 1o10 10 10o 14 1014 1 4 6 4 10 1 0 2F10 agr I d I ýcal 09O JlM 1 A 0 52 S0057 10052 0046 0038 00311 0028 0025 o02 0 2 038 A 0042 9038 o0 33o 0o028 0o023 0020 0 018 oo0 0 E 43 2 AV w 7Z E M 000ý E Xz V1101111 b4 2fatm a 76 Section II Steelreinforced rubber hose Friction coefficient Diagram 210 0 ts 10 dcalc 2g where X is determined from tile curves fRe dniomPatln of iraph a dcalc calculated diameter determined as a function of the mean internal pressure Patm from graph b LItr ki where k is determined as a function of the mean internal pressure Patrn front graplh c Wtdnom Re V v is taken according to 13b A Ainoill mm HAI URI a j 4 if 8 a2r z 1T q Re 4 4 4 5 5 55 4 10 6104 810 10 L410 210 5 105 4 10 025 003 003 003 003 003 003 05 004 003 003 003 003 003 003 003 10 005 005 005 004 004 004 004 003 15 007 007 007 007 007 006 006 006 20 009 009 009 009 009 008 008 007 25 011 011 011 011 011 011 011 bi 6calednomlfmm a A72mm i Ur 100RIott pz Fez I I b Ci 4 4 5 5 5 5 5 25 10 4 410 10 8 10 10 1410 2 10 2510 410 6 10 025 003 003 003 002 002 002 0 003 003 003 002 002 002 10 0 03 003 003 003 002 002 002 15 003 003 003 003 003 0 03 003 002 20 005 005 004 004 004 004 004 003 5 006 006 006 005 005 005 di to Uj LO Zfratni I J 4fr U 4JfW04 Abt 0 4f S V Zf at i C2 77 Section II Pipe from tarpaulintype rubberized material Friction coefficient Diagram 211 Wor A where z number of pipe joints I distance between joints K is determined from curve a for different degrees of pipe tension 29g Do db a 4 r mY Wis determined from curve b Re vw is taken according to 13b I R 10 210 310S 4 10s 5105 610s 710s 810 910 1 0024 0020 0018 0016 0014 0013 0012 0U011 0011 2 0064 0042 0034 0028 0025 0023 0021 0020 0019 3 10273 0195 0139 0110 0091 0074 0063 0054 0048 Pipe ension 1 ldrge 2 rMedium 3 small a a 02 I I I I I I V i 71 I I I I I A fl10o 1110 V Ogu b 78 Plywood pipe birch with longitudinal grain Friction I Section II coefficient at turbulent flow Diagram 212 D h i W 1 perim eter 1 C ircular cross section 6 Y10H I is determined from the curves 4 c fti for different A A h mean height of the roughness protuberances taken from Table 21 Re h V I is taken according to 13b Re 2104 3104 14 6104 8104 105 15105 2105 3105 4105 610 810 lot 2 10 000140 0030 0028 0027 0025 0024 0023 000055 0021 0021 0019 0018 0017 0018 0018 000030 0018 0017 0017 0016 0016 0016 000015 0018 0017 0016 0015 0014 0014 0014 0013 000009 0018 0017 0016 0014 0014 0013 0012 0012 0011 A II I I I H l H il I I j It 4 907 78o 2C 6Z 5OA ad4 SPA l 79 Section Three STREAM INTAKE IN PIPES AND CHANNELS Resisltace coefficients of inlet sections 3 1 LIST OF SYMBOLS P area of the narrowet cross section of the inlet stretch n 2 F area of the widest cross section of the inlet stretch m2 P crosssection area total area of the orifices of the perforated plate screen or orifice m 2 F frontal area of the perforated plate screenor orifice m 2 area of the contracted jet section at entrance into a channel orifice mi 2 h0 area of one orifice of the plate screen M2 For crosssection coefficient of the plate or screen n plate areacontraction ratio of the conduit section coefficient of jet contraction I0 perimeter of the cross section of the conduit or the orifice of the plate m D D diameters of the narrowest and widest sections of the stretch m Dor DPc diameter0 of the perforated plate orifice and contracted jet section at channel inlet m Dh hydraulic diameter four times the hydraulic radius of conduit section m 4h hydraulic diameter of the perforated plate orifice m width of the slit of a standard louver distance between the louver slatp in the direction perpendicular to their axis m b distance if rom the inlet edge to wall in which conduit is fixed m h distance of the screen from the inlet orifice of the conduit m length of the contracting inlet stretch depth of orifices in the perforaed plate mi r radius ofcurvature m C resistance coefficient of the inlet stretch thicknes6 of the inletpipe wall edge m central cPnvergence angle of the inlet stretch or of the edge of the perforated plate orifice o mean velocity of the stream in the narrowest and widest sections of the stretch msec mean velocity in the perforated plate screen orifice and the contracted jet section insec pressure loss resistance in the stretch kgim2 A a 80 32 EXPLANATIONS AND RECOMMENDATIONS 1 The entry of a stream into a straight pipe or channel of constant cross section Figure 31 depends on two characteristics the relative thickness Dh of the pipeinlet wall and the relative distance I from the pipe edge to the wall where it is mounted The coefficient of resistance t of the straight inlet stretch is maximum at a completely sharp edge h 0 and infinite distance of the pipe edge from the wall ok 0 In this case 10 Its minimum value is equal to 05 and is obtained at a thick inlet edge or at a pipe orifice flush with the wall f 0 The effect of the wall on the coefficient of resistance of the inlet almost ceases at b Y 05 This case corresponds to a stream entrance into a conduit whose edge is at a Dh great distance from the wall 2 When entering a straight conduit the stream flows past the inlet edge if however this is insufficiently rounded the stream separates near the entrance Figure 31 This stream separation and the resulting formation of eddies are the main cause of pressure losses at the inlet The stream separation from the pipe walls leads to a decrease of the F0 jet cross section The coefficient of jet contraction a for a sharpedged straight inlet orifice is equal to 05 in the case of turbulent flow 3 The thickening cutting or rounding of the inlet wall and the nearness of the conduit edge to the wall in which the pipe is mounted all lead to a smoother motion of the stream about the inlet edge and to a smaller zone of stream separation with a smaller inlet resistance FIGURE 31 Flow at the inlet to a straight pipe from an unlimited space 4 The greatest decrease of resistance is obtained for a stream entrance through a smooth bellmouthwhose section forms an arc of a curve circle lemniscate etc Figure 32a Thus in the case of a circular intake with relative radius of curvature h02 the resistance coefficient t drops to 004 or 005 as against 10 at r h10 sharp edge 5 A relatively low resistance is also created by a stream entrance through inlets shaped as truncated cones Figure 32bc or as contracting stretches with transitions from rectangular to circular or from circular to rectangular Figure 32d The resistance coefficient of such transition pieces is a function of both the convergence angle 81 a and the relative length For each length of a conical transition section there is an optimuýfi value of a at which the resistance coefficient C is minimum The optimum value of a for a relatively wide range of 1 01 D1 10 lies within the limits 40 to 600 At such angles e g h 02 the resistance coefficient is only 02 ab c d FIGURE 32 Plan of smooth inlet stretches abellnbuth Whose section forms arc of a circle b and cbellmouths shaped like truncated cones dtransition pieces 6 When an inlet stretch is mounted in the end wall under an angle 8 Figure 33 the inlet resistance increases The resistance coefficient is determined in this case by the Weisbach formula 315 AHf S 05 3CosS02cos8 31 2g 7 mintAofasre Figure 34 at a relative distance h 08 10 before the inlet stretch ircreases the resistance of the inlet the nearer the screen to the inlet opening of th6 conduit i e the smaller is the greater is this increase The resistance coefficient of inlet stretches of different thickness with rounded or cut0ff inlet edgd without a screen can be determined by the authors approximate formula 33 82 TUno 32 where 17 is the coefficient allowing for the influence of the inlet edge shape and is determined as t from diagrams 31 33 and 35 a is the coefficient allowing for the influence of the screen and determined from the curve cft of diagram 38 The resistance coefficient of smooth intakes mounted flush with the wall is determined in the presence of a screen determined from the curve C of diagram 34 FIGURE 33 Entrance at an angle to the wall FIGURE 34 Inlet stretch with screen before the entrance FIGURE 35 Flow pattern at sudden contraction 8 The phenomenon observed in inlet stretches in which the stream suddenly contracts ie passes suddenly from a large section F to a smaller section Fo Figure 35 is similar to the one observed at the entrance to a straight inlet from a very large volume The only difference here is that at large values of Reynolds number Re 4 10 the 83 resistance coefficientisafunction of the area ratio This coefficient is calculated by the followingformula established by the author 31 C 4H VP 1133 where Cis a coefficient depending on the shape of the inlet edge of the narrowchannel and is determined as C from diagrams 31 35 and 36 8 2 0 a b FIGURE 36 Sudden contraction a inlet edge of a pipe of smaller section mounted flush with the end wall of a pipe of larger section b inlet edge of the pipe of smaller section moved forward In the case of thei inlet edge of a narrow channel mounted flush with the end wall of a wider channel Figure 36a the resistance coefficient can vary within the limits 0 C 05 when this edge is moved forward Borda mouthpiece Figure 36bit can vary withinthe limits 0 C 10 9 The resistance coefficient of an inlet with a sudden contraction at Reynolds numbers withinithe limits J10Re 1 04 is a function not only of the area ratio 9 but also of the Reynolds numberarid at Re 10 of this number only The values ofC in the caseofa sudden contraction with the narrow inlet section mounted flushwith the wall can be determined at 10 Re 104 from Karevs data 35 diagram 3410 andiat Re 10 from the usual formula of resistance at laminar flojw C 34 where according to Karevs experiments 35 A c 27 84 10 The resistance of a contracting stretch can be decreased considerably if the transition from the wide section to the narrow one is accomplished smoothly by means of a rectilinear or curvilinear adapter Figure 37 The contraction losses decrease with the increase of the transition smoothness In the case of a perfectly smooth contraction of the section where the convergence angle is very small or the length of the contracting stretch sufficiently large and where this stretch has a very smooth curvi linear generatrix the streamdoes not separate from the wall and the pressure losses reduce to friction losses a FIGURE 37 Adapters a rectilinear b curvilinear 11 The resistance coefficient of a rectilinear transition section Figure 37a can be approximately determined by the formula 1 35 where the first term on the right is determined as in formula 33 the second term is determined as friction coefficient of a transition piece with the same geometric parameters as for a convergent nozzle diagrams 52 to 54 The resistance coefficient of a smooth curvilinear adapter Figure 37b is determined either as the friction coefficient of a bellmouth orifice given in diagram 57 or as the friction coefficient of a rectilinear adapter with the same length and contraction ratio from the data of diagrams 52 to 54 ft36 85 12 The resistance coefficient of inlet sections is also a function of their location and method of mounting in the wall of the vessel or container into which they discharge A low resistance coefficient can be achieved by installing an annular rib or ledge before the inlet stretch enclosing the opening Figure 38 If the rib or ledge has a sharp edge the phenomenon of stream separation will occur at the entrance to the widened section which is formed by these devices The eddies formed in the region of separation contribute to the smooth flow of the stream into the main inlet stretch of the pipe without separation As a result the resistance of the inlet is considerably reduced 0 4 FIGURE 38 Entrance through an annular belhinouth The optimum dimensions of the widened stretch in which a bellmouth ledge is placed must closely correspond to the dimensions of the eddy region a at a point upstream from the most contracted section of the stream jet at the inlet into a straight pipe with sharp edges b to a pipe mounted flush with the wall In fact Khanzhonkovs experiments established 3 11 that the minimum resistance coefficient t 010 is obtained in the case of a rib at a 025 and 13 and in the case of a ledge at Lo 02 and A 12 The values of with variious other methods of mounting the inlet stretches in the end wall or betweenwall are given in diagrams 3 11 and 3 12 13 The pressurellosses in the case of a lateral entrance of a stream through the first orifice in a constantsection collecting pipe are much larger than in the case of a straight entrance The resistance of a oneway entrance is much smaller than that of a twoway entrance through two orifices located on two opposite sides cf diagram 313 In this last diagram the resistance coefficients of a side entrance in a circular pipe through a lateral slit of constant height h 0875 D are given 86 The resistance coefficients of side entrances corresponding to rectangular pipes and to slits of different relative heights can differ somewhat from the values given in diagram 313 14 Entrance through side orifices is frequently used in rectangularsection ventilating shafts In order to prevent the penetration of sediments louvers are mounted in the orifices The resistance coefficient of such shafts is a function not only of the relative area of the orifices but of their relative location as well The resistance coefficients of intake shafts with differently disposed lateral orifices are given in diagrams 314 and 315 The values of ý are given for both orifices with and without fixed louvers 15 The resistance of intake shafts with straight entrance and canopies cf diagram 316 is similar to the resistance of ordinary inlet stretches with screens In the case of normal ventilating shafts of circular section in which the relative thickness of the inlet edges lies within the limits 0002 8 4 001 the influence of this parameter can be neglected and the value of the resistance coefficient t of all shafts can be determined from diagrams corresponding to sharpedged shafts h The ratio I between the canopy hood and the inlet edge of the shaft can be taken as equal to 04 An increase of this distance would require building too large a canopy hood in view of the possibility of rain or snow entering the shaft a or b FIGURE 39 Stream entrance in a straight stretch 1 through an orifice b through a perforated plate For cross section The recommended shaft design is the one with conical inlet stretch This shaft is characterized by a minimum resistance coefficient C 048 39 16 The resistance coefficient of an inlet stretch through an orifice or perforated platewith sudden expansionFoo Figure 39 at Re War dhPIO0 is calculated in the general case by the authors approximate formulas 32 and 33 A xd 37 2g More detailed studies of such entrances are currently being conducted 87 where C is determined asthe coefficient C for inlet stretches in the presence of walls from diagrams31 to 33 and 36 is a coefficient allowing for the influence of the perforatedplate wall thickness the inletedge shape and the conditions of stream flow through the orifice I isdetermined from diagrams 22 to 25 as a functions of A T tor 1 th Re and A T F is the crosssection coefficient of the perforatedplate 17 The general caseof entrance through orifice or perforated plate is reduced to a number of particular casesL a sharp orifice edges L 0 at which V 05 and t 141 and expression37 is dh reduced to the following formula of the author 31 to 33 C 1707a 1707 1 38 b thick orifice edges at Which C 05and t is determined from the curve f of diagram 3198 c orifice edges beveled or rounded at which it is assumed that 110 21f as a resuIt it is obtained that 0 7 V39 W9 where the coefficient C is determined in the case of edges beveled alonig the flow direction as C for a conical cdllectdr with end wall from curve a of diagram 319 as a function of the contraction angle a and the length ratio 7 and in the case of rounded edges as of a circular collector ith end wall from curve b of the same diagram as a function of 7 18 At Re 10 and sharp orifice edges the resistance coefficient of an inletthrough an orifice or perforatedplate is calculated by the following formula proposed by the author 34 1 0342 Re AH170ffjI 1 0l y 310 2g where y velocitycoefficient of the stream discharge from a sharpedged orifice and depehds on Re and cT ee coefficient of filling of the section of a sharpedged orifice at For r I O and dependbone C 1 is determined from the curve CfReflon grapha of diagram 410 Roe is determined from the curve 0fRe on the same grapha The calculation as underb and c can be performed for Re 104 and more 88 At Re IOP and thick orifice edges the resistance coefficient of an inlet with perforated plate or orifice is calculated from the formula 311 19 When a perforated plate is installed at the stream entrance the total resistance coefficient can be approximately determined as sum of the resistance coefficients of the plate and the inlet no J 312 where resistance coefficient of the inlet without a plate determined as for a given shape of the inlet edge from the corresponding curves of diagrams 31 to 36 9p resist ance coefficient of the plate determined as t from the corresponding curves of diagram 86 n ratio of area of the cross section where the plate is mounted to the narrowest cross section of the inlet stretch 20 The resistance coefficient of a fixed louver is a function both of its crosssection coefficient IOr and of the relative depth of the channels To each crosssection coefficient there is an optimum value of the relative depth bopI at which the resistance coefficient is minimum The selection of the louver with the optimum value of is recommended This can be determined by using the formula 111 313 21 In the case of standard grids with fixed louvers the inlet edges of the slats are cut along the vertical Figure 3 10a From the point of view of the resistance it is more expedient however to use louvers with inlet edges cut along the horizontal Figure 310b A 40 decrease in the resistance is achieved as a result 313 22 The following formulas are proposed for calculating the resistance coefficient of grids with fixed louvers installed at the entrance to a channel T 314 0 85 1a1 frft8 I his formula aas abtained on the basis of Beviers data 313 The agreement between these formulas and the experimental data of Bevier 313 and Cobb 314 is satisfactory 89 33 LIST OF THE DIAGRAMS OF RESISTANCE COEFFICIENTS OF SECTION III No of Type of diagram Source dia gram Note Straight entrance into a conduit of constant cross section Re 104 Straight entrance into a conduit mounted 4 flush in the wall at an arbitrary angle a1 Re 104 Smooth converging bellmouth made by an arc of a circle without screen Re 104 Smooth converging bellmouth made by an arc of a circle with flat end wall and with screen re 104 Conical converging bellmouth with end wall Re 104 Conical converging bellmouth without end wall Re 104 Inlet with smooth contraction Re i04 Various inlets with screen Re 104 Various inlets with sudden contraction or sudden contraction only Re 104 Inlet with sudden contraction or sudden contrac tion only inlet section in the end wall Re 104 Straight inlets with various mountings in the end wall Re 104 Straight inlets with various mountings between walls Re 104 Side entrance into a circular straight pipe through the first orifice Re 104 Straight intake shafts of rectangular section side orifices with fixed louvers and without them Rectangularsection intake shafts with a bend side orifices with fixed louvers or without them Straight indraft shafts of circular section Re 104 Entrance to a straight conduit through a perforated plate with sharpedged orifices Entrance to a straight conduit through a perforated plate with thickedged orifices 7hoio015 Entrance to a straight conduit through a perforated plate with orifice edges beveled or rounded Re 10 Various entrances to a conduit with a screen at the inlet Eintrance to a straight channeI through a fixed louver f 0 1 to 0 9 Entrance to a straight channel through stamped or cast shaped perforated plates Idelchik 31 Weissbach 315 Idelchik 31 Nosova 36 Idelchik 31 The same Idelchik 31 The same Karev 35 Idelchik 31 The same Nosova and Tarasov The same Khanzhon kov 3 9 Idelchik 31 Idelchik T32 The same 31 32 33 34 35 36 37 38 39 310 311 312 313 314 315 316 317 318 319 320 321 322 Some of the curves were obtained approxi mately by extrapolating experimental data Experimental data The same Some of the curves were obtained approxi mately by extrapolating experimental data The same Tentative Experimental data Calculating formula Experimental data some of the curves were obtained approximately by extrapolation Experimental data The same Authors experimental data Experimental data The same Calculating formula The same Approximate According to the authors approximate formula allowing for the experiments of Bevier 313 and Cobb 314 Approximate based on the authors formula for entrance through a flat grid 4 L 91 34 DIAGRAMS OF RESISTANCE COEFFICIENTS Straight entrance into a conduit of constant cross section Re LDh 1i Section III Diagram 31 1 Entrance at a distance 05 from the wall in which the conduit is mounted 3 Entrance at a large distance 0 from the wall in which the conduit is mounted C A is determined from the curve f N b at v is taken frpm 13b 2 Entrance flush with the wall h0 DhY a0 O perimeter 1 and 2 C is determined from the curves C 1 at given Values of C bIOh a2 1 0 Ioo5 Ioo I Ioo oso Ijo1W 02 Io 300 100 0 0050057 063 068 073 080 086 092 097 100 100 0 004 050 054 058 063 067 074 080 086 090 094 094 0008050 053 055 058 062 068 074 081 085 088 088 0012050 052 053 055 058 063 068 075 079 083 083 0016050 051 051 053 055 058 064 070 074 077 077 0020050 051 051 052 053 055 060 066 069 0472 072 0024050 050 050 051 052 053 058 062 065 068 068 0030050 050 050 051 052 052 054 057 059 061 061 0040050 050 050 051 051 051 051 052 052 054 054 0050050 050 050 050 050 050 050 050 050 050 050 0oO50 050 050 050 050 050 050 050 050 050 050 j I I I I a 92 Straight entrance into a conduit mounted flush with the wall at an Section III arbitrary angle r Re A aO Diagram 32 Dh U perimeter A m 05 03 co8 02 cos2a6 is determined from the curve Cm16 vis taken from 13b Smooth converging bellmouth made by an arc of a circle without screen Re wgDh IO4 Section III Diagram 33 Dh ý C Be perimeter C LM 1 Without end wall 2 With end wall is determined from curves a b c as a function of FlDh v is taken from 13 b I o 0 001 002 003 004 005 006 008 012 016 020 a Without end wall not sharpened C 10 087 074 10611 051 1040 032 1020 010 006 003 b Without end wall sharpened C 10 10651 049 10391 032 10271 022 1018 1010 10 06 1003 c With end wall not sharpened 050 043 o0 3 031 026 1o022 1020 o015 o 009 006 003 a S 0 b a2 U DAM go5 am am1 OwN I4 93 5mppthconvergingýbe1lmouthimadebyanarcof a Section III circle withiflat end wall an with screen Re 10 Diagram 34 h a C2 0f perimeter Screen AH Twp is determined from the curves t r v is taken from 13b I j 1 010I0125 0151020 025 030 040 0501OD09010S rIDh 02 C 050jo34 j017 0iot0 0 006 005 004 j04 rIDh 05 0 l65 036 025101l07 00140041003 003 94 Conical converging bellmouth without end wall Section III Re 0 Diagram 3 5 i i V Dh k g perimeter c Aff is determined approximately from the curves a for different v is taken from 13b Values of C approximately 00 0 10 20 30 40 60 100 140 180 0025 10 096 093 090 086 080 069 059 050 0050 10 093 086 080 075 067 058 053 050 0015 10 087 075 065 058 050 048 049 050 010 10 080 06q 055 048 041 041 044 050 015 10 076 058 043 033 025 027 038 050 025 10 068 045 030 022 017 022 034 050 060 10 046 027 018 014 013 021 033 050 10 10 032 020 014 011 010 018 030 050 0 0 W MD ND W0 120 M8 4 95 Conical convergijigbellrfiouth with end wvll Section III Ri 0Diagram 36 Dh m0W U6 perimeter values oa 4approximately 0 10 20 30 40 60 100 140 180 0026 050 047 045 043 041 040 042 045 050 0050 050 045 041 036 033 030 035 042 050 0075 050 042 035 030 026 023 030 040 050 010 050 039 032 025 022 018 027 038 050 015 050 037 027 020 016 0 15 025 037 050 060 050 027 018 013 011 012 023 036 050 4 29 is determined approximately from the curves Ci for different 1D v is taken from 13b where C isdetermined as C from diagram 36 tfr is deter mined from diagrams 62 55 7A 96 Various inlets with screen Re S 0 Dection III Dh perimeter hDh 020 030 040 050 060 070 080 10 0 ot 160 065 037 025 015 007 004 0 0 V 4 C 42 4 4 4 O Z Am C C approximate where 1 C is determined from thecurve C at b h 0 50 on diagram 31 2 C is determined from the curves C on diagram 33 curves a and b 3 lis determined from the curve Cau t on diagram 35 ag is determined from the curve a I hIDhf v is taken from 13b 97 Various inlets with sudden contraction or sudden Section III contraction onlyaRem 1 Diagram 39 Resistance coefficient C Inlet conditions Diagram W A Inletsection in the end wall 0 perimeter Inlet edge blunt Atmmo5SA Fl Inlet edge rounded t where Ir is determined from the curves b on diagram 33 curve c Inlet edge beveled c IF Inlet where C is determined trom the curve C on diagram 36 B Inlet edge moved forward relative to the end wall Inlet edge sharp or b thick where C is determined from the curves C a on diagram 31 Inlet edge rounded where C is determined from the curvesC t on diagram 33curves a and c Inlet edge beveled wee i Dh VPt 91 where C is determined from the curve C b on diagram 35 v is taken from 13b A 4 98 Inlet with sudden contraction or sudden contraction only Section III inlet section in the end wall RelO Diagram 310 DI o perimeter iI 1 At 10 Re 1 AM ii is determined from the curves C Recorresponding to different O 2 At 1 Re 8 AM 27 V4 Re v is taken from 13b Re2 1 2 3 3 3 4 4 10 20 30 40 50 102 2102 50 2 10s 2203 410 5 104 10 01 500 320 240 200 180 130 104 082 064 050 080 075 050 045 02 500 310 230 184 162 120 095 070 050 040 060 060 040 040 03 500 295 215 170 150 110 085 060 044 030 055 055 035 035 04 500 280 200 160 140 100 078 050 035 025 045 050 030 030 05 500 270 180 146 130 090 065 042 030 020 040 042 025 025 06 500 260 170 135 120 080 056 035 024 015 035 035 020 020 44 IM I I A If 6 IV I 0 AV z 5 V 99 Strdiaiht ihiets with Vairious Intintings in the end wiall Section III Rea ie l 10 Diagram 3 11 Resistance coefficient Inlet conditions Diagram Ti Entrance with end wall on 058 one side of the conduit Entrance with end walfson 05 two opposite sides of the cbnduit 055 S 4 Entrance with end wails on two adjacent sides of the conduit Entrance with end wallson thee 052 thfree sides of the cdnduiit 0 Entrance with end walli on four sides of the conduit 050 v is taken from 13b 100 Straight inlets with various mountings between walls Section III Re 10 iOI Diagram 312 Inlet conditions Entrance with deflector at one side of L the conduit atI 06 46 Entrance withdeflector at two sides of the conduit at 05 Entrance to a conduit mounted on a wall Entrance to a conduit mounted between two walls Entrance to a conduit in an angle between two walls Resistance coefficient C 0 10 0 0O20 030 040 050 1060 063 es0065 06 6068 082 063 071 077 092 ý4 Entrance to a conduit clamped between three walls I01 Side entranceinto acircularýstraightpipethrough thefirst orifice Section III W bi Re 10 Diagram 313 C is determined from the curves J N s II U 99Z A L0 Lu fu U f 15 to t 0 0o 103 1 04 0 051 061 071 081 091 10 12 1 4 16 1 18 1 One orifice 645 300 149 900 627 1454 1354 270 228 160oii 2 Two orifices C 065 365 170 1 120 875 1685 1550 1 454 384 276 201 J140 11 10 102 A Straight intake shafts of rectangular section side orifice with Section III fixed louvers and without them Diagram 314 ho j4m Resistance coefficient Layout of the orifices 0 ht bap 0 8 0 Z without with 8b A 0 louvers louvers 114 o blb EiI l 044 15 126 175 2 088 15 360 540 2 088 15 420 630 3 D E 130 15180 320 4 1 174 15 120 250 380 4 116 10 200 360 600 4 j 058 05 800 137 215 103 Rectangularsection intake shafts with a bend side orifices with fixed louvers or without them Section III Diagram 315 h n bh Pp a 5 r P O F v 104 I WDe Section III Straight indraft shafts of circular section Re104 Diagram 316 Values of C A ing No 01 1 02 1 03 1o04 05 06 07 o 08 09 10 1C I No 2 w4th section 1 2 3 4 5 6 440 480 263 183 213 130 290 190 132 077 215 640 153 095 159 060 1 78 272 I39 084 141 048 158 135 123 113 110 173 147 126 116 107 131 119 115 108 107 075 070 065 063 060 133 125 115 110 107 041 030 029 028 025 106 105 105 060 106 025 106 106 106 060 106 L025 No 3 with hood at sharp inlet edge No 4 with hood at thick ened inlet edge No 5 with hood and slots No 6 with diffuser and hood 105 Entrance to a straight conduit through a Section III perforated plate with sharpedged orifices 00015 Diagram 317 31 Flat grid 4 Ior perimeter of the orifices b For For ioog Worfor o or I area ofoneorifice 7 Re for dh 10 O r All P AE 1707 lyfr2 is determined from the curve Orifice plate 2 Re 105 approximate or r 4 1 005 010 015 020 025 030 035 040 045 050 055 060 065 070 075 080 090 10 1100 258 98 57 38 24 15 11 78 58 44 35 26 20 17 13 08 05 where 4 is determined from the curve iý 1 Reflon graph a of diagram 410 tORe is determined from the curve OR 2 Reon the same graph v is taken from 13b of 42 VJ 00 05 0 07 08 106 Entrance to a straight conduit through a perforated plate Section III with thickedged orifices OOI Diagram 318 i or 4 4f or d or ire perimeter for area of one orifice For free grid washer section F Fo 1 Re 2r h 10 V 105 ITr171 XjC LI 2g where is determined from the curve X is determined A d as a function of Re and Ah from diagrams 2225 A is taken from Table 21 v is taken from 13b 2 Re 105 approximate where 1 and 10 are found from diagram 410 o05 I 7l I I 11di 0 1 02j1 04 106j1 0 Iio 1 12j 16120124 1 135 1 122 1110I1084 1042 1024 1016 1007 10021 0 a a v4 441 1z 1 15 JZ4 107 Entraneie to a s traight conduit through a perforated plate Section III withorifice edges beVeled or rounded Re Wor dh 1Ip Diagram 319 Grid Resistance coefficient characteristic 0ID I where I is determined from the curve Orifices with 7 beveled edges ld 001 002 003 004 0 o 012 10 qor or I vor 4A 0a 4 a ON dtxr art where C is determined from the curve dt Orifices with rounded edges or for r 0 001 002 003 004 OOS 006 008 012 016 0J 0 C 050 j044 j037 f031 026 022 019 015 J00006 J002 Waor o r C4 4 0 0 4b b A 108 Various entrances to a conduit with a screen at the inlet Section III I Diagram 320 Entrance Resisiance coefficient C AM2 characteristic D iagra R n f t Screen For cross section Ci21 C Entrance with sharp inlet edge where Cs is determined as C for a screen from diagram 86 Dth 0 4where C is determined from the curves C h Entrance with rein A on diagram 31 forced inlet edge I Ct Csas above seenor where Ir is determined from the curve C h on diagram Converging bell mouth orifice I C as above forming the arc of a circle Screen ot a Without end wall Conic converging where C is determined from the curve C on bellmouth W diagrams 35 and 36 respectively orifice t Csas above tScreen for A b With end wall Screenfor 109 Entrance to a straight channel through a fixed louver at Section III T01 09 Diagram 321 No 1 inlet edges of the fins cut vertically No 2 inlet edges of the fins cur horizontally U or wor bHb pt ýk 8 7 rFCf 2 h T1214 10OSS f Al 2 L 9t LifA TWO 294 where k 10 for No1 h 06 for No2 A is determined from diagrams 21 to 25 1 01 02 03 04 05 06 07 0S 09 10 91 235 525 205 105 600 360 235 156 118 085 For 7 FPgrid front area Forgrid cross section I 1 For For At FV O and A m 0064 I FO at Re a103 the values of CI are determined from the curve C v is taken from 13 b II0 Entrance to a straight channel through stamped or cast Section III shaped perforated plates Diagram 322 w Q or For or free grid section Waor or ILN C is determined approximately from the curve f on diagram 317 III Section Four SUDDEN VARIATION OF VELOCITY IN STREAM PASSAGE THROUGH AN ORIFICE Resistance coefficients of stretches with sudden expansion orifice plates apertures etc 41 LIST OF SYMBOLS Fq area of the narrowest section of the stretch of the orifice M 2 F area of the channel section before the narrow section of the stretch of the orifice m 2 F area of the channel section behind the narrow section of the stretch of orifice M 2 F area of the contractedjet section at the entrance to the orifice m 2 coefficient of jet contraction Re F o coefficient depending on Re of jet contraction in the section of a sharpedged orifice at E610 n 2 area ratio 11 section perimeter m 00 diameter of the narrowest section of the orifice m D D diameters of the sectionbefore the orifice and the section behind it respectively m Dh hydraulic diameter 4X hydraulic radius m abo sides of the rectangular section or semiaxes of the ellipse m I length of the stretch depth of the orifice m r radius of cutvature of the inletorifice edge m a central angle of divergence of the diffuser or of convergent bell mouth or of the opening of the aperture flaps in the wall wo mean stream velocity in the narrowest section of the orifice msec w w mean stream velocities in the sections before and behind it msec AH pressure loss or resistance of the stretch kgim2 resistance coefficient of the stretch M momentum coefficient or Mach number N kineticenergy coefficient 42 EXPLANATIONS AND RECOMMENDATIONS 1 The sudden enlargement of the cross section of a conduit is the cause of sorcalled shock losses The resistance coefficient of a shock with uniform velocity distribution over the section befdrethe expansion and turbulent flowReDh35O isafunctionof N ttecuwthafunctionow 0 Not to be confused with shock losses in supersonic flow I 112 F2 the area ratio nf only and is calculated by the BordaCarnot formula F F2 2g 2 When a stream suddenly expands a jet is formed in the expanded section This jet is separated from the remaining part of the medium by a surface of separation which disintegrates into powerful eddies Figure 41 The length 1 of the stretch along which the formation of eddies their gradual reabsorption and the complete spreading of the stream over the section takes place equals 8 to 10 D2h D 2h hydraulic diameter of the expanded section The shock losses at sudden expansion are due to the formation of eddies in stretch 1 21 FIGURE 41 Flow pattern at sudden expansion 3 Within the limits of Reynolds number 10 Re 3500 the resistance coefficient of shock is a function not only of the area ratio but of Re as well and at Re 10 of Re only The values of C at 10 Re 3500 can be determined from the data of diagram 4 1 and at 1 Re 10 from the formula AH A 42 2 e where A 26 according to Karevs data 415 4 Actually the velocity distribution in the stretch before a sudden expansion is generally nonuniform Figure 42 This has a strong effect on the actual pressure losses and considerably increases them above the values given by 41 FIGURE 42 Nonuniform velocity distribution before a sudden expansion In order to calculate the resistance coefficient of a shock in a stream with nonuniform velocity distribution it is necessary to use a general formula for the shock which allows 113 for this nonuniformity if the velocity distribution over the channel section is known ZAH 2M 43 2g where M4 dF coefficient of momentum at the exit from the narrow channel into the wide one N L dF coefficient of kinetic energy of the stream in the same section It can be approximated that Na3M2 The accuracy of this formula is the higher the nearer N and M are to unity Using the last expression the following approximate formula is obtained for the resistance coefficients CHNI2 4 423 5 If the velocity distribution over a section is known the coefficients M and N can be easily determined If the velocity distribution is unknown it must be determ ined empirically The values of M and N can then be determined by graphic integration from the velocity profiles obtained 6 The velocity distribution is roughly exponential in the sections of expanding channels of divergence angles a 8 to 100 Figure 43 in lengthy straight streitches of constant cross section with developed turbulent velocity profile cf 17 and other stretches R0 44 max I where w wmax the velocity at the given point and the maximum velocity over the section msec R0 radius of the section m y distance from the pipe axis m m exponent which can vary inthe general case between 1 and co 7 At m 1 the velocity profile resembles a triangle Figure 44 At moo it resembles a rectangle meaning that the velocity distribution over the section is completely uniformn In practice a velocity profile approximating a rectangle is obtained for m as low as 8to 10 Figure 44 Such a value of m can be assumed for lengthy Thegeneral formula fol shock with allowance for a nonuniform velocity distribution was derived separately by Frenkel 419 and the author 411 114 straight stretches at turbulent flow The values m 2 to 6 can be assumed for lengthy diffusersn2 in accordance with the following table at 20mvm6 ata6ma3 at 40 m4 ata8 0 ma2 FIGURE 43 Smooth diffuser am 8 to 10ý 8 The values of M and N in 43 can be calculated at the exponential velocity profile from the following formulas obtained by the author 411 a in the case of conduits of circular and square sections M 2m Im 1 45 4m m 2 and 2mINmIP 46 W4m 2m3Xm 3 b in the case of a plane pipe or diffuser with sides ratio of the rectangular section a 0 3 30 IP 47 mm F 2 and Nm 43 48 9 The velocity profile in lengthy straight stretches of conduits with a distance from the inlet larger than IODh and laminar flow is parabolic Figure 44 WI Oa 49 The values of M and N obtained here are M4 133 N 2 in the casie of a conduit of circular or square section and M 12 N 155 in the case of a plane pipe 10 The velocity profile is roughly sinusoidal Figure 45 in conduits in the vicinity of grids elbows behind guide vanes and in other similar obstructions in the case of a plane channel it is calculated by the following formula 411 1 A sin 2k 2v 410 Wo U0 410 115 where b width of the plane channel m Aw deviation of the velocity at the given point of a narrow channel section from the mean velocity w over that section msec k integer v 3341 m Wmaxl xWma parabol Experiment I I FIGURE 44 Velocity distribution in plane diffusers with divergence an gles not wider than 80 and comparison with the exponential law Here the coefficients M and N are expressed as follows and Mtaw 3 k 411 412 11 A nonsymmetrical velocity field is established behind diffusers with divergence angles sufficient to cause stream separation a10 behind elbows branches etc Figure 46 In particular the velocity distribution in plane diffusers with divergence angles a 15 to 200 anol in straight elbows 6900 is found by the following formula 411 W 0585 164 sin 02 19 I 413 The values obtained in this case for M and N are M 187 and N 37 12 When a nonuniform velocity field is established in a conduit of constant cross section n 1 the equalization of stream velocity is accompanied by irreversible pressure 116 losses which are calculated by the following formula derived from 43 V A or IN2M AlNIV 414 4141 where M and N are determined in accordance with the nonuniform pattern obtained These losses are taken into account only where they have been neglected in determining the local resistance of fittings or obstructions in the straight stretch FIGURE 45 Sinusoidal velocity profile behind grids and guide vanes 13 The coefficients M and N for the intake of the mixing chamber of an ejector at the point of entry of the main zone of the free jet Figure 47 are calculated by the following formulas 4 11 I F e F and 4 15 416 y 1 2 3 e For the definition of the concept of main zone of a free jet cf Section XI 117 where F2 section of free jet in mixing chamber Fsection of jet in inlet nozzle dimensionless discharge through the given section i e ratio of the discharge through the pipe to the discharge through the inlet nozzle e ratio of the energy of the jet at its entry to the mixing chamber to the initial energy of the jet Diffuser It Df Diffuser a 1s005 0 a70 5 FIGURE 46 Nonsymmetric velocity distribution behind an elbow or a diffuser with a di vergence angle causing stream division The magnitudes d i are functions of the relative length of the free jet 0 Dh and are determined from the corresponding graphs of diagrams 1132 and 1133 14 The resistance of a stretch with a sudden enlargement canbe reduced by installing baffles cf diagram 41 Correct installation of these baffles reduces the lossesby 35 to 40 so that the resistance coefficient of such a stretch can be approximated by the formula I 0 ý4 17 where V resistance coefficient of a stretchkwith sudden enlargement without baffles Oeter determined from the data in diagram 41 15 In thegeneral case the passage of a stream from one volume into another through a hole in a wall is accompanied bythe phenomena illustrated inFigure 48 The stream passes from channel 1 located before the partition A with orifice of diameter D into channel 2 located behind this partition The two channels can have cross sections of arbitrary dimensions provtided they are not smaller than the cross section of the orifice of passage Thee passage of the stream through the orifice is accompanied by the bending of the trajectories of the particles the inertial forces causing them to continue The basic data to be used in the installation of such baffles are given in 52 paragraph 16 118 4 M Straight section of the ejector mixing chamber i 0 FIGURE 47 Velocity distribution in the main zone of the free jet after its entrance into the mixing chamber of the ejector theoretical curve for the free jet experimental curve for the jet in the channel 7 2 FC w4 ujA 0 4A a b c d FIGURE 48 General case of stream flow from one volume into another through an orifice asharpedgcd orifice 0 bthickwalled orifice b 0 c orifice with edges beveled in the flow direction dorifice edges rounded in the flow dircction their motion toward the orifice axis This leads to a decrease of the jet section from its initial area F to an area F section cc smaller than the area F of the orifice section Starting with section cc the trajectories of the moving particles are straightened and the normal phenomenon of sudden jet expansion takes places farther on 16 The resistance coefficient of the stream passage through a sharpedged orifice h0 Figure 48 a is calculated in the general case described under 15 at Dhas Re Oh 10s by the formula 4 10 74F 0 F 0 S oo 418 At Re 105 the resistance coefficient can be calculated by the approximate formula 414 C 0342 10 2 419 where g velocity coefficient at discharge from a sharpedged orifice depending on the IF Re P Reynolds number Re and the area ratio a coefficient of filling of the section of a sharpedged orifice at 0 depending on Reynolds number 1 is determined ý FC 19 i from the curves C 1Re on graph a of diagram 410 i43 is determined from the curveRe on graph a of the same diagram CO IO0707JY14e 17 The thickening Figure 48b beveling Figure 48 c or roundingFigure 48d of the orifice edges dead to the weakening of the jetcontraction effects in the orifice ie to the decrease of the jet velocity in its narrowest section FF ww Since it is this velocity which basically determines the shock losses at the discharge from the orifice the total resistance of the passage through the orifice is decreased 18 The resistance coefficient of the passage of a stream through a wall orifice of arbitrary edge shape and thickness is calculated as described under 15 at large Reynolds numbers practically at Re 105 by the authors formulas 412 and 413 AN 2 420 2g where C is a coefficient depending on the shape of the inlet edge of the orifice and is determined as Cfrom diagrams 31 to 33 and 36 coefficient allowing for the influence of wall thickness the inlet edge shape and conditions of passag6 of a stream across the orifice it is determined at thickwalled orifices from the 120 curve tf Wof diagram 411 and approximately at orifices with rounded or beveled edges by the formulatg 2 C Cr3 I friction coefficient of the entire depth of the orifice friction coefficient of unit depth of the orifice determined by diagrams 21 to 25 In the case of beveled or rounded orifice edges Cfr is assumed to be equal to zero The following formula similar to 4 19 can be used at Re 105 for thickwalled orifices Ca Fo 80 421 0W2 19 In general flow through an orifice in a wall can assume several distinct forms a FF sudden expansion of the section Figure 4 1 for which the resistance formula 420 reduces to 41 b FF sudden contraction of the section Figure 36a for which the resistance formula 420 reduces to 33 c F co entrance with sudden enlargement entrance through a flat plate orifice or perforated plate Figure 39 for which the resistance formula 420 reduces to the following if C is expressed through the velocity w behind the orifice Fa Ft2rr 422 d Foo discharge from the orifice into an unlimited space stream discharge through an orifice plate or perforated plate at the pipe end Figure 113 for which the resistance formula 420 reduces to thefollowing if C is expressed through the velocity W before the orifice 7 3 2 F CfIr 423 2g e F F restrictor orifice plate etc Figure 49 for which the resistance formula 420 reduces to the following if C is expressed through the velocity w before the orifice C IF F F1 424 The subscript o corresponds here to the subscript orand the subscript 2 to the subscript o in Section 111 The subscript o corresponds here to the subscript or and the subscript 1 to the subscript o in Section XI 121 f FF o0 aperture in a wallof unlimited area flow through an orifice from some large volume into another large volume Figure 4 10 for which the resistance formula 420 reduces to the following AH 425 FIGURE 49 Restrictor FIGURE 412 Open test section of a wind tunnel 20 Theresistance coefficient of a restrictor reduces to the following expressions at different shapes of the brifice edges and Re 10 a Sharpedgedorifice Inthis case V 05 and 141 so that formula 424 reduces to the following formula 410 412 and 413 07071 Fp 5 5 426 2g b Thickwaliled orifice In this icase too C 05 so that hd from5t uve f r 411 427 where t is determined from the curve t4 Eh of diagram 4 11 122 c Orifice edges beveled or rounded Assuming approximately 2VCiand CfrO the following expression is obtained for the resistance coefficient where C is determined in the case of beveled edges from graph a of diagram 412 as a function of I and in the case of rounded edges as C from graph b of diagram 412 as a function of 21 The resistance coefficient of a restrictor at Re 105 and sharpedged orificesis calculated by a formula derived from the general formula 419 0I 342 Q 7 0 7 j 1 F Lif 2 Re 2F 70 Fo F J7 FF 429 Re FReF where p so I ao and C are determined as indicated under 16 At Re 1 0b and with a thickedged orifice it follows from 421 and 427 that FI E 430 22 The resistance coefficient of an aperture in a wall at different shapes of the orifice edges and Re 10 reduces to the following expressions a Sharp edged orifice In this case V 05 t 141 and Cfr 0 so that on the basis of 425 SH 229 431 2g b Thick edged orifice In this case too C 05 so that 425 gives H I5 frC fr 432 2g where C 15 t was obtained experimentally by the author and is plotted in graph a of diagram 418 as a function of V I According to the authors experiments C g 28 123 c Orifice edges beveled or rounded AssumingCfr 0 and 21e we obtain C 433 2g frp where C is determined from the curves C graph b and C fJgraph C of diagram 418 respectively 23 The resistance coefficient of an aperture in a wall with sharpedged orifice at Re 105 is determined from the following formula which follows from 4 19 AH 2 where Co is determined from the curve C fRe of diagram 417 Re is determined IFRe from the curve e fARe of the same diagram At Re 105 and thickwalled orifice it follows from 421 and 432 C N 1 f 0C342e20Cb C 435 where C and e are determined as in the case of an aperture with sharpedged orifice V is determined as under 22b 24 At low crosssection coefficients Lo of the restrictor large velocities are obtained in its orifice even at relatively low stream velocities in the pipe The influence of compression begins to be felt here leading to an increase in the resistance coefficient of the restrictor The resistance coefficient of a restrictor taking the influence of compression into account can be determined by the formula C4C 436 where CM resistance coefficient of theirestrictor at large Mach numbers C resist ance coefficient ofthe restrictor at lowMach numbers determined as indicated under 14 to 17 k1 coefficient allowirig for the influence of compressibility in the vena contracta of the jet at its passage through an orifice determined from the graph diagram419 M Mach number before the restrictor axb velocity of propagation of sound msec CW ratio of specific heats p T1 static pressure absolute kgm 2 and specific gravity kgm 3 respectively of the medium before the restrictor 124 25 As with entry into a straight channel a sharp decrease of orifice resistance is achieved by installing an annular rib or ledge at the orifice inlet Figure 4 11 Thus according to Khanzhonkovs experiments 311 the installation of an annular rib with D B70122 and 106025 reduces the resistance coefficient C of an orifice in a wall from 27 28 to 115 a b FIGURE 411 Entrance to an orifice through an annular rib a or ledgeb 26 When the stream passes through a smooth belImouth orifice set into a wall cf diagram 420 the resistance is equal to the sum of the resistances of entrance into the bell mouth frictional resistance in the straight stretch and exit resistance The resistance coefficient of such a stretch can be determined by the formula C Af 437 where coefficient simultaneously allowing for the inlet and exit losses and deter mined from the curves Cf i b7 of diagram 420 Cfr I L friction coefficient of the straight stretch of a bellmouth 27 When the stream passes through apertures in a wall fitted with various flaps the resistance is higher than in the absence of flaps since they cause a complex flow pattern Here the resistance coefficient becomes a function of the angle of opening of Ifl the flaps a and their relative length If 28 The open test section of a wind tunnel Figure 412 can likewise be considered as a stretch with suddenenlargement Ejection dissipation of energy is the main cause of losses in the open test section of a wind tunnel Another cause of losses is that part of the free jet is cut off by the diffuser The kinetic energy of this portion of the jet is lost for the wind tunnel and there fore represents a part of the resistance of the throat 125 FIGURE 412 Open test section of a wind tunnel The coefficient of total resistance of the test section is calculated by Abramovich s formula 41 AH O 45ItsLts 2 0 0 84 Dh 438 where Dh hydraulic diameter of the exit section of the tunnel nozzle m and in the case of an elliptic cross section of the test section approximately l ose i 439 D T a j l It s length of the test section m a bo ellipse semiaxes m 126 43 LIST OF DIAGRAMS OF RESISTANCE COEFFICIENTS OF SECTION IV No of Diagram Source diagram Note I Sudden expansion of a stream with uniform velocity distribution Sudden expansion after a long straight stretch diffuser etc with exponential velocity distributions Circular or rectangular cross section Re 35X103 Sudden expansion after long plane and straight stretches plane diffusers etc with exponential velocity distribution Re35x10 3 Sudden enlargement of a plane channel behind orifice plates baffles in elbows etc with sinusoidal velocity distribution Re 35x1O 3 Sudden expansion behind plane diffusers with U10 elbows etc with asymmetric velocity distribution Re 35x O0 Sudden expansion after stretches with parabolic velocity distributions Re35x10 3 Stream deformation in a straight conduit Re35X 10 3 Stream deformation in a straight conduit with the entry of a free jet into it ejector Re 35 x 103 Sharpedged IDh 0i0015 orifice at the passage of the stream from a conduit of one size to another Re 1 0 The same for Re 105 Thickedged lDh0l5 orifice at the passage of the stream from a conduit of one size to another The same but beveled or rounded orifice edges Sharpedged lIDh 00015 orifice in a straight conduit Thickedged lDh 0 0 15 orifice in a straight conduit Orifice with edges beveled facing the stream flow a 440W in a straight pipe Re 04 Orifice with rounded edges in a straight pipe Re10i4 Sharpedged orifice I0001S in a large wall Orifices with various orifice edges in large walls Perforated plate at high Mach numbers Bellmouth set in a large wall Re104 Exhaust flap single tophinged Intake flap single tophinged Single flap centerhinged Double flap both tophinged Double flap top and bottomhinged Stamped louver with adjustable slats in a large wall 108 complete opening of the louver Test section of a wind tunnel ldelchik 411 The same Idelchik 412413 Edelchik414 Idelchik 412413 The same Idelchik 412 414 The same Khanzhonkov 420 Bromlei 47 The same Abramovich 41 41 42 43 44 45 46 47 48 BordatCarnot formula at low Re Karevs experiments 415 Calculation formulas The same 49 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 approximate On the basis of calculating data 42J Experimental data The same Tentative Theoretical formula A I 127 44 DIAGRAM OF THE RESISTANCE COEFFICIENTS Section IV Sudden expansion of a stream with uniform velocity distribution Diagram 41 p Dh perimeter j7 Baffles A WA f 1 Re mDb 35i10 3O a Without baffles f I is determined from the curve 2g Cm4 2 curve 1 on graph a b With baffles C N 0 6 1 F F is determined from the curve Y e T2 curve 2 on graph a U 45 Re XFOA 0 F a 0 01 021 03 04 051 06 j 071 081 1 Without baffles J 100 0810641050 1 036 1 025 o016 o0o0 0o01 2 With ba ffles 01601049 039 1030 021 1015 010 0oo05 oo2 10 0 0 0 a 04 of a0 IO Re 10 Is 20 30 40 50 102 2102 51021 03 2103 3103 3 5103 01 310 320 300 240 215 195 170 165 170 200 160 IQ0 081 02 310 320 280 220 185 165 140 130 130 160 125 070 064 03 310 310 260 200 160 140 120 110 110 130 095 000 050 04 310 3M00 240 180 150 130 110 100 085 105 080 040 036 05 310 280 230 165 135 115 090 075 065 090 065 030 025 06 310 270 215 155 125 105 080 060 040 060 050 0P0 016 2 IORe3510i AH is determined from the curves f Re on graph b 3 IRe8 AH 26 Tis dt0m Re is determined from 13tb b b 128 Sudden expansion after a long straight stretch diffuser etc Section IV with exponential velocity distribution WoDh Circular or rectangular cross section Re 36510 Diagram 42 A DhJ perimeter n F I UOm F AH 2 f N ý is determined from graph a rg I M 2m Jhm 4m m 2 2m Y m i 4 2m 3 m 3 v is taken from 13b I are determined from graph b Values of C 0 01 02 03 04 05 06 07 08 10 10 270 242 214 190 166 145 126 109 094 070 135 200 174 151 129 100 093 077 065 053 036 20 150 128 108 089 072 059 046 035 027 016 30 125 104 085 068 053 041 030 020 014 007 40 115 095 077 062 047 035 025 017 011 005 70 106 086 069 053 041 029 019 012 006 002 CC 1 100 1082 064 048 036 025 016 009 004 0 a m 10 135 20 30 40 70 Co N 270 200 150 125 115 106 10 M 150 132 117 109 105 102 10 b 129 Sudden expansion after long plane and straight stretches Section IV plane diffusers etc with exponential velocity di wDh Diagram 43 stribution Re 7 35109 Dh F 0perimeter nfu 110 Fo Wm2x L N is determined from graph a 2g M m 2 N in 13 mtm 3 I are determined from graph b v is taken from 13b I Values of C 0 o 1 o1 I 0Io2 10 04 5 I 06 o07 o0 1 10 10 200 174 151 128 119 092 077 064 051 034 135 165 140 120 100 083 067 053 041 032 020 20 135 114 094 077 062 048 036 026 V019 010 30 119 098 080 064 049 037 024 018 A012 005 40 112 092 074 060 046 033 023 014 009 004 70 104 085 067 054 041 028 018 008 005 002 Co 100 081 064 049 036 025 015 008 004 0 W LI b m 10 135 20 30 40 70 co N 200 164 135 118 112 104 10 M 133 122 113 107 104 102 10 1ý 130 Sudden enlargement of a plane channel behind orifice plates Section IV baffles in elbows etc with sinusoidal velocity dn eDh Diagram 44 distribution Re 35103 a perimeter W ý sin 22 k integer AH I Am L N 2M is determined from graph a N I W I is determined from graph b v is taken from 13b Values of C I 1F 0 1 0 1 02 03 1 04 05 07 1 1 30 01 101 083 066 050 038 026 017 010 006 001 02 106 088 070 054 040 029 020 013 007 002 04 124 104 084 068 054 041 030 022 016 008 06 154 131 118 092 075 061 048 039 029 018 08 196 170 147 127 107 089 075 060 049 032 10 250 221 195 170 146 125 105 088 074 050 a 01 02 03 04 05 N 10 106 113 124 137 M 100 102 104 308 112 Au II 06 07 08 09 10 SI154 173 1961222250 M 118 124 132 140 150 b ý 131 Sudden expansion behind plane diffusers with alOo elbows Section IV etc with asymmetric velocity distribution we 35h Diagrarn 4 5 MR e 374 5 Uq pj 0 01 02 0o3 j 04 05 f 06 07 08 i0 z 370 34 299 266 I236 1209 I182 158 135 096 Sudden expansion after stretches with parabolic velocity SectionIV distribution Rei take35n Diagrao 4 6 Wmax 01006lo a Circular pipe S200 I175 151 0 130 110 092 078 063 051 034 b Rectangular pipe C 7 3a29 26 23 29 18 155 1325 1 092607 0 047 03 7o 4F 2 F Dfii f1 0operimeter n a Circular pipe AK 266 a C i fl 2 ft are also Jetermined t 20 75 151 30 11 2 01 06 01 03 from the corresponding hb Rectangular pip curves O06 a cua pipeA N AH 1 24 Cf L 1 tke from55 F v is taken from 1 h C0 a2 a 6 426 to 0 I 132 Section IV Stream deformation in a straight conduit Re wDAl3510 Diagram 47 1 Exponential velocity profile 6 4 4F0 Dh i 110 perimeter Wmax w I N 2M is determined from the corresponding curve Cf M and N are determined from graph b of diagrams 42 and 43 n 10 1351 20 40 170 Ico a Circular pipe C 0o7 Io1060160051002o0 b Rectangular pipe 1 031 1 o1010 004 1002 0 04l m Oz r qI S 08 a s 2 Parabolic velocity profile Wnmax a circular pipe C 034 2g b I ectang ularC 015 pipe w 0 v is taken from 13b w 133 Stream deformation in a straight conduit with the entry of a Section IV free jet into it ejector Rev3510o Diagram 48 F 11o perimeter 4 AM I N2A I F21 The magnitudes C M and N are determined from the graph of S this diagram as a function of the length of the free jet DOh Fj ancii FO FO are determined as a function of the length of the free jet from the corresponding graphs of diagrams 1132 and 1133 is taken from 13b I 9 SIDI 05 10 15 20 25 30 40 50 60 80 19 C 016 046 084 143 202 254 326 365 380 381 381 N 165 289 390 485 565 635 720 755 768 770 770 M 25 171 200 220 230 240 245 245 1 245 245 145 134 Sharpedged 1000l5 orifice at the passage of the stream Section IV from a ondut o9 from a conduit of one size to another Re 10 Diagram 49 L Oh M6 perimeter 1014 J 0 Ta W02 I0 is determined from CF I r the curves corresponding to different P 4a e is taken from 13b Values of C 0 J01 02 103 104 105 06 107 108 09 110 0 290 280 267 253 240 225 209 198 175 150 100 02 227 217 205 194 182 169 155 140 126 105 064 04 170 162 152 142 132 120 110 098 085 068 036 06 123 115 107 098 090 080 072 062 052 039 016 08 082 076 069 063 056 049 042 035 028 018 004 10 050 045 040 035 030 025 020 015 010 005 0 4 ý A 135 Sharpedged orifice at the passage of the stream Section IV from a conduit of one size to another Re wCD1 105 Diagram 4 10 Dh A L If n perimeter f4e1 03 02 S o approximate where is determined from the curves Re of graph a 4e is determined from the curvesoR heof graph a Co I 0707 V1 is determined from the culve of graph b v is taken from 13b Re 26 101 410 E6 10 I 1 4102 i sf i 10 H 2103 4 10P I 0 lo 100 l 05 1 2 101 101 Re 0634 036 037 040 042 046 053 09 064 01 094 0 09 Values of C9 0 194 138 114 089 069 064 039 030 022 015 011 004 001 0 02 178 136 105 085 067 057 036 026 020 013 009 003 001 0 03 157 116 088 075 057 043 030 022 017 010 007 002 001 0 04 135 099 079 057 040 028 019 014 010 006 004 OO 001 0 05 110 075 055 034 019 012 007 005 003 002 001 001 001 0 06 085 056 030 019 010 006 003 002 001 001 0 0 0 0 07 058 037 023 011 006 003 002 001 0 0 0 0 0 0 08 040 024 013 006 003 002 001 0 0 0 0 0 0 0 09 020 013 008 003 001 0 0 0 0 0 0 0 0 0 095 003 003 002 0 0 0 o 0 0 0 o0 o 0 0 0 11 NM11 H I 1 11 1111 Re as I 1 60 01 00ý N V H I I 07 11 111111 11 A 7AL 111 11 41 N N I I 11 02019 NIN NYYY1ý1 N a IV a so0 2 S 8 03 Z 0 6 Io 2 4 Values of 4 F o 0 01 02 03 04 05 06 07 08 09 20 6 O5 b U 4 V C L171 167 163 159 155 1350 1145 139 132 1221 100 RI 17 t 1I 5 5 L of5 ON ZO 136 k Thickedged k0015 orifice at the passage of the stream Section IV from a conduit of one size to another Diagram 4 11 40 4F D1 Mý U perimeter A 1 Re os o P I F Dr D il AH 0 5 1 Fo F 2 1 F x 2g where t is determined from the curve v t X is determined from diagrams 22 to 25 as a function of Re and A Kh A is taken from Table 21 o is taken from 13b 2 Re10 5 approximately where and gl0 cf diagram 410 F F Fl r LO D4 p11 S ad 2 iS d 137 Thick edged I Dh 0015 orifice with edges beveled or rounded at Section IV the passage of a stream from a conduit of one size to another Diagram 412 Schematic diagram Resistance coefficient c Orifice with beveled FF edges 2 where C is determined from the curve C I b7 of graph a oDh o 001002 003 004 006008 02 a1 4 046 042 038 035 029 023 016 013 a vo u es 00u am a Orifice with rounded F F edges l W 2V I F P where C is determined from the curve C t ofgraph b o o 0 0oo1 002003o004I000Io06iS08 0I12oil06 2 0 0 C 50 044 037 031 0261 2210 1910151009j4i 061 003 0 170 00 CAP dAr 0 Ze ONa b 04 9 W I9 a 138 Sagection IV Sharpedged Lýo 0015 orifice in a straight conduit Diagra 1 4Ff 7 105 Dh 9 o Iperimeter I ReWD W4 0707V 1 F is determined from the curve C 2 Re105 approximately where is determined from the curves r L ItRe pon graph a of diagram 410 iwere is determined from the curve s2 fRe on the same graph Reis etemind fomthecure J Re onthesam grpha of diagram 410 Io I O 7 OV is determined from the curve on graph b of the same diagram 410 p 136 v is taken from 13b S 2 aa C 2 ID 4 45 44 01 0 47 4z 4j OW4 as 46 07 to rt 16 08 020 02 024 026 02 0 FS 002 003 004 005 006 006 010 012 014 016 028 020 02 024 026 026 030 C 7 000 3 100 1670 1050 730 400 245 165 117 860 655 515 406 320 268 223 182 156 F 034 036 038 040 043 047 00 0582 05 060 06 070 078 080 088 090 0 00 C 131 116 955 825 662 495 400 348 285 200 141 097 065 042 025 013 005 0 139 I Section III Thickedged 0015 orifice in a straight conduit Diagram 414 4F fIT perimeter I Re 10 U 0 o JCk o where C his determined from the table or more accurately from the graph of diagram 411 Values of C I FIda 5h 002 004 006 008 010 015 020 025 030 040 050 060 070 080 090 10 0 135 7000 1670 730 400 245 960 515 300 182 825 400 200 097 042 013 0 02 122 6600 1600 687 374 230 940 480 280 174 770 375 187 091 040 013 001 04 110 6310 1530 660 356 221 890 460 265 166 740 360 180 088 039 013 001 06 084 5700 1380 590 322 199 810 420 240 150 660 320 160 080 036 012 001 08 042 4680 1 130 486 264 164 660 340 196 122 550 270 134 066 031 011 002 10 024 4260 1030 443 240 149 600 310 178 111 500 240 120 061 029 011 002 14 010 3930 950 408 221 137 556 284 164 103 460 225 115 058 028 0111 003 20 002 3770 910 391 212 134 530 274 158 930 440 220 1 13 058 028 012 004 30 0 3765 913 392 214 132 535 275 159 100 450 224 117 061 031 016 006 40 0 3775 930 400 215 132 538 277 162 100 460 225 120 064 035 016 008 50 0 3850 936 400 220 133 555 285 165 105 475 240 128 069 037 022b 010 60 0 3870 940 400 222 133 558 285 166 105 480 242 132 070 040 021 012 70 0 4000 950 405 230 135 559 290 170 109 500 250 138 074 043 023 014 80 0 4000 965 410 236 137 560 300 172 112 510 258 145 078 045 025 016 90 0 4080 985 420 240 140 570 300 174 114 530 262 150 080 050 02 018 10 0 4110 11000 430 245 146 597 310 182 115 540 280 157 089 053 032 020 N I 1 6 2 6l 5 A is determined from diagrams 22 to 25 as a fuhction of Re and E A At X 002 the values of C are completely determined from the curves CT77 corresponding to different FP or from the table 2 Re 105 approximately 2g a I I where C and 00 cf diagram 410 Cc is determined as F under 1 1 is taken from 13 b A istaken from Table21 I z 4IV j 140 Orifice with edges beveled facing the stream flow Section IV woDh 640600 in a straight pipe Re H0 Diagram 415 4F D h ITo U per imeter 2g where is taken from the table or more accurately from graph a of diagram 412 The values of C are completely determined from the curves C or from the table v is taken from 13b Values of C I 0 a U jiFMj0OS01 L J 020 1 025 T 1 lb 11 ow 110 001 002 003 004 006 008 012 016 046 042 038 036 029 023 016 013 6800 6540 6310 6 130 5750 5300 4 730 4460 1 650 1 590 1 530 1 480 1385 i 275 1 140 I 080 710 683 657 636 600 549 490 462 386 371 357 345 323 298 265 251 238 230 220 214 200 184 164 154 968 932 894 865 800 743 660 620 495 477 457 442 412 378 335 316 286 275 264 256 234 218 192 181 179 172 165 158 146 135 119 112 790 760 725 700 685 592 518 480 384 368 350 336 308 280 244 228 192 183 172 167 153 137 118 110 092 088 083 080 073 064 055 050 040 038 035 034 030 027 022 020 012 012 011 010 009 008 006 005 00 0 0 0 0 0 0 141 Orifice with rounded edges in a straight pipe Section IV RewDh 101 Diagram 416 Re0 4F Dh 4 perimeter where r is taken from the table or more accurately from graph b of diagram 412 The values of ý are deterriiined from the curves t A9 or from the table o is taken from 13b a Values of C r p h 09 1 0ý 10018 0151012 03D lo4o Io4j5105 1S0550 O1065 1 070 107S31n61si4i10 001 002 003 004 006 008 012 016 044 037 031 026 019 015 009 006 6620 6200 5850 5510 5 000 4 450 3860 3320 1 600 1 500 1 400 1 330 1 200 1 100 925 797 690 542 600 570 518 437 39e 340 375 348 327 310 278 ý255 216 184 232 216 201 192 173 158 133 113 940 876 820 775 699 636 535 454 480 277 455 258 420 242 390 227 365 203 322 185 270 150 230 129 173 161 149 141 125 114 930 790 110 770 560 107 710 500 9 50 6 56 450 900 619 420 800 550400 750 500 340 650 4161300 530 340220 370 348 320 300 2660 230 190 1 60 265 233 222 200 172 152 124 100 184 169 155 145 127 113 089 070 125 118 10 095 085 078 060 050 090 082 075 070 060 053 040 0 32 060 056 050 045 040 034 027 020 038 034 031 029 0 24 021 016 012 ý012 010 0oi 00 007 006ý 004 003 0 0 0 0 0 0 0 0 a I I 142 Sharpedged orifice 0i0015 in a wall Section IV h large Diagram 4 17 Dh F 0O perimeter 1 Ret lO 285 2 Re 10s approximately where C is determined from the curve fRe is determined from the curve c0RehRek v is taken from 13b 2510 410 610 10 2 102 4102 103 2103 4103 104 210 10 210 102 194 138 114 089 069 054 039 030 022 015 011 004 001 0 to 100 105 109 115 123 137 156 171 188 217 238 256 272 285 L N T IIIIII l I li I I I I I I II Ill q i l Il 1 i1 1111 II IIII I IIIII 11 11111 I ii1V1 143 Orifices with various edges in large walls Section IV Diagram 418 Thickwalled orifice deep orifice L0015 woDh 1 Re lS C h where 4 is determined from the curve I on graph a A is determined from diagrams 22 to 25 as a function of Re and A A A is taken from Table 21 v is taken from 13b 2 Re 105 approximately 4 C 034f A where and 1 oRe are determined as in diagram 417 4 is determined as for Re IOr 4 t sIJ 0 49 40 11 IS ZO ZE 2 11 34 Orifice with beveled edges F e I Aow 5Sao Vis determined from the curve V I on graph b is determined from the curve Wh of graph c Orifice with rounded edges qC I Wg 4V 041 AM AW W a k 6 144 Perforated plate at high Mach numbers Section IV Diagram 4 19 A4 1 Sharpedged orifices CM kMC where C is determined from the data of diagrams 49 to 411 413 and 414 kM is determined from the curves k I fMJt Min a xgý velocity of sound x L specificheat ratio determined from Table 13 CW 2 Orifice edges beveled or rounded cf diagram 88 Values of kM M r 0 005 010 015 020 025 030 035 040 045 050 055 060 065 02 100 109 130 03 100 103 113 151 04 100 000 103 141 141 0 5 1 0 0 1 0 0 1 0 0 1 0 3 1 1 0 1 2 7 1 8 5 06 100 000 100 100 112 130 13 0 177 07 100 100 100 100 103 108 118 135 168 08 100 100 100 100 101 103 107 112 120 137 163 201 09 100 100 100 100 100 100 102 104 107 113 121 133 150 175 Z2 N1 41 411 1 1 05 Clo 9 9W4 w w os vs s s OF oa oi 145 Bellxiibuth set in a large wall Re vaDh w S6ction IV Diagram 420 D 4F e Dh ij 0 perimeter hi 7 4fr 29 where fr Dh is determined from the curves corresponding to different rDh A is determined from diagrams woDh A 22 to 25 as a function of Re andA is taken from 13b A is taken from Table 21 Values of lIDh riDh 025 056 075 100 125 150 175 20 25 30 35 40 002 264 225 189 168 160 156 154 158 151 150 149 148 004 220 170 142 137 134 133 133 132 132 132 131 130 006 190 130 123 122 122 121 121 121 121 121 120 120 008 i44 119 116 115 115 115 115 115 115 115 115 115 010 112 110 110 110 110 110 110 110 110 110 110 110 012 108 108 108 107 107 107 107 107 107 108 108 108 020 104 104 104 104 104 104 104 104 104 105 105 105 050 103 103 103 103 103 103 103 103 103 103 103 103 146 Exhaust flap single tophinged Section IV Diagram 421 Qit 15 20 25 30 45 60 90 1 fl 1 11 63 45 40 30 25 20 2 22 fl 17 12 85 69 40 31 25 i 3 zo 30 16 11 86 47 33 25 AH is determined from the curves 4 f a cor responding to different values of If 5 o Intake flap single tophinged Section IV Diagram 422 4 1161 11 80I I I 3 1 26 44 ftH 2 Ifl 10 is determined from the 0 1 1 curves C f a cor fl responding to different 4 2 20 1f1 I A values of bf 3 o 2V AO io o 0 V 0 wo b fl 147 S ectio n IV Single flap centerhinged Diagram 423 I flap lengthwomo o 15 20 2 30 45 60 90 S 46 26 151 0 30 20 I fl 2 i co 59 f5 21 14 50 30 24 2Vo I 2 is determined from the curves a cor responding to different Ifl values of I f zo o 0 Double flaps both tophinged Section IV Diagram 4 24 Ifl flap lengthwo 15 20 2 30 5 6 90 b fl S 14 90 60 49 38 30 24 0 fl N2 ý ý 20 31 21 j14 98 52 35 24 A0 CmAlf is determined fromn the curvesIa cor responding to different values of If N an we S 148 4 Double flaps top and bottomhinged D Section IV Diagram 425 fl flap length W O u 5 2 flplegh0Wi 7 15 20 25 30 45 60 90 fl I mo 19 1 13 185 163 1381 301 24 2 1 fl 20 C 44 24 I 1 11 60 40 28 3 I fl 59 36 24 17 86 57 28 0 2 7g is determined from the curves Cf cor responding to different I fi 61 values of F 7 Vl x V so 0 V s 0 Stamped louver with adjustable slats in a large wall Section IV T 08 complete opening of the louver Diagram 426 G AH F 7 2 F louver cross section 2g uw mean velocity over the total section of the 000000000oD louver in the wall 000000o0ooo o0000000000 ooo0o0o000o UOoO ooIDo DEI0000 000000000D0DO 0000000000D 00000000C000IO 00000000000D 000 00000DODOD 16 000O0D 00000 149 Test section of a wind tunnel Section IV Diagram 427 Dh l Uo perimeter I For a rectangle Dhb for an ellipse Dh 4a 1 5 a b g where a and b sides of the rectangle or semiaxes of the ellipse i it s 1 2 ts is determined from the curve C D o it a000 ON8 ON om U t 10 30 Ca 150 Section Five SMOOTH VELOCITY VARIATION Resistance coefficients of diffusers 51 LIST OF SYMBOLS F area of the narrow section of the diffuser m 2 F area of the wide section of the diffuser in the case of a multistage diffuser of the wide section of its smooth part m 2 F area of the widest section of a multistage diffuser m 2 njL area ratio of the diffuser in the caseof a multistage diffuser area ratio of Fe its smooth part area ratio of sudden enlargement of a multistage diffuser n f total area ratio of a multistage diffuser II perimeter of the narrow section of the diffuser m D diameter of the narrow section of the diffuser m b hydraulic diameter of the narrow section of the diffuser m a b sides of the rectangular narrow section of the diffuser m a b sides of the rectangular wide section of the diffuser m Ld diffuser length m a central divergence angle of a diffuser of arbitrary shape w0 w2 mean stream velocity in the narrow and wide sections of the diffuser respectively msec wo mean stream velocity before the perforated plate msec Wmax maximum stream velocity through the cross section msec AW pressure loss or resistance kgm 2 total resistance coefficient of the diffuser p coefficient of local resistance due to diffuser enlargement Cfr friction coefficient of diffuser d total coefficient of shock allowing for the total losses in the diffuser Texp coefficient of shock allowing for the local losses due to diffuser enlargement only 52 EXPLANATIONS AND RECOMMENDATIONS 1 A diffuser is a gradually widening passage to make the transition from a narrow conduit to a wide one and the transformation of the kinetic energy of the stream into pressure energy with minimum pressure losses In such a divergent pipe the intensity of turbulence is greater than in a straight pipe and the local friction resistances are also greater The increase in the pipe section is accompanied by a drop in the mean stream velocity Therefore the total resistance coefficient of the diffuser expressed in terms of the velocity in the initial section is less for divergence angles below a certain 151 value than for the equivalent length of a constantsection pipe whose area is equal to the initial section of the diffuser An increase of the divergence angle beyond this limit leads to a considerable increase in the resistance coefficient so that it finally becomes much larger than for the equivalent length of straight pipe 2 The increase of the resistance coefficient of a diffuser with the increase of its divergence angle is mainly a result of the separation of the boundary layer from the diffuser walls and of intensification of the stream turbulence with the resulting formation of turbulence in the entire stream czsaD U AW FIGURE 51 Flow patterns in diffusers with different divergence angles at n L 33 FO aa 240 ba 3840 cm 60 d 90 e a 180 The separation of the boundary layer from the walls Figure 5 1 is due to a positive pressure gradient existing in the diffuser as a result of the velocity drop which accompanies the ijincrease in cross section Bernoulli equation The beginning of stream separation in a plane diffuser can be approximately deter mined from the following relation proposed by Levin 520 Fsep i 95 51 A plane diffuser is a length of conduit with expansion in one plane only 152 k j where Fsep is the area of the section in which the stream separation starts 3 The velocities over the cross section in narrowangle diffusers with nonseparating boundary layers are distributed symmetrically about the longitudinal axis Figure 44 The separation in wideangle diffusers up to a 50600 generally starts from only one of the walls i e from the wall where the velocity is lowest With the beginning of stream separation from one of the walls the pressure increase through the diffuser is interrupted or reduced and as a result there will be no stream separation from the opposite wall Consequently the distribution of velocities over the diffuser section will be asymmetric Figures 51 and 52 FIGURE 52 Velocity profiles in plane diffusers with different divergence angles In a perfectly symmetrical wideangle diffuser the separation occurs alternately at one or the other side of the diffuser Figure 52 leading to strong fluctuations of the whole stream 4 The resistance coefficient of a diffuser is a function of several parameters 1 the divergence angle a 2 the area ratio n the crosssection shape 4 the shape of the generatrix 5 the inlet conditions 6 the regime of flow value of Re 7 and 7 the Mach number wa AH C o fReM a nIk 1 k 2 ka 2 WO 52 153 where k is the coefficient characterizing the state of the boundary layer the velocity distribution at the diffuser inlet k is the coefficient characterizing the shape of the diffuser cross section k3 is the coefficient characterizing the shape of the diffuser generatrix a is the velocity of propagation of sound in the stream msec 5 In practice an arbitrary method of loss separation is used This is due to the scarcity of available data on the dependence of diffuser resistance on these parameters and particularly on the Reynolds number With this method the total resistance of the diffuserAHdif is considered as the sum of the local resistance due to the stream expansion AHexp and the frictional resistance Atffr The total resistance coefficient dif is correspondingly considered as the sum of the local resistance coefficient due to the expansion Cexp and the friction coefficient f Cdif 2 Cexp Cfr 53 Here the influence of the Reynolds number is accounted for by the friction coefficient Cfr while exp is considered practically independent of Re 6 It is convenient to express the expansion losses by the coefficient of shock bf 516 defined as the ratio of expansion losses in a smooth diffuser to the theoretical losses at shock in the case of sudden expansion of the cross section a 1800 exp 54 f we W In the case of uniform velocity distribution at the inlet k 1 Othe coefficient of shock of diffusers with divergence angles 040 can be calculated by the following approximate formula 5 16 Yexp k2 tgj tgj 55 where a is the general divergence angle In the case of a pyramidal diffuser with uneqlial divergence angles in the two planes a is the larger angle The following value of k is used for conical and plane diffusers k 32 the following value is tentatively used in lieu of more accurate experimental data for pyramidal diffusers with expansionin two planes k 40 The subscript dif will he dropped in what follows The recent studies of Solodkin and Ginevskii 58 59 and 526 to 529 BamZelikovich 52 53 and Ovchinnikov 5 24 iii regard to the boundary layer in pipes with positive pressure gradient enable the establishment of a relationship between the total resistance coefficient of a narrowangle diffuser and the boundary layer before the diffuser entrance Currently there is no theoretical analysis of the corresponding situation for wideangle diffusers which is by far tfie most interesting case 154 The value of qpp for the entire range of a from 0 to 1800 is determined from the curves exp 1ain diagrams 52 to 54 The coefficient of local resistance of expansion is expressed through the coefficient of shock as follows Cexp g exp I k tg t2 g i1 56 Zg 7 The friction coefficient of a diffuser of circular or rectangular section with equal divergence angles in the two planes is calculated by the formula I L 57 frj S2g2 where I is the friction coefficient of unit length of the diffuser determined from the corresponding graphs of diagrams 22 to 2 5 as a function of the Reynolds number Re and the relative roughness AAh 1ne friction coefficient of a pyramidal diffuser with unequal divergence angles 00 in the two planes is calculated by the following formula cf 516 f 58 TI 3 02 tl 6I 92 n2AfhIf The friction coefficient of a plane diffuser with inletsection sides a and b where b is constant along the diffuser is calculated by 4f 1r0 I IiI 0 g 2 sin 2iI The following simplified formula can be used in practice ýfr I b 05 1 L9 8 The resistance coefficients of diffusers where the rectangular section changes to circular or vice versa can be determined from the data for pyramidal diffusers with equivalent divergence angles The equivalent angle ae is determined on the basis of the following formulaz Obviously at n exp ex For the derivation cf Eiffel 539 and also 5161 The magnitude of IL actually varies along the diffuser but in practice it is assumed to be constant 155 1 transition from circle to rectangle tg 510 2 transition from rectangle to circle 9 In the case of a nonuniform velocity distribution at the inlet section i e at k 10 as when the diffuser is placed behind a long straight stretch or any other fitting behind a throttle etc the coefficient ofloca7 resistance due to expansion in the diffuser is determined by the formula exp kexp 512 where C1xp is determined as Cexp of a diffuser with uniform velocity distribution at the inlet cf point 6 k is determined as a function of the velocity profile at the inlet of the diffuser and of its divergence angle 10 At the inlet the dependence of the diffuser resistance coefficient on the state of the boundary layer the velocity distribution is complex In narrowangle diffusers a nonuniform symmetric velocity profile with a maximum at thecenter and mininrnum at the walls leads to a decrease ofthe total resistance since the frictional stress at the walls is decreased At the same time this velocity profile increases the possibility of stream s eparationiand displaces the point of separation toward the initial section of the diffuser so that with the subsequent increase of the divergence angle the resistance will increase compared with resistance at a uniform velocity distribution In a nonuniform velocity profile with lower velocities at the center and higher ones at the walls the opposite will be observed the total resistance of the diffuser tieing higher at small divergence angles and lower at larger ones 11 The dependence of the coefficient k on the divergence angle for a symmetric velocity profile at the inlet has been plotted in diagram 51 for different values of the ratio of the maximum to the mean velocities Wmax over the section The dependenceof the ratio UL on the relative length of the initial straight stretch has likewise beenplotted in We D the same diagram for different values of Re Solodkin and Ginevskii 526 In the case of anonsymmetric velocity profile whichexists behind various fittings throttles etc limited use can be made of the values of k given in diagrams 56 and 5 18 The data ofrdiagram 5 6 were obtained on the basis of the processing of results of Winters investigations 565 of a conic diffuser placedbehind branches with different geometric parameters The data of diagram 5 18 were obtained on the basis ofJthe processing of the results of Johnsons investigations 547 of annular diffusersat whose inlet different velocity distributions were created by means of special screens 12 Up to a 40 to 500 the coefficient of shock 4cxp is smaller than unity This shows that losses in a diffuser are smaller than shock losses in the case of sudden expansion O 1800 At divergence angles 50 a 900 the value of Texp becomes 156 somewhat larger than unity i e losses in a diffuser increase slightly compared with losses at shock Starting with a 900 and up to a 1800 the value of Yexp again drops and approaches unity indicating that the losses in the diffuser approach the losses at sudden expansion If therefore auniform velocity distribution at the diffuser exit is not required it will be inexpedient to use diffusers with divergence angle a 40 to 500 If a very short transition stretch is required by design considerations this can be b achieved by means of sudden expansion a 1801 If it is required to obtain a uniform velocity profile behind the transition stretch and if this purpose is to be achieved by means of baffles dividing walls or grids then any diffuser even with a large divergence angle a 50 is to be preferred to sudden expansion a 1800 13 Since the smooth increase of a pipe section with narrow divergence angles leads to a decrease in the pressure losses compared with those in a pipe of constant section and at wide divergence angles to the increase of these losses there must obviously exist an optimum divergence angle at which minimum losses are obtained This angle can be calculated for the case of a straight diffuser of circular section by 4opt 043 513 24 1 3 Thus at 1 0015 n 225 and i 10 one obtains aopt 6 For a diffuser of rectangular section a opt lies approximately within the same limits For a plane diffuser this angle lies within the limits aopt 10 to 120 14 The flow conditions of a stream in short wideangled diffusers can be considerably improved by preventing stream separation or reducing the formation of eddies d U AI tot 4i d e f FIGURE 53 Different methods for improving the work of short diffusers a suction of the boundary layer bblowing away of the boundary layer cguide vanes or baffles d dividing walls e curved diffuser f multistage stepped diffuser 157 The main measures contributing to an improvement of flow in diffusers are Figure 53 1 the suction of the boundary layer 2 the blowing away of the boundary layer 3 the installation of baffles or guide vanes 4 the installation of dividing walls 5 the use of curved walls 4 6 the use of stepped walls 15 When the boundary layer is suckedFigure 53a thepart of the streamseparated from the wall again adheres to the surface and as a result the zone of separation is displaced downstream the flow becomes smoother and the resistance decreases A 30 to 50 reduction of losses can be achieved as a result The blowing away of the boundary layer Figure 53b leads to an increase of stream velocity near the walls As a result the separation zone is also displaced downstream 16 Guide vanes or baffles Figure 53c deflect a part of the highvelocity stream core toward the boundary zone of separation The latter is reduced or even completely eliminated as a result The effect of guide vanes is greatest at wide divergence At a 50 to 1800 the resistance coefficient is reduced by a factor of almost two Several general rules can be given for positioning the baffles in the diffuser 5 56 a The vanes should be placed before and behind the entrance angle to the diffuser Figure 53c and their number should be increased with the increase of theidivergence angle b The chanriels between the vanes and the walls must contract as a rule however at wide divergence angles satisfactory results can be obtained even with expanding channels It is necessary to permit the stream to expand in the peripheral channels just as in the main channel c The relative distance h must be equal to 095 for a 900 and to 14 for a 1800 Figure 53c d The vanes must have a small curvature and can be made of sheet metal e The chord of the vanes can represent 20 to 25 of the diameter or the height of the diffuser section f The best angle of inclination of the vanes can be selected by arranging thelm first one behind the other and rotating each of them through an angle until the diffuser resistance becomes minimum 17 The dividing walls divide a wideangle diffuser into several narrowahgle diffusers Figure 53d As a result the resistance is decreased and a more uniform velocity distribution over the section is achieved 5 19 The dividing walls are more efficient with the increase of the total divergence angle of the diffuser At relatively narrow divergence angles the dividing walls can een increase the diffuser resistance since ihey increase the total frictionsurface The following procedure is used when selecting and installing dividing wallis in wide angle diffusers a The number z of dividing walls is selected from Table 51 as a function of the divergence angre TABLE 51 30 45 60 90 120 158 b The dividing walls are positioned so that the distances aL between them at the diffuser inlet are exactly equal and the distances a between them at the exit are approximately equal c The dividing walls extend in both directions beyond the diffuser with protruding parts parallel to the diffuser axis The length of the protruding parts must not be smaller than 01a and01a respectively 18 The variation of the pressure gradient along the diffuser is smoother in a diffuser with curved walls Figure 53e in which the rate of increaseof the crosssection area is lower in the initial section than in the end section As a result the main cause of stream Feparation is weakened and the main source of losses is attenuated A diffuser in which the pressure gradient remains constant along the channel L const at potential flow will be dthe best choice The losses in such diffusers may be as much as 40 lower than corresponding straight diffusers at divergence angles 25 a 900 the reduction increasing with an increase of the divergence angle within these limits 5 16 At lower divergence angles eg a 15 to 200 the losses in curved diffusers are higher than in straight ones The use of curved diffusers is therefore expedient at wide divergence angles only The equation of the generatrix of a curved diffuser with a section which fulfills the dp condition d const Figure 53e is Y 514 1 1 4 1T The equation of the generatrix for a plane diffuser is Y 515 xd dp The resistance coefficient of a curvilinear diffuser at x const within the limits F 01 7 09 can be calculated by the following approximate formula 516 AH 13 1 3 516 1 0 143 n 1 where 4p is a coefficient depending on the relative length d of the curved diffuser and determined from the data of diagram 57 19 In a multistage diffuser Figure 53f in which a sudden expansion takes place after a smooth variation of crosssection area the main shock losses occur at relatively low velocities As a result the losses in the diffuser are reduced by a factor of two to The frictional losses in very wideangled diffusers arc quite small It is not necessary therefore to separate these losses from the total losses with curved diffusers which correspond to wideangle straight diffusers 159 three The coefficient of total resistance of a multistage diffuser of circular or rectangular section can be approximately calculated by the following formula 516 1 d I X 29tg X Xr 517 r I 2L t9 a 2Ld a it where k 32 for a diffuser of circular section k 4 to 6 for a diffuser of rectangular section n is total area ratio of the multistage diffuser ie ratio of the area of the widest part of the diffuser to the area of its narrowest part Figure 53f The coefficient of total resistance of a plane multistage diffuser can be approximately calculated as follows 5 16 C AH X I 2 dg a L Q Id g ar b a 2 a 2 2g a dt2 2a 32tg t I 1 518 4G with b constant along the diffuser 20 To each area ratio n and each relative length L or d of the multistage diffuser there corresponds an optimum divergence angle aopt at which the total coefficient of resistance is minimum cf diagrams 58 to 5 10 The use of multistage diffusers with optimum expansion angles is recommended The resistance coefficient of such diffusers is determined by the formula 5 16 As A 0 ioC 519 where rin minimum resistance coefficient depending on the relative length of the Id smooth part of the diffuserT or Id and the total area ratio n of the multistage diffuser The curves of diagram 510 were calculated for k2 60 which gives a certain safety factor in the calculation 160 this relationship has been plotted in diagrams 58 to 5 10 3 is a corrective factor deter mined from the same diagrams as a function of 21 The limiting divergence angle ali 1of the smooth part of the multistagediffuser i e the angle at which for the given overall area ratio n and relative length I ora Dh a of the smooth part a straight diffuser is obtained is given by 6 lir Vn I or 520 tg alim n I 2 Id 2 d In practice it is expedient to select the relative length Dhof the multistage diffuser not on the basis of the minimum value Cmi but on a value approximately 10 higher which makes possible a considerable reduction in diffuser length without noticeably increasing Id the losses in it The lines of optimum values of y are represented in graphs a of diagrams 58 to 5 10 by dotted lines 22 If the diffuser is installed behind a fan it becomes necessary to allow for the flow pattern at the fan exit which is quite different from that at an inlet to an isolated diffuser placed behind a straight stretch of constant section As a rule the velocity profile behind a centrifugal fan is nonsymmetric due to a certain stream deflection in the direction of fan rotation The velocity profile is a function of the type of fan and its type of work characterized by the output coefficient QQpwhere Qopt output at maximum efficiency of the fan 23 The stream deflection in the direction of fan rotation makes it possible to use unusually wide divergence angles behind centrifugal fans and diffusers If these are plane diffusers of divergence angle a 250 it is best to make them asymmetric so that the outer wall is either a continuation of the housing or deviates from it by a small angle up to 100 toward the side of the housing while the inner wall deviates toward the side of the impeller The deflection of the diffuser axis toward the side of the fan housing is impractical since the resistance of such diffusers at a 150 is 2 to 25 times higher than that of symmetric diffusers in which the axis is deflected toward the side of the impeller cf Lokshin and Gazirbekova 522 24 The resistance coefficient of plane diffusers with divergence angles a 15 and pyramidal diffusers with divergence angles a 10 installed behind centrifugal fans of any type can be calculated from the data given above for isolated diffusers taking for their inlet section the ratio of velocities W nax 11 W0 161 The values of C obtained for isolated diffusers cannot be used at wider divergence angles than those given above here the values of C must be determined from the data of diagrams 5 12 to 5 17 These are applicable for QQop and Q SQopt 25 When the space available for the diffuser behind the centrifugal fan is restricted use can be made of a multistage diffuser which is much shorter than a straight diffuser at equal resistance The optimum divergence angle of the diffuser at which a minimum coefficient is obtained can be calculated from the corresponding curves of diagram 5 17 26 The resistance coefficient of an annular diffuser formed by installing a conical diffuser behind an axial fan or compressor with converging back fairing cf diagram 1518 can be determined by the formula 1r 7 W2 k dId 521 2g where d total coefficient of shock determined from graph a of diagram 518 as a function of the divergence angle a k is a correction coefficient characterizing the velocity distribution in the narrow section of the diffuser and determined from graph b of the same diagram as a function of the divergence angle a these curves correspond to different velocity profiles in the narrow section of the diffuser represented in graph c of the same diagram F and F are crosssection areas less the crosssection area of the fairing in the narrow and wide parts of the diffuser respectively 27 The resistance coefficient of an annular diffuser formed by installing a conic diffuser behind an axial fan with diverging back fairing can be approximated by the formula C f ka 522 2g where C resistance coefficient of the same diffuser at uniform velocity distribution at the inlet determined from table 5 3 in diagram 518 k correction coefficient deter mined under 11 28 Axial turbines use radialannular diffusers in which the increase of area is mainly due to theradial dimensions of the diffuser Figure 54a The areaexpansion ratio of radialannular diffusers can be determined from the relation n 2LD 523 where D and d are the relative diameters of the diffuser and of the hbi b respectively is the relative width of the exit section of the diffuser The resistance coefficient of a radialannular diffuser mounted behind an operating turbocompresscor is 15 to 20 greater than the corresponding value for the same diffuser when the compressor is not operating The magnitude of the resistance The total coefficient of shock allows for the total losses in diffusers 516 It is assumed that thetapproximate velocity distribution to be expected behind the fan or compressor is known 162 A coefficient is also a function of the type of work of the compressor that is of the discharge coefficient C where a peripheral impeller velocity at the maxi mum radius cf Dovzhik and Ginevskii 512 a b FIGURE 54 a radial annular diffuser b axialradialannular The values of the resistance coefficients of radialannular diffusers of an operating at c0 05 and nonoperating compressor are given in diagram 519 29 The axialradialannular diffuser is somewhat better from the aerodynamic point of view Here a radial bend follows a short annular diffuser Figure 54 b In this diffuser the radial turn is achieved at lower stream velocities and the pressure losses are accordingly somewhat lower At the same time the axial dimensions are much larger than those of a radialannular diffuser When installed behind an operating turbocompressor at c0 05 the values of the resistance coefficients are given in diagram 519 30 The existence of a uniformly distributed resistance behind the diffuser promotes orderly streamline flow in the diffuser itself and in the channel behind it This some what reduces the losses in the diffuser itself The total losses in the diffuser however remain roughly the same Specifically for curved diffusers and for straight diffusers of divergence angles from 40 to 600 these losses remain equal to the sum of the losses taken separately for the diffuser and the grid screen etc cf 517 T 524 LH where C resistance coefficient of the diffuser determined as C from the data 780 163 of the corresponding diagrams of this section 4aN resistance coefficient in front of VEg 2 2g the grids screens nozzles etc expressed through the stream velocity determined as FI Cfrom the data of the corresponding diagrams of section VIII n area ratio of the diffuser t 164 53 LIST OF THE DIAGRAMS OF RESISTANCE COEFFICIENTS OF SECTION V Diagram description Source Noof Note diagram I Diffusers of arbitrary shape located at the discharge of long stretches with nonuniform but symmetric velocity profile Conical diffuser in a line Pyramidal diffuser in a line Plane diffuser in a line Transition diffuser transition from circle to rectangle or from rectangle to circle in a line Diffusers of arbitrary shape at a 812 located at discharges of branches or other fittings with similar velocity profiles Curved diffusers dpdx const in a line Stepped conical diffuser of optimum divergence angle opt Stepped pyramidal diffuser of optimum divergence angle goopt Stepped plane diffuser of optimum divergence angle goopt at 0 5 a 20 Short diffusers with guiding devices or with resistance at the exit Plane symmetric diffuser behind a centrifugal fan in a duct forced chaff Plane asymmetric diffuser at I 0 behind a centrifugal fan in a duct forced draft Plane asymmetric diffuser at a 10 behind a centri fugal fan in a duct forced draft Plane asymmetric diffuser at a e 1 O behind a centri fugal fan in a duct forced draft Pryamidal diffuser behind a centrifugal fan in a duct forced draft M ultistage diffuser of optimum divergence angle aopt behind a centrifugal fan in a duct forced draft Annular diffusers with deflecting baffles iii a duct Radial annular and axialradialannular diffusers in a line Abramovich 51Solod kin and Gi nevskii 526 Peters 557 Gibson 5 6 543 544 Idelchik 516518 Peters 5 57 The same The same Winter 565 T delschik516 The same The same The same Idelchik 519 Lokshin and Gazirbekova 522 The same Bushel 54 Johnston 547 Dovzhik and Ginevskii 512 51 52 53 54 55 56 57 58 59 510 511 512 513 514 515 516 517 518 519 The nonuniformity is compensated for approximately Experimental data at large diverg ence angles the curves are an extrapolation Very tentative to be used until refined by new data Experimental data the curves are extrapolated for large divergence angles Tentative Experimental data Based on experimental data Approximate calculations First one according to the authors experimental data the other tentative Experimental data The same 165 54 DIAGRAMS OF RESISTANCE COEFFICIENTS Diffusers of arbitrary shape located at the discharge of long Section V stretches with nonuniform but symmetric velocity profile Diagram 5 1 A h 1I perimeter Initial zone 2 Free jet ts AH te where Cexp and Cfr are taken from the diagrams of Section V k is determined as a Wni4s Wfnax function of a from the curves of graph a corresponding to differeint Iis determined as a function of LIDh from the curves of graphs b and c corresponding to LDh different values of Re is taken from 13b Values of kh Wmax we 1 6 0 114 120 24 s 100 100 100 100 100 100 10 100 102 110 112 114 115 i00 107 102 104 114 120 123 126 i19 1 10 103 106 117 127 131 136 124 i14 104 108 119 142 149 149 131 118 105 110 119 154 162 154 134 120 106 112 122 162 168 157 136 121 106 114 122 168 181 160 136 1i21 105 116 122 178 189 161 136 121 106 a 2 Initial zone free jet 1 Initial zone straight pipe W LI 0 J I W 15 b C a 166 Conical diffuser in a line Section V Diagram 5 2 1 Uniform velocity distribution at the diffuser inlet AH 4 Aff Cexp Cfr where exp Texp ex 2f Values of texp P IIn 0 3 1 L1A 1 101 12 114 1 it D12 61 4oI wIs 0 00 003 008 011 015 019 023 027 036 047 065 092 115 110 102 005 20 003 007 010 014 016 020 024 032 042 058 083 104 099 092 0075 133 003 007 009 013 016 019 023 030 040 055 079 099 095 088 010 10 003 007 009 012 015 018 022 029 038 052 075 093 089 083 15 67 002 006 008 011 014 017 020 026 034 046 067 084 079 074 20 50 002 005 007 010 012 015 017 023 030 041 059 074 070 065 025 40 002 005 006 008 010 013 015 020 026 035 047 065 062 058 030 33 002 004 005 007 009 011 013 018 023 031 040 057 054 050 040 25 001 003 004 006 007 008 010 013 017 023 033 041 039 037 050 20 001 002 003 004 005 006 007 009 012 016 023 029 028 026 060 17 001 001 002 003 003 004 005 006 008 010 015 018 017 016 I I R fexD If g 10 Fýý r IIT Oj I rr II II II I J1 raw II II I11 1 IV ZD x4 W d0 J SW 167 Conical diffuser in a line contd Section V Diagram 52 exp is determined from the curve Cexp fa at 0 on graph a Within the limits 0a400 The values ofexp are determined from the curvesexpI oof graph a ep 32 tg o2 0fr at X 002 tfr is determined from the curves ýfr 4 a0 of graph b A is determined from the curves X Re WoD a on diagrams 22 to 25 v is taken from 13b A is taken from Table 21 2 Nonuniform velocity distribution at the diffuser inlet AH whrk Cexp fra where k is determined from the data of diagrams 51 56 and b18 t Values of Cfr P I e 005 20 014 010 005 004 003 003 002 002 001 0075 133 014 010 005 004 003 002 002 002 001 010 10 014 010 005 004 003 002 002 002 001 015 67 014 010 005 004 003 002 002 002 001 020 50 014 010 005 003 003 002 002 002 001 025 40 014 010 005 003 003 V 002 002 001 030 3 3 013 009 004 003 003 002 002 002 001 040 25 Q12 008 004 003 002 002 002 002 001 050 20 011 007 004 003 002 002 002 002 001 060 17 009 006 003 002 002 002 002 002 001 Cfr ROx b wz Si 168 4 Pyramidal diffuser in a line DSection V I Diagram 5 3 Dh P U perimeter 1 Uniform velocity distribution at the diffuser inlet AH C 2 Cexp Cfr where Cexp Yexp i 3 Vexp is only approximately determined from the curvetexp Icorresponding to r 0 on graph a Within the limits 0a 250 Thexp vl e0 tgq2 tg 2 The values Of Cexp are determined from the curves Cexp POon graph a C f F 2 Ln I6sin 2 2A At 1 C fr 8 sin 4 2Afr 8n2 At k002 Atfr is determined from the curves AtfraI a on graph b ACfr is determined from the curve hfrr on graph b I is determined from the curves X f Re A j on diagrams 22 to 25 v is taken from 13b A is taken from Table 21 2 Nonuniform velocity distribution at the diffuser inlet AHe fr6 where k is determined from the data of diagrams 51 56 and 518 169 Pyramidal diffuser in a line contd I Section V Diagram 53 Values of ýexp 2 1 441 6 JI 1 j 0112 114 1 6 3 8 120 24 1 24 1 3214 I01s 8 0 005 007 010 015 020 025 030 040 050 060 00 20 133 10 67 50 40 33 25 20 17 003 003 003 002 002 002 002 001 001 001 001 006 005 005 005 004 004 003 003 002 0013 001 010 009 008 008 007 006 006 005 004 002 002 014 013 012 011 010 009 008 007 005 003 002 019 017 016 015 014 012 011 009 007 005 003 023 021 020 019 017 015 013 011 008 006 004 029 0 26 025 024 021 018 016 014 010 007 005 034 031 029 028 024 022 019 017 012 008 005 040 036 034 032 029 026 022 020 014 030 006 045 040 038 036 032 029 025 022 016 011 007 059 053 050 048 042 038 033 029 021 015 009 073 066 062 059 052 047 041 036 026 018 012 089 080 076 072 064 057 050 044 032 O 22 014 105 094 090 085 076 067 059 051 033 026 017 1 10 0 99 0 1 I 089 079 070 062 054 040 027 018 3In 0 p u89 079 070 062 054 040 027 0318 2 330 0 99 094 089 079 070 062 054 040 027 018 2 4 Cg2XJ r tu1t1O1 412 IKf usa 1 low I I II I I I 0 a f F a to wO X aNNAV a Values of Afr or ACfr F 01 21 4 161 110 112 111 16 20 0 05 20 007 004 002 002 002 002 002 001 001 010 10 007 003 002 002 002 002 802 001 001 015 67 007 003 002 002 002 002 002 002 001 020 50 007 003 002 002 002 002 002 001 001 025 40 007 003 002 002 002 002 002 001 001 030 33 007 003 002 002 002 002 002 001 001 040 25 006 003 002 002 002 001 001 001 001 050 20 006 003 002 002 001 001 001 001 003 060 17 005 002 002 001 001 001 001 001 001 10 IV M b 4F 170 4 Plane diffuser in a line Section V Diagram 54 4Fo DhF boperimcter F nI1 I Uniform velocity distribution at the diffuser inlet A H SO Cexp Cfr 2g where texp TYexp Fi Texp is determined approximately from the curve texpIaat F0 0 on graph a Values of Cexp II 0 oo 003 008 011 015 019 023 027 036 047 065 092 115 110 102 005 20 003 007 010 014 016 020 024 032 042 058 083 104 099 092 0 075 133 003 007 009 013 016 019 023 030 040 05b 079 099 095 088 010 30 002 007 009 012 015 018 022 029 038 052 075 093 089 083 015 67 002 006 008 011 014 017 020 026 034 046 067 084 079 074 020 50 002 005 007 010 012 015 017 023 030 041 059 074 070 065 025 40 002 004 006 008 010 013 015 020 026 035 047 065 062 058 030 33 002 004 005 007 009 011 013 018 023 031 040 057 054 050 040 25 001 003 004 005 007 008 010 013 017 023 033 041 039 037 050 20 001 002 003 004 005 006 007 009 012 016 023 029 028 026 060 17 001 001 002 003 003 004 005 006 008 0 1 01b 018 017 016 SX it LaJ tr IT J b I T In the range Oa40 exp m3 2 tg tg 2 The values of Cexp are determined from the curves exp on graph a t fa 0 0 1 F 4 siI At 0 002 tr is determined from the curves tfr I ae o F on graphs bcde and f A is determined from the curves I Re on diagrams 22 to 25 bh v is taken from 13b A is taken from Table 21 2 Nonuniform velocity distribution at the diffuser inlet AH i 1 k Cexp fr where k is determined from the data of diagrams 51 56 and 518 05 I II Fr I I La10 d III III Igil 0 tog x WJ0 a Nix W a 171 Plane diffuser in a line contd DSection V F Diagram 5 4 44 Values of Cfr at aoboO5 parso 2 4 6 8 10 20 30 400 010 10 027 014 009 007 005 003 002 001 020 50 025 013 008 006 005 003 002 001 030 33 022 011 008 006 005 002 002 001 050 20 018 009 006 004 004 002 001 001 Values of tfr at albo 076 FJF a 2 4 6 80 10 200 30 400 010 10 034 017 011 008 007 003 002 002 020 50 031 0115 010 008 006 003 002 002 030 33 028 014 009 007 006 003 002 001 050 20 021 011 007 005 004 002 001 001 404 Cfr 7 7V L 02 U F 2v 0 b 4pe Values of Cfr at aofb 10 2 4 6 8 10 20 30W 40 50 010 10 040 020 013 010 008 004 003 002 002 020 50 037 018 013 009 007 004 003 002 002 0310 33 033 017 011 008 007 003 002 002 002 050 20 025 013 008 006 005 003 002 001 001 d 172 Plane diffuser in a line contd Section V Diagram 54 Values of Cfr at ahbo 15 2 4 6 8 100 20T 30V 40 010 10 053 026 018 013 011 025 004 003 010 50 048 024 016 012 010 005 003 002 030 33 043 021 014 010 009 004 003 002 050 20 032 016 010 008 006 003 002 002 Values of Cfr at ab20 FgIF a 2 4 6 81 100 200 30W 40W 50V 60 010 10 065 033 022 016 013 006 004 003 003 002 020 50 060 030 028 015 012 006 004 003 003 002 030 33 053 026 018 013 011 005 004 003 002 002 050 20 039 019 013 010 008 004 003 002 002 001 as do a2 49 006 VOW fr I 43 05 i U044 I I LL I iKtb a0 v0 f WS 50 AV JW 173 Transition diffuser transition from circle to rectangle or from Section V rectangle to circle in a line Diagram 5 5 Ali 2g is determined from the data in diagram 53 for a pyramidal diffuserwithequivalent divergence angle determined from the relations 1 transition from circle to rectangle tg 2 1d 2 transition from rectangle to circle dtg2 21d Diffusers of Arbitrary shape at a 8 120 located at SectionýV discharges of branches or other fittings with similar velocityDiga 56 profilesDiga 5 Dhf 4F I6 perimeter kC where V is determined depending on the diffuser shape as r from the Concentric varies Diffuser corresponding one of diagrams 52 to 55 Ci is taken from Table 52 as a function of the branch characteristic or tl velocity profile the velocity profiles themselves are represented on the rap the curves We r TABLE 52 Branch parameters Velocity Number of profile concentric 4j vanes 1 2 1 0810 0 0 6S 2 0810 0 2 21 16 08 10 0 3 111 S 20 0 0 20 1 20 10 0 I L t 3 0 0 1 VOP 40 5 10 1 1 we 1 c4 174 Curved diffusers j conE No 1 Circular or pyramidal diffuser z Wr t in a line Section V I Diagram 5 7 0 yod formula applicable in the range 01 K09 where c 43 is determined from the curve a U of graph a d 1 is determined from the curve d Is of graph a hand o 4 is determined from the corresponding curves of graph b FJIF 01 02 03 04 05 06 07 08 09 a 130 117 104 091 0 78 065 052 039 026 d 081 064 049 036 025 016 009 004 001 No 2 Plane diffuser 7 1d 4 7I Z 0J 0 095 M6 07 01 02 a Id L 0 1 1 5 20 I 25 30 3 40 45 50 00 No1 Circular or pyramidal diffuser to 10210751 062 053 047 1 0431 1 038 10 I 0 1 No 2 Plane diffuser I 012 083 072 064 057 052 048 045 043 041 I 039 037 215 V0 115 J 49 7 5j s b 175 Stepped conical diffuser of optimum divergence angle Section V Geopt Diagram 5 8 The formula may be used for selecting the optimum angle a from graph b Id op Cmin is determined from graph a as a function of Y and a a is determined approximately from graph c as a functiji of SF 2 F Values of Cmin tdI 0 5 1 1 2 1 0 1 0 1 50 1 6 1 80 1 0 1 12 140 15 003 002 003 003 004 005 006 008 010 011 013 20 008 006 004 004 004 005 005 006 008 009 010 25 013 009 006 006 006 006 006 006 007 008 009 30 017 012 009 007 007 006 006 007 007 008 008 40 023 017 012 010 009 008 008 008 008 008 008 60 030 022 016 013 012 010 010 009 009 009 008 80 034 026 018 015 013 012 011 010 009 009 009 10 036 028 020 016 014 013 012 011 010 009 009 14 039 030 022 018 016 014 013 012 010 010 010 20 041 032 024 020 017 015 014 012 011 011 010 4 176 Stepped conical diffuser of optimum divergence angle Section V e p cont Id Diagram 58 Values of eopt i d Do 1 0o5 1 10 1 20 1 30 1 40 1 60 1 60 1 80 1 10 1 12 1 1 15 20 25 30 40 60 80 10 14 90 17 21 25 27 29 31 32 33 33 34 10 14 16 17 20 21 22 23 24 24 65 85 10 I1 13 14 15 15 16 16 45 62 74 85 98 11 12 12 13 13 35 50 60 70 80 94 10 11 11 il 28 43 54 61 72 82 88 94 96 98 22 38 48 56 66 74 80 84 87 90 17 30 40 48 58 62 66 70 73 75 12 23 35 42 52 56 58 62 63 65 10 20 30 38 48 52 54 55 56 60 08 16 25 32 44 47 50 52 54 56 x2 P tI2Irz Ii I I I b 9 U UU ZU U U0Z q 49S 08U W 177 Section V Stepped pyramidal diffuser of optimum divergence angle aopt Diagram 5 9 Dh 4F p Ohj y Irq perimeter AH I Cr Cni in The formula may be used for selecting the optimum ange aopt from graph b Cmin is determined fiom graph a as a fiict ic ItIDh aind fl a is determined approximately frum iolý Ii of F At Fj I2 F2 Dhp 12 0 Values of tm in IdIDh 05 1 10 1 20 1 30 40 1 50 60 80 10 1 2 1 14 15 004 003 003 004 005 005 006 008 010 011 013 20 011 008 006 006 006 006 007 007 008 009 010 25 016 013 009 008 008 007 008 007 008 008 009 30 021 017 012 010 009 0C9 009 009 009 009 009 40 027 022 017 014 012 011 011 011 011 010 010 60 036 028 021 018 016 015 014 013 012 012 011 80 041 032 024 021 018 017 016 014 013 012 012 10 044 035 026 022 020 018 017 015 014 013 0131 14 047 037 028 024 021 020 018 016 015 014 014 20 049 040 030 026 1 023 021 019 017 016 015 014 a 178 Stepped pyramidal diffuser of optimum divergence angle aopt Section V cont d Diagram 59 Values of aopt Id Mh fli1 101 201 30 140 15I0 1 0100 1 012 1 14 15 14 90 53 40 33 27 22 17 12 10 10 20 18 12 80 63 52 45 38 30 23 20 18 25 20 14 90 72 61 54 48 40 32 29 24 30 21 15 i0 78 65 58 52 44 36 33 29 40 22 16 II 85 71 62 55 48 40 38 35 60 24 17 12 94 80 69 62 52 45 43 40 80 25 17 12 97 83 73 65 55 48 46 42 10 25 18 12 10 87 76 69 58 50 48 45 14 26 18 13 10 90 78 71 61 52 50 47 20 26 19 13 II 92 81 73 64 55 52 49 1 1 1 1 1 b U I 0 0P2 6W 05 as f0 C 179 Stepped plane diffuser of optimum divergence angle pt Section V at 05 a 20 Diagram 510 mV AH YOC I The formula may be used for selecting the optimum angle Zopt from graph b Cmin is determined from graph a as a function of Idao and n is determined approximately from graph c as a function of 7 as Id 02 ps 02 Values of Cmin 105 1 0 1 20 1 30 1 40 1 5o 1 00 1 80 10 1 12 14 15 004 004 004 004 005 006 006 008 010 011 013 20 012 009 007 007 006 007 007 007 008 010 012 25 018 014 011 010 009 009 009 009 009 010 010 30 023 018 014 012 011 011 010 010 010 010 011 40 030 024 019 016 015 014 013 012 012 012 012 60 038 031 025 021 019 018 017 016 015 014 014 80 043 036 028 025 022 020 019 017 016 016 015 10 046 038 030 026 024 022 021 019 018 017 016 14 050 041 033 029 026 024 022 020 019 018 018 20 053 044 035 031 028 025 024 022 020 019 019 1 a 180 Stepped plane diffuser of optimum divergence angle oap Section V at 05 20 contd Diagram 5 10 Values of Wopt 05 10120 30 40 150 160 80 30 IS 34 15 25 18 I1 80 64 54 47 35 28 24 20 20 33 23 15 12 97 84 75 60 52 47 43 25 37 26 18 14 12 10 94 80 70 63 56 30 39 27 20 16 13 12 11 91 80 72 64 40 42 30 21 17 15 13 12 10 90 82 74 60 45 31 23 18 16 14 13 II 10 94 85 80 47 32 23 19 17 15 14 12 ii 10 91 10 48332420 17 15 14 12 11 10 95 14 49342520 17 16 14 13 12 11 99 20 50352521 18 16 15 13 12 11 10 2I A L I 46 0 r a b 0 a ju it 1 iI I 1 itTT1 I az a U as 7 C 181 Short diffusers with guiding devices or with resistance at the exit Section V Diagram 511 Resistance coefficient C Guiding device Schematic diagram 4 With dividing walls Number of dividing wallsz ra a a Z do 3 0 45 60 90 120 where Cd is determined as from diagrams 52 to 55 aI tst With bafflesC Ad m where Cd is determined as t from diagrams 52 to 551 a a 0I to 6 With resislance at theScenR exit screen perforated bc 600 Cý2ol 1 3 1n L where C is determined as C from diagrams 5i2 to i C is determiined as C of a screen or grid from diagrarm 81 to 87 n 182 Plane symmetric diffuser behind a centrifugal fan Section V in a duct forced draftI Diagram 512 4 Az a Jo Values of 4 J 15 20 25 30 35 40 10 005 007 009 010 011 011 15 006 009 011 013 013 014 AH 20 0078 0130 0136 0159 016 01623 is determined from the curves C correspond 30 016 024 029 032 034 035 35 024 034 039 044 048 050 2g ing to different a9 Plane asymmetric diffuser at a 0 behind a centrifugal fan Section V in a duct forced draft Diagram 513 4 o12I 1000I I Values of C t 12 2 JO J 7 15 j 20 25 FF 353 40 10 008 009 010 010 011 011 15 010 011 012 013 014 015 AH F 20 012 014 015 016 017 018 4 is determined from the curves CJ correspond 25 015 018 021 023 025 026 wo 30 018 O25 030 033 035 035 F 35 021 031 038 041 043 044 ing to different ao 183 Plane asymmetric diffuser at a 10 behind a Section V centrifugal fan in a duct forced draftI Diagram 514 OF 0 7 A Z0 tgo 37 00 42 Values of C 15 20 25 3 0 I 40 10 011 013 014 014 014 014 15 013 015 016 017 018 018 A 20 019 022 024 026 028 030 i is determined from the curves C cO I curescIcorresponding 25 029 032 035 037 039 040 30 036 042 046 049 051 051 35 04 054 061 064 o66 066 Y to different a Plane asymmetric diffuser at a 10behinda Section V centrifugal fan in a duct forced draft Diagram 515 00 s Values 6f C V 1o 20 26 0 I 40 E 10 005 008 0 1f 013 013 I014 15 006 010 012 014 015 015 AmP 20 007 011 014 015 016 016 is determined from the curves C correspond 25 009 014 018 020 021 022 s r n 30 013 018 023 026 028 029 35 015 023 028 033 035 036 ing to different e 184 S1 Pyramidal diffuser behind a centrifugal fan in a duct Section V forced draft Diagram 516 1 b a H is determined from the curves C corresponding to different a Value of I pip 15 20 25 30 35 40 10 010 018 021 023 024 025 15 023 033 038 040 042 044 200 031 043 048 053 056 058 25 036 049 055 058 062 064 30 042 053 059 064 067 069 185 Multistage diffuser of optimum divergence angle t Section V behind a centrifugal fan in a duct forced draft Diagram 517 9A wo is determined from the curves Cm inf T94 Id corresponding to different values of on graph a opt is determined from the c Irves aopt corresponding to different on graph b 0 Values of Croii I 3 F 4 60 2 lb 2o 1 0 1o35 10 1 45 1 5 1 0 10 016 025033 03810 43f047 059056 15 0 13020 026 031 034 1038 041 016 20 0120170 22026 029 033 035 038 30 0091013018021024102610281031 40 0 0801210 158018020 1022 024 O026 50 1O06 1010j10 13015 1017 1018 20 10122 O O ooo Z2 10 Values of opt 00 is 3 35 140 451 Q 60 10 9 10 10 11 i1 11111 12 15 8 9 9 10 10 W0 10 i0 20 7 8 8 9 9 9 9 9 30 6 7 7 7 7 8 8 8 40 4 5 6 6 7 7 7 8 50 3 4 5 6 6 6 6 7 b 186 Annular diffusers with deflecting baffles in a duct Diagram 518 1 Diffuser with converging fairing Section 11 I C Yo ika d jr 29i where d is determined from graph a as a function of the divergence angle a kI is determined from graph b as a function of the divergence angle 2 for the different velocity profiles shown in graph c Values of k rd e I d 7 025 8 025 30 030 12 037 14 044 a 7 8 i0 12 14 1o 0140 200 116 090 10 160 210 121 115 10 160 210 120 136 101145 200 110 142 101140 186 108 150 No of velocity profilecurve c 112 J1 31 41 5l 274 298 302 270 248 I a 2 Diffuser with diverging fairing Alf b TABLE 53 d 075 10 J 5 178 20 where q is taken from Table 53 k is taken from the data in diagrams 51 56 and 5181 2 125 0 017 17 9 027 87 67 6 3 011 009 60 3 008 187 Radialannular and axial radial annular diffuers Section V in a line Diagram 519 I Radjia I a nu lar 2 AxialradialainnuIar T 0 a8 C8 0 05 1 Values of 4 18 22 26 30 34 42 a Diffuser behind operating compressor at 05 15 045 055 062 065 17 034 048 056 061 062 19 037 049 056 062 065 22 035 045 052 060 0 b Diffuser without operating compressor 14 031 041 048 055 060 16 025 033 040 046 052 055 18 019 026 033 039 044 048 051 20 020 025 030 035 040 043 4 W 2 b 1 B Dd d nh d Do do cGOow a u T D2 d 2 OKI 0000 000 00 I OF 00 00 000 000 z CaOo COO U Q discharge m 3sec u peripheral velocity at the maximum radius msec All W is determined from the curves C1 nD graphs a and b and CJnaj graph c 10 ý 92 ZI at Jr q 0 qd 1Z ZU 8 b 2 Values of I8 22 26 a0 3 36 40 2 028 I 0310 I 0 038 040 041 I 2 014 022 027 031 035 037 041 4 008 013 018 024 029 032 039 Ic a 0 188 K Section Six Fo F1 Dg D DI a bo b bCh to Io 1e R r ro r1z t1 A 6 e Wo Wa AH Cl VARIATION OF THE STREAM DIRECTION Resistance coefficient of curved stretches branches elbows etc 61 LIST OF SYMBOLS areas of the inlet and exit cross sections respectively of a curved conduit M 2 diameters of the inlet and exit cross sections respectively of the curved conduit m hydraulic diameter of the inlet section of the curved conduit height of the section of the curved conduit m width of section at inlet measured in plane of bending of width of section at outlet I curved conduit width of section in intermediate channel length along the axis of a curved conduit m length of the intermediate straight stretch of the curved pipe the stretch between two branches or elbows m distance between the axes of coupled elbows m mean radius of curvature of the bend or elbow m radius of curvature of the elbow wall m radii of curvature ofthe inner and outer bend walls respectively m chord of the guide vanes m mean height of roughness peaks of the walls m relative roughness of the walls angle of bend of the curved channel angle between the direction of the impinging stream and the chord angle of attack of the guide vanes angle at which guide vanes are mounted in the elbow angle subtended by the arc of curvature of the guide vanes mean stream velocity at the inlet and exit sections of the curved channel respectively msec pressure loss or resistance kgim2 total resistance coefficient of the curved conduit local resistance coefficient of the curved conduit friction coefficient of the entire length of the curved conduit friction coefficient of unit relative length of the curved conduit 189 r 1 TPVVI AXTArETChT ATP R1rtV AlNT TJSL1 L5 LL 1 P AAtl I IVlIr At LL r1 A1 rr Sfl 1 The variation of the stream direction in curved conduits elbows branches bends and bypasses leads to the appearance of centrifugal forces directed from the center of curvature toward the outer wall of the pipe As a result the passage of a stream from the straight to the curved portion of the pipe is accompanied by an increase of the pressure at the outer wall and its decrease at the inner wall and by a corresponding decrease of the stream velocity at the outer wall and its increase at the inner wail Figure 61 At the bend therefore a diffuser effect occurs near the outer wall and a bellmouth effect near the inner wall The passage of a stream from the curved part of a pipe to the straight part following it is accompanied by the opposite effect ie diffuser effect near the inner wall and the opposite effect near the outer wall Velocity profile Pressure profile Eddy zone at the outer wall FIGURE 61 Variation of the profiles of velocities and pressures in an elbow and the straight stretch following it 2 The diffuser phenomena lead to a separation of the stream from both walls Figure 62 The separation from the inner wall is intensified by the inertial forces acting in the curved zone which tend to move the stream particles toward the outer wall The eddy zone whichis formed as a result of the separation from the inner wall propagates far ahead and across considerably reducing the main stream section 3 The appearande of a centrifugal force and the existence of a boundary layer at the walls explain the appearance of a transverse flow in a curved pipe It also explains An elbow is a curved stretch with equal radii of curvature of the inner and outer walls a bend is a stretch whose inner and ote walls represent arcs of concentric circles rin 0 and rout rin bo where rin is the radius of crvature of the inner wall and rout is the radius of curvature of the outer wall Since the two walls of abend have the same center of curvature the bend can be characterized by the radius of curvature Roof its axis which always satisfies the inequality Rb 05 190 the formation of the socalled vortex pair which superimposed on the main stream parallel to the channel axis gives the streamlines a helical shape Figure 63 Section 11 a b c FIGURE 62 Stream pattern in a 90V elbow FIGURE 63 Vortex pair in an elbow a longitudinal section b cross section of rectangular conduit c cross section of a circular pipe 4 The pressure losses in curved pipes are mainly due to the formation of eddies at the inner wall This eddy formation also determines the pattern of velocity distribution beyond the bend The magnitude of the resistance coefficient in curved pipes varies as a function of the factors determining the turbulent intensity the Reynolds number Re the relative roughness of the walls 6 the inlet conditions etc It is also a function of the pipe Dh R shape the angle of bend 80 the relative radius of curvature b the side ratio of the cross section L the ratio of the inlet to exit areas 5 etc b5 P Ce 5 The total resistance coefficient of bends and elbows is determined as the sum of the coefficient of local resistance of the bend C1 and the friction coefficient Cfr ft C Cfrp 61 12 where C1 is determined from the data given in this section C f is calculated as C for 5h straight stretches with A determined from diagrams 21 to 25 as a function of Re and the relative roughness A I length of the bend or elbow measured along the axis so that R0 0 17 5Ro 6 2 I Dhb b Dh Thus Cr 001751 R P 6 3 191 6 With other conditions constant the resistance of a curved pipe is highest when its inner wall makes a sharp corner at the bend the stream separation from this wall is then most intense At an angle of bend a 900 Figure 62 the zone of stream separation at the inner wall beyond the bend reaches 05 of the pipe width 623 It follows that the intensity of eddy formation and the resistance of a curved conduit increase with an increase in the angle of bend The rounding of the corners especially the inner wall considerably attenuates the separation and reduces the resistance as a result 7 If only the inner corner of the elbow is rounded radius of curvature r 0 radius of curvature r0 0 Figure 64 the resistance of a 900 elbow will be minimum at LO 12 to 15 With the subsequent increase of L the resistance starts to increase considerably Figure 64 Such an increase of resistance is explained in that when the inner corner is rounded a substantial area increase and a corresponding velocity drop are obtained at the bend This leads to the intensification of the separation of the stream at the place of passage from the inlet stretch to the elbow ry variable oO i I as I I 05 I 4Z variable a If 90 FIGURE 64 Plan of the rounding of an elbow and resistance coefficient of the elbow as a function of the radius of curvatureb 8 The rounding of the outer wall while the inner corner is kept sharp r 0 0 does not lead to a noticeable drop in the elbow resistance A considerable increase of the radius of curvature of the outer wall wilt lead to an increase in the elbow resistance Figure 64 In fact the rounding of the outer wall only sharp inner corner reduces the stream area at the place of the bend and so increases the diffuser losses accompany ing the passage of the stream from the elbow to the exit stretch of the pipe 4 r1 r0 Minimum resistance is achieved in an elbow where 06 elbow of optimum shape a resistance close to the minimum is achieved in a bend or in a hormal elbow 192 in which r 10 Since a bend is easier to make it can replace the optimum elbow in most cases 9 A considerable reduction in elbow resistances can also be achieved simply by cutting off along the chord the sharp corners particularly the inner one cf diagrams 610 and 611 10 The variation of the ratio of areas F fteebwiltadei etoslast F 10 he aritio oftherato o aras ofthe elbow inlet and exit sections leads to avarviation of the resistance The increase of this ratio intensifies the diffuser effect beyond the turn which leads to a greater stream separation the formation of eddies and a simultaneous decrease at constant discharge of the stream velocity in the exit section Expressed as a decrease of pressure losses the effect of this drop in the velocity is greater up to a certain value of than the effect of increase of the eddy zone which leads to an increase of the losses As a result when the elbow section widens up to a limit the total losses decrease 11 The resistance of rightangled elbows 8 900 with sharp corners is a minimum F F for 12 20 The optimum value of F in elbows andbends with smooth turns is closer to unity and in some cases is even smaller than unity If no data are available on the resistance of diverging elbows and bends the decreases of pressure losses in the above range of can be neglected and the resistance coefficient can be considered equal to its value for 10 The increase of resistance cannot be neglected at values of F lower than unity or considerably higher than the optimum values a b aC b FIGURE 65 Flow patterns in nshaped conduits 12 The resistance of curved conduits decreases with the increase of the side ratio 4l a0 of the elbow cross section and increases with the decrease of ý in the range below unity 193 13 The resistance of combirned elbows depends a great deal on the relative distance between the two elbows In the case of a 11 shaped elbow made from a couple of 900 with sharp corners and small relative distance o0 the stream separation eb from the inner wall takes place only after the complete turn by an angle 8 1800 Figure 6 5a The stream separation is most intense at such a large angle of turn and the resistance coefficient is highest as a result When the relative distance is considerably increased 4 to 5 and more the stream will spread almost completely over the section in the straight stretch following the first 90 turn and the conditions of the stream turning at the following 900 will be roughly the same as for the first turn Figure 6 5b As a result the total resistance coefficient of such a Ishaped elbow will be close to twice the resistance coefficient of a rightangled elbow a 900 At some intermediate value of KL near 10 the zone of separation behind the first 900 turn will not develop completely Thus at the inner wall before the second 90 turn smooth rounding of the main stream will occur Figure 65 c Under these conditions the second turn of the stream takes place almost without separation and therefore with low pressure losses The total resistance coefficient of such a nlshaped elbow is therefore minimum The rounding of the corners of flshaped elbows decreases the difference between the values of C corresponding to different values of A but does not alter the patternof the resistance curves or of the flow V FIGURE 66 Flow pattern in a Zshaped elbow FIGURE 67 Flow pattern in a combined elbow with a 90W turn in two mutually per pendicular planes 14 In the case of a Z formed by rightangled elbows Figure 6 6 the increase of the relative distance between the axes of the two single elbows leads at the beiginning to a sharp increase of the total resistance coefficient As this ratio continues to increase the resistance passes through a maximum and then gradually dropsuntil it reaches a magnitude roughly equal to twice the resistance coefficient of a single right angled elbow 8 900 194 The resistance coefficient of a Zshaped conduit is a maximum when the second of the two single elbows forming it is placed near the widest section of the eddy zone formed after the first 900 turn Figure 66 A maximum reduction of the stream cross section is then obtained at the second turn 15 The total resistance coefficient of combined elbows in two mutually perpendicular planes Figure 67 increases with the increase of the relative distance LObetween the axes of the two constituent rightangled elbows This increase from an initial value equal to the resistance coefficient of a single rightangled elbow reaches a maximum at a small value of 0 It then decreases with the further increase of this ratio and tends to a value approximately equal to twice the resistance coefficient of a rightangled elbow 8 900 16 The coefficient of local resistance of smooth bends is calculated by the following formula proposed by Abramovich 61 1 ABCl 64 1W2 where A is a coefficient allowing for the influence of the bend angle 8 B is a coefficient allo gfor the influence of the relative radius of curvature of the bendR is a allowing frteifune tebn ac coefficient allowing for the influence of the side ratio of the bend cross sectionT The value of A is found from the following table established by Nekrasov 6 11 at 8900 A 10 at 8700 A09sin6 65 at 8 1000 A 07 035 5 or from graph a of diagrams 61 or 62 The value of B can be calculated by the following approximate formulas at B 021 0o21 66 at 00 B R VDh or from graphb of diagrams 61 or 62 The value of C is determined from graph c of diagrams 61 or 62 17 The coefficient of local resistance of elbows with sharp corners can be calculated in the entire range 0 8 1800 by the formula l C At 67 2g The formula given in 6 1 contains a numerical factor 0 73 which is included here in the magnitude B 195 where C is determined by Weisbachs formula 643 C095sin 205 sin F 68 A is the correctioncoefficient obtained from Richters 613 637 and Schubarts 639 data and determined from the curve Af0 of diagram 67 18 The coefficient of local resistance of bends and elbows can be considered as constant and independent of Re only for Re WDh2101 to 2510 Below this value Re starts to influence the value of the local resistance coefficient and this influence is the stronger the lower the value of Re This is particularly true of bends and also of elbows with smooth inner curvature The analytic relationship between the local resistance coefficient and Re is complex cf 68and so far has not been accurately determined 19 The value of C I for elbows and bends of very small relative radii of inner r R curvature within the range 0 h 005 05 Kh 055 can be considered practically constant and indepbndent of the Reynolds number at Re 4 104 The following fbrmula can be tentatively used for determining the resistance coefficient in the range 3 103 Re 4 104 AH 1 6 9 Wo where g kRe WRe 452Re 610 Re410O C is the coefficientof local resistance of the bend or elbow considered at a given R e 410 CRe 410 is the coefficient of local resistance of the bend or elbow considered deterrmfined as C1 for Re410 4 from the data of diagrams 61 and 66 kRe is the coefficient allowing for the the influence of the R eynolds number IRe 4104 is the friction coefficient of unit relAtive length of a smooth pipe equal to 0022 at Re 4 104 1 e is the friction coefficient of unit relative length of a smooth pipe determined as I at Re 4 104 from the data of diagrams 22 to 25 20 The value 6f C of elbows and bends with relative radius of inner curvature Dh 005 D0055 can be considered as practically constant at all values Re 2 105 its value in the range 3 103 Re 2105 can be tentatively determined by formulas similar to 69 and 6 10 AH I AH kR 210 611 where R XRe 64A e 6 1 1a Re e 2I O e CRe is the local iesistance coefficient of the bend or elbow considered determined as C at Re 2 105 fr0m the data of diagrams 61 62 and 69 196 21 The total resistance of very smoothly curved pipes and channels 1 such as are used in coils can be considered as an increased friction coefficient depending not only on Reynolds number and roughness but also on the relative radius of curvature Dh m 001752 DR V fr Dh Dh where 1 is the friction coefficient of unit length of the curved pipe The value of I for smooth pipes made of glass brass lead rubber etc can be calculated by the following formulas obtained by Aronov 62 on the basis of his experiments and those ofAdler 622 and White 6444 5OKejf600 600Re 1 140O 104 Oh2S 6 13 140 Re 2i5 000 20 tDhO 614 22 The state of the inner surface of bends and elbows immediately before the turn has a stronger influence on the coefficient of local resistance than on the friction coefficient at high values of Reynolds number 68 The exact determination of the influence of this factor is impossible at present as it has not been widely studied 23 The influence of the general roughness is for very small relative radii 0h 005 or 05 hR 055 considerably weaker than for smoothly curved elbows and bends since the place of stream separation is near the corner of the bend The influence of the general roughness in such elbows and bends can be tentatively These formulas were given by Aronov and before him by Prandtl and Adler 613 in a somewhat different form namely eor 6 2R where A is a numerical coefficient 197 calculated by the formula O k ASM 615 A where Re 4 104 and E0001 k n I 05 104 and Re 4 104 and Z 0001 617 kA 15 J Csm is determined as C for smooth walls A 0 24 The influenbe of general roughness in elbows and bends with relative radii of curvature within the limitsO05j10055 L15 can be allowed for by the coefficient ka in expression 615 which for 4 104Re2 i05 and d0001 is given tentatively by Abrainovichs formula 61 ka Asm 6 18 at Re 2 105 and A0001 tentatively by the following formula based on the authors data 68 kA I 108 6 19 and at Re 4 104 and A0001 tentatively by the formula kA 2 620 where Ism friction coefficient of a smooth pipe determined as 1 at given Re 4 104 from diagram 24 1 is friction coefficient of a rough pipe determined as I at given Re 4 104 and A 0 0001 from the data of diagrams 22 to 25 25 The influenice of the general roughness on bends with 15 can be allowed for Dh approximately onthe basis of the authors 68 and Hofman s 632 data at R e 41 04 and A 0001 by the fdrmula k A I A2 10r 6 21 and at Re 4 104 and 0001 by the formula ka 20 622 26 AtRe4 104 the resistance coefficient of allbends and elbows can be considered practically independent of the general roughness being a function of the Reynolds number only It is accordingly calculated according to points 19 to 21 of this selction 198 27 The resistance coefficient of elbows with rounded corners and converging or diverging discharge sections Le l can be approximated by the following formula proposed by Richter 6 16 on the basis of a large amount of experimental data 2g where A f 60 and Cf A are determined as above kln C resistance coefficient of the elbow at F 10 and 8 90 w mean velocity in the narrow section of the elbow b width of the narrow section of the elbow e 2718 28 The coefficients of local resistance of welded branches are higher than those of nonwelded branches with all other conditions unchanged since welding seams on the inner surfaces increase the local roughness The relative magnitude of this local roughness decreases with the increase in diameter and the resistance coefficient will accordingly decrease The coefficient of local resistance of corrugated bends is higher than for welded or nonwelded bends the absolute dimensions of the corrugations increasing with the increase of the bend diameter the resistance coefficient will increase likewise Bends from sheet material either corrugated or made from several interlocked links also belong to the category of curved stretches of increased resistance coefficient 29 In the case of castiron or steel bends with threaded joints a projection is formed at the junction between the straight part and the curved one causing a sharp variation of cross section at this point Figure 68 which creates additional pressure losses The smaller the dimensions of such bends the larger is the relative magnitude of the projection As a result small standard gas fittings have a resistance coefficient much higher than that of ordinary bends with a flanged joint The data given in diagram 64 on the resistance coefficients of gas fittings can be extended to all standard OST bends of dimensions similar to those given 30 The resistance of elbows can be decreased not only by rounding or cutting off corners but also by installing guide vanes These have the advantage that they do not lead to an increase in the channel dimensions The guide vanes can be airfoils Figure 69a simplified and bent along the surface of a circular cylinder Figure 69b and c or thin concentric Figure 69d arcs of circles Vanes of identical shape and dimensions are usually mounted in the elbows and in a majority of cases they are placed along the line of bend of the conduit Figure 69 a b and c Concentric vanes should be used in bends Figure 69d 31 An aerodynamic cascade in an elbow formed of guide vanes deflects the stream toward the inner wall as a result of the aerodynamic force developed in it When the dimensions number and angle of the vanes are correctly selected this stream deflection will prevent the separation of the jet from the wall and the formation of an eddy zone The velocity distribution over the section behind the turn is improved as a result Figure 6 10 and the elbow resistance is decreased o Obshchesoyuznyi Standart AllUnion Standard 199 Projection FIGURE 68 Threaded cast iron bends Designa Relative tion dimensions t 10t x1 05191 x 0 489t 06631 0 553t A 04631 As 0 215t Z 00139t z2 03381 23 O268t p 0033t C K Vtill d ep FIGURE 69 Guide vanes in elbows and bends a airfoils bthin along a 95 arc cthin along a 107 arc d concentric e staggered 32 Since the inost effective means for decreasing the resistance and equalizing the velocity distribution is the elimination of the eddy zone at the inner wall of the channel the vanes located near the inner rounding will produce the largest effect This makes it possible to remove some of the vanes located near the outer wall without altering the flow characteristics cf Baulin and Idelchik 63 33 In those cases when it is especially important to obtain a uniform velocity distribution immediately after the turn the number of vanes is not reduced the normal number of vanes is used and is determined by the formula 66 flnormý213 1 623 In most practicalcases it is sufficient to use a reduced number of vanes determined by the following formulas obtained by the author 66 n ot 4h 624 or fln 09 r 625 In ordinary elbows lower resistance and a better distribution of the velocities are obtained with theoptimum number of vanes cf formula 624 200 The chord t of the airfoil vane is taken as the chord of a 900 arc of circle ie as the chord of the inner curvature of the elbow and therefore 1trV 626 or t DB7 r 627 Formulas 623 to 625 are only correct for this relation between the dimensions of the vane chord and the radius of curvature of the elbow The profiles of the guide vanes are plotted on the basis of the data given in Figure 69 34 If the elbow does not have smooth curvatures but sharp or cutoff corners the vanechord length can be taken within the limits t015 to 06Dh The number of vanes can be determined in this case by the following formulas 66 3Dn 1 628 nnormt nopt 2 Dh 629 mi 15 t1 6 30 35 The number of vanes in elbows with diverging section bb is determined by the following formulas respectively tnorm231 631 14n 632 n fzz 09 633 S b 634 36 When the normal number of vanes are used they are uniformly mounted along the line of bending of the elbow so that the distance between the chords of the vanes is S When a reduced number is used it is recommended 66 that a distance a between the chords be taken varying according to an arithmetic progression such that in the case of the optimum number of vanes a 2 and in the case of the minimum a number a 3 Here a is the distance from the chord of the arc of the inner rounding as of the elbow to the chord of the first vane Figure 69 a is the distance between the chords of the last vane and the outer rounding The distances between vanes are determined by the following formulas 67 201 when the optimum number of vanes is used a1O67 S i1 63 5 when the minimum number of vanes is used a S 05LZ 636 aln I 37 The vanes used in practice in a majority of the cases in elbows are the simplified thin vanes disposed in the case of a 900 turn on the average along a circular arc of angle 4 950 independently of the elbow parameters the relative radius of curvature the area ratio etc The disposition and the angle of installation of such vanes are selected according to the same criteria as for airfoil vanes The resistance coefficient of elbows with such vanes is considerably higher than for elbows with airfoil varnes 0CS925 ybb 11 a 2 FIGURE 610 Distribution of dimensionless velocities in an elbow a without vanes b with a no rmal number of vanes c with a reduced number of vanes 38 A low valueof resistance similar to the resistance of elbows with airfoil vanes is obtained by selecting thin vanes by the Yudin method 620 The optimum angle of the vane arc and the vane angle are a function of both the relative radius of curvature of the elbow and its area ratio This relationship is represented in diagrams 634 to 636 202 1 39 The installation of guide vanes in elbows is expedient as long as the relative radius of curvature is small In the case of elbows of constant section the installation of vanes is efficient as long as 04 05 In the case of diffuser elbows the limiting Dh value of L is increased roughly to 10 In the case of elbows with reduced exit section this value is decreased roughly to 02 40 The action of concentric vanes installed in bends mainly results in splitting the given bend into a number of bends of more elongated cross section which leads to a decrease of the pressure losses The normal number z of thin optimally installed concentric vanes in a bend is determined on the basis of the data of Khanzhonkov and Taliev 618 Table 61 TABLE 61 001 0104 0410 10 b z 34 2 1 The optimum disposition of the vanes in the bend is determined by the formula r 1 26r 007b 637 41 The resistance coefficient of a bend with normal number of optimally installed concentric vanes can be determined approximately by the following formula of the above authors 618 H R0461004 v 638 where Cwv is the resistance coefficient of the bend without vanes 42 When guide vanes are installed in combined elbows the resistance coefficient is determined as the sum of the resistance coefficients of the single elbows with vanes C 2Cv 639 where v is resistance coefficient of a single elbow with vanes 203 63 LIST OF THE DIAGRAMS OF RESISTANCE COEFFICIENTS OF SECTION VI 1NOof Diagram description Source diagram Note Sharp bends at 05R15 and 0801809 Smooth bends at RoDh 15 and O8olS0 Very smooth bends RjIDhi55 in conduits cast iron bends a50Re210 Standard threaded castiron bends Re210s Combined bends Ushaped Sshaped at different 80 and RO5 Sharp h0elbows of rectangular section with converging Or diverging exit section Sharp rlDh 0 elbows at 080 Elbows with rounded corners and converging or diverging exit section 0 O Elbows with rounded corners at O05rDh05 and 060i80 90V elbows of rectangular section with rounded inner corner and sharp outer corner 90 elbows of rectangulay section with cutoff corners Elbows made from separate elements at different P 90 elbow made from five elements 90W elbow made from four elements 90 elbow made from three elements 900 elbow made from three elements atRD924 welded with welding seams at Re106 Corrugated bend Z5 Re210s Zshaped elbow made from two 30W elbows Zshaped elbow Re104 Combined elbow made from two 90 elbows lying in different planes Re10 Abramovich 61 Vasilevskii 642 Idelchik 68 Nekrasov 611 Nippert 636 Richter 613 Fritzsche 628 Hofmann 632 The same Aronov 62 Adler 622 Richter 613 Vuskovich 641 Data according to 612 Abramovich 61 Weisbach 643 Idelchik 66 Nippert 536 Richter 613 Schubart 639 and Richter 616 Cf diagram 61 Nippert 636 Richter 615 Richter 615 Kirchbach 634 Schubart 639 The same Kamershtein and Karev 69 The same Kirchbach 634 Schubart 639 Data according to 612 The same 61 62 63 64 65 66 67 Based on experiments The influence of Reynolds number ard the roughness allowed for approximately on the basis of the data from 6168 and 513 Tobe used until iefined by experimenta data The same Experimental data The same Approximately according to diagrams 61 and 62 the influence of 1 Dh allowed for by the data of 629 To beused until refined on the basis of new experiments Experimental data Cf diagram 61 0 68 69 610 611 612 613 614 615 616 617 618 619 620 Empirical formula Cf diagram ý61 Experimental data The same 204 Coit d Diagram description Source Diarmb Note flshaped elbow 180 with equal inlet and exit sectionsg10o Re410 Iflshaped elbow 180W with airfoil guide vanes section 5b flshaped elbow 180 with widened exit section o 44 flshaped elbow 180M with widenedexit section i 6i 20 Ushaped elbow 180 with contracted exit section F bo 5 Ushaped elbow 180 with equal inlet and exit sections Ushaped elbow 180 with widened exit section Ushaped elbow 180 with widened exit section IF bs Parts made from galvanized sheet for RdDO10 DO100mm Rel510I Corrugated elbows made from galvanized sheet for RoDo07 DolG0mm Rel510 90W bend with concentric guide vanes ReIO 90W elbow of rectangular section at different ribo with airfoil guide vanes Re106 90W elbow of rectangular section at different ribo with thin guide vanes yf9o Re lO 900 elbow of rectangular section with thin guide vanes 95 under different conditions ReslO 90 smooth elbow r bO02 of rectangular F section at 05 with thin guide vanes 90 smooth elbow rbo02 of rectangular F section at F 10 with thin guide vanes T 1i07 k01O 90r elbow of rectangular section at FLIF0 20 with thin guide vanes ReI104 90f elbow of circular section with airfoil guide vanes ReO Data according to 612 The same Conn Colborne and Brown 624 The same Khanzhonkov and Taliev 618 Baulin and ldelchik 63 The same Yudin 620 The same 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 6 38 Experimental data The same ldelchik 66 205 64 DIAGRAMS OF RESISTANCE COEFFICIENTS R Section VI Sharp bends at 05 0 15and 0S 180 Diagram 6 woDh 1 Smooth walls A 0and Re 2103 AH where C1ABC Cfr00175XR0B at L t002 Cfr 0 0 0 0 35 D V A1 is determined as a function of V from graph a or approximately by the formulas of Table 62 R B1 is determined as a function of L from graph b or approximately by the formulas of Table 63 h aO C is determined approximately from graph c as a function of in the case of circular or square section Cj 10 LP 020 30 45 60 75 90 110 130 150 180 h 050 060 070 080 090 1O0 125 150 A 0 1031 045 0o60 08 70 90 1i00j 113 1i2 1o28 j140 B1 118 1077 1051 1037 1028 0Jfi 19 1017 TABLE 62 70 900 W 100 I I I W TA1BLE 63 0510 10 D h I 021 021 B Jp 4 5 h RIDh 4f aff 040 4 IN IV W0 W iD UP iWO V N 206 Sharp bends at 05 L i5 and o 4 i8 contd I Section VI i Diagram 61 00 025 050 075 10 15 20 30 40 50 60 70 80 C 130 117 109 100 090 085 1085 1090 095 098 100 100 r4 I ore 2C jASC C 2 Rough walls A 0 and Re 2 10D AM 72 kakieCl Cfr where k and kR are determined tentatively from Table 64 as a functions of Re and A TABLE 64 RoIDh 05055 05515 A iRe 310 34 104 4104 3 10 34 104 3 104210 5 210 eRe ka kle kA eRe It kRe kh kRe Rh 0 45 1ie 10 10 10 64 Re 10 64 Re 10 10 10 00001 45IRe 10 10 1 05101 64Re 10 641Re Aaksm 10 1 W10 001 451R 10 10 z1 5 64Re 10 64Lfe 2 20 10 20 ýRe and X sm are determined as I for commercially smooth pipes A 0 at given Re from diagram 22 I and X are determined as X for rough pipes 16 0 at given Re and A from diagrams 23 to 25 v is taken from 13 b A is taken from Table 21 207 I Section VI Smooth bends at h 15 and 0 40 MO Diagram 62 DO 1 Smooth bends A 0 and Re Dh 210 Ail where C 1 4jBC X f 002fr000035 S Dh As is determined as a function of from graph a or by the formulas of Table 6 5 TABLE 65 0 70 90s 100 A 09 sin V 10 07 035 So B is determined as a function of A from graph b or by the formula Dh B 021 C isdetermined from graph c as a function offor circular or square cross sectsonC 10 2 Rough walls A 0 and Re i 2109 AH I ARC Cfr 2g where kA kR are determined tentatively from Table 66 as a function of Re and 5h TA13LE 66 Re T 3 1 30 4 1 0 4 1 0 4 2 10 5 2 1 0 kRe kA kRe kA kRe 0 641Ie 10 6 4 1 R 10 10 10 00001 64lRe 10 641Re 1 6 10U 10 1 Ai 106 0001 64 1Re 10 6 4 1Re Z20 10 20 1 is determined as a function of the given Re and A from diagramis 22 to 25 ie is determined as I for commercially smooth pipes A 0 at given Re from diagram22 v is taken from 13b A is taken from Table 21 208 R USection VI Smooth bends at is5 and O ISO contd Diagram 62 r 1 01 20 1o 3014 0175 1 D 1 110 1 130 1150 1 ISO At 1 0 I 031 10451 0601 0781 0901 1001I1131 1201 1281 140 1 411 am A 00 A z0 Wf 55 aS W IN NO mu A d 4 1 HIMa 1 8 aJ b v J O wv C af 0 J25 0 I75 10 15 2013014015060 7010 C i80 1 45j 120j 100 068 045 040 043 048 055 058j 060 209 Very smooth bends bh 15 in conduits coils of Section VI wDh arbitrary angle of bend 40 50Re210 Diagram 63 Dhm r10 periniecer SJoe 1I 4 0w 0 1 75 1w 4 2g where I is dutcsriined from Hit curvu I Re or from the followinjg table a e020 DhOi a 50e R 0 0 50Re Re 0 R0 104Dh 2 b 600 Re 1 400 1 10 1 0 M D75 fD c 1 400 Re 5R 0M 1 R 0 2R0 v is taken from 13b Re 441021610218 IP1103 12 10 4P 410316 1iP 10 RoDh 31 034 10261 021101810121 00810061 05 Ro DI 39 X 030 1023101910171010100710061005 Ro Dh 51 X 0281021 101810151 011 10610051004 Dh 69 X 026 1 020 01710141 009100610051004 Ro Dh 12 1 0241 0181 015 10131 008100510041004 Rh 21 A 022 1016I 014 1012100710 05 1004 1003 R D 43 0 20 1015101 3 10 Ii007100410041 003 Ro 160 Dh A 018 10131011 100910051004 1004 J003 V II 210 MOD Section VI Standard threaded castiron bendsRe e2t105io Diagram 6 4 Resistance coefficient c AH Characteristics Schematic diagram 100 of bends De 1Y 2 L mm 30 44 56 66 a K 0020 0010 00075 0005 081 052 032 019 L mm 36 52 68 81 45 0020 0010 00075 0005 073 038 027 023 o 90 L mm 30 40 55 65 knee bend a A Y D 0020 0010 00075 0005 219 198 160 107 L mm 45 63 85 98 O 90 R A D 002 001 00075 0005 136 to 167 120 080 081 05S 211 Standard threaded castiron bends Re e a2108 contd Section VI Diagram 64 Resistance coefficient t Bend Schematic diagram 2 characteristic 2g I 1k L mm 55 85 116 n1O 6 23 0 A 0020 0010 00075 0005 to t213 D0 082 053 053 035 L mm 38 102 102 127 a 18T 0020 0010 00075 0005 123 070 065 058 Combined bends at different r and 05 I Section VI Dh Diagram 65 Resistance coefficient t No Bend characteristic Schematic diagram 7 f9 Ushaped C 4 C where V is determined as for a single bend from diagrams 61 and 62 Cfr is determined by the formula at z002Cfr 002 L 00007 B any A is determined from diagrams 22 to 25 A is taken from Table 67 tentatively TABLE 67 lejDh 0 at 1 0 A 14 2 u 4 AB 212 RSection VI Twin bent bends at different r and L 05 Diagram 65 Dh Diaram 6 The same as in No 1 but the values of A are taken from Table 6 8 tentatively The same as in No 1 but the values of A are taken from Table 69 tentatively The same as in No 1 but the values of A are taken from Table 610 tentatively TABLE 610 IoIDh i 0 I 10 213 Sharp O elbows of rectangular section Section VI with converging or diverging exit section j Diagram 66 2aobo Dh ab 106 0101 12 14 18 1 abo 025 C 176 143 124 114 109 106 106 2 ab 1 0 Cl 170 136 115 102 0 95 020 084 3 albo 4 0 CI 146 110 090 081 076 072 066 4 adb0 oo C1 150 104 079 069 063 060 055 a tDGDh 1 Smooth walls A 0 and Re 24V AN 2g is determined from the curves C1 1ko corresponding to different values of b0 2 TRough wals A0 and Rc 2x 10s 2g wherc k arid kRe are determinjed from diagram 67 as functions of Re and A D v is taken from 13b A is takcn from Table 21 4 214 Sharp o elbows at 0 8o i0 Diagram 6V7 1 Elbow without recess 1 Smooth walls A 0 and Re v h 4 IVý where C is determined approximately from graph a as a function of a0 be in the case of circular or square section C 10 A is determined trom the curveA IV of graph b tj 0 95 sin 2 205 sin4 is determined from the curve C1 5 d of graph b 025 050It 075 j 1o15 2030 40 50 6070 80 C o 10 tC71 104 1 100 1 095 0 08 78 1 0072 071 1070 a TABLE 611 Re h fo4m I 4o o ý R o10 11 10 00001 I Re 1010 105o 1 iA 0 001 451LR 10I0 5 215 Sharp ih 0 elbows at oa 1800 contdSeto V Diagram 6 7 2 Rough walls A0 and any Re SkakRCIAPi where ki and kRe are determined tentatively from Table 611 as a function of Re and fD i is determined from diagrams 22 to 25 as a function of Re and 1C XRe is determined from diagram 22 as A for commercially smooth pipes A0at given Re I is taken from Table 21 v is taken from 13b be O 2D V 45 60 75 9DII 110J 130j150 jN 01005 007 I017 037I06309 156 26I267 300 A I j 250 1 222 I 187 I 150 I 128 1 120 I20 120 I 120 120 41A 0 21M 4W N 11 70 7IN IM 1 Me 0 Ww b 11 ýElbow with recess AKf yr r er ut eces rs 29 whtretwr is determined as C for an elbow without recess 216 Elbows with rounded corners and converging or diverging Section VI exit section FDiagram 68 Ci 0 1 width of the narrow section 1 Smooth Valls A 0 and Re b 2105 AK C A Ce ACa 2g where C e is determined from the curves 4 Fe jof graph a As is determined from the curve A f00 of graph b C is determined approximately from the curve C of graph c kIn C resistance coefficient of the elbow at 10 and 8 90 W mean stream velocity in the narrow section 2 Rough walls A 0 and Re 2x10 29 A where kA and kV are determined as functions of Re and l from Table 612 of diagram 69 v is taken from 13 b A is taken from Table 21 Values of Ir I F r Fe bc 02 105 1 1o I 1 i 20 3o0 1 40 50 03 020 0451069o078 083 088 091 093 015 013 03210571068 076 083 087 089 020 008 020 0451 058 067 076 081 085 030 006 0131030 045 056 067 074 079 040 004 01010251040 051 064 070 076 10 004 00910211035 047 059 067 073 217 Elbows with rounded corners and converging or diverging j Section VI exit section 510 contd Diagram 68 20 1o 30 Iaj45 160 l IsD I tol 130 150 ISO A 01 0j 031 1 045 060 0781090 1001i13 120 128 140 0 25 v0 6V 04 Ix Me NO WI A we b L ae1 251 50 1 75I1 10 1 5j1 201 30 1 40 150 160 170 1IS0 C 1 1301 I1t7l10911001 0901 0851 0851 0 90109510981 1 oI 00 17 1I 171 I 11 7 j11IJt1 75 tfItV4 4 CiV 07127 v4 C 5 6 7 218 Elbows with rounded corners at 005rlDh05and 0 80 O II Section VI Diagram 69 1 Smooth walls A 0 and Re h2109 AH 2g where C AIIC If 00175 LBO A at 1 002 C 002000035 r A is determined from graph a as a function of 80 B is determined approximately from graph b as a function of C1 is determined approximately from graph c as a function of SO 2 Rough walls A 0e id ReZ2 105O A H C k2kRCI Cft 2g where ka and kR are tentatively determined from Table 612 as functions of Re and A ARe and Asmare determined from diagram 22 as Afor commercially smooth pipes A 0 at givenRe A and XA are determined from diagrams 23 to 25 as A for rough pipes A 0 at given AADh v is taken from 13b is determined by Table 21 TABLE 612 Re 3 a101o1o 410 2HP 2o kR AAh ke kA tR kA 0 6 41R 10 6 4Re 10 10 10 00001 6 4ARe 10 6 4ARe A Asm 10 i AW 103 0001 64ARe 10 6 4XRe 20 10 z20 219 Elbows with rounded co rners at 005rlD05 and o86two contd Section VI I Diagram 69 r 0 20I3VI5 W60 7s90 10IM O 150 In A 0f 0 31 0 45 060 0781090 f 00 113 120f 1410 a IIV Of A A fl zop ve Wi ao S 1W xvD no a 005 010 020 030 040 050 06 S 1087 10701 044031o1026 a 05 6 491 02 494 5 PC5 b a o25 050 075 10II5I20 30 40l 50 60 170 00 ci C 1i30 177 109 100 090 085 085 90 095 098 100 100 220 900 elbows of rectangular section with rounded inner corner Section VI and sharp outer corner Diagram 610 No 1 No 2 Dho U perimeter 1 Smooth walls A O and ReUw 2 105 AH Cfr where for No 1 C1 is determined from graph a as a function of Dh D h forNo 2 C I O2C CfrI 5 at X 002 0frOO 2 OOl rh C is determined approximatelyfrom graph b as a function of0 2 Rough walls AO and any Re AH where kA and kRe are determined from Table 612 of diagram 69 X is deterrflined from diagrams 22 to 25 as a function of Re and A v is taken from 13b A is taken from Table 2 1 r0 h I 0051 01 02 1 03 1 05 1 07j 120 11101 0881 0701 0561 0481 0431 040 adb I 025 10o0 o5I1 LooD 51 20 1 30 140 50 1 60 1 701 80 C 1301I17lI109 100 0901085085 090 095109811001L00 C 10 ofI 4I 141 V9 702 e 77 h a 40 40 F0 a 221 Section VI 900 elbow of rectanIgular section with cutoff corners Diagram 6I1 iDiagram6 1 4 Dh U perimeter No 2No 1 Smooth walls A O and Re o2106 where for No1 C1 is determined from the curve for No 2 C 047C for No 3 C 1 28C C is determined approximately from graph b of diagram 610 2 Rough wallsA 0 and Ret2X105 AH C 4 W ItkROCClI 2g where ka and kRe are determined from Table 612 of diagram 6 9 v is taken from 13b It 0 1 02 03 04 05 C1 110 090 080 069 060 t 1 o 42 41 DV 1 222 Elbows made from separate elements at different soSetonV Diagram 6 12 Resistance coefficient c Am No Elbow characteristic Schematic diagram 29 45 three 1 Smooth walls A0 and Re v 2 2 10 elements 5 ir q 2 RoughwallsA 0and Re 210 C Y Cl Cfr d whereC1 011 CfrlinkDB7 at A02 Cfr002D k kA kRe 0 and A cf diagram 61 2 860 three o The same as in No 1 but l 015 elements 6 fur 0 3 8 60 four The same as in No 1 but cfr 2A elements TDf at IL002 Cfr 0D4 D 4 W three The same as in No 1 but 1 040 elements CAs A 223 900 elbow made from five elements Section VI Diagram 613 0 02 04 06 08 10 20 30 40 50 60 RIo 0 049 98 TA1W4 250 500 17 50 100125 150 IAo 075 ON5 034 OAS 012 010 012 014 014 014 1 Smooth walls A 0 and Re h 2 10 C ieLAAhROl frl where C1 is determined from the curve C1 A N or RL Cfr 3UD at 002 CfrO06o 2 Rough walls A0and ReZ210 5 AH i Cl fr 2g where kA and kReare determined from Table 64 of diagram I A is determined by diagrams 22 to 25 I is taken from l3b A is taken from Table 21 224 90 elbow from three elements Section VI SDiagram 615 0 0 02 04 06 08 10 20 30 40 60 60 RD 0 024 048 070 097 120 235 360 460 600 725 C 110 095 72 060 042 038 032 038 041 001 041 1 Smooth walls A0and ReDh210P AH C i c Cfr 2g where 4 is determined from the curve C to Nor o r fr at K002 Cfr002 L 2 Rough wallsA0 and ReZ2X10 5 Iaj kAkfe 4fr where kA and kRe are taken by Table 64 of diagram 61 is determined by diagrams 22 to 25 I t 2 j 4 V is taken from 13b JD Vi 0Z0 Io f to ZU44A A is taken from Table 21 90 elbow made from three elements at 24 Section VI welded with welding seams at Re 10 Diagram 616 Dmm 5o too 15O 2W 25o 00 a 0O 080 060 045 038 032 030 030 C 4S a is determined from the curve C fDommý O o v is taken from 13b 50 150 M 2IF JO mm 226 6 31 rl i i i i ISection VI 900 elbow made from four elements Diagram 614 Diga 61 0 02 04 A6 08 LO 20 30 40 50 60 0 03 0371412 f50j 197 374 560 74619301113 1 110 0920270 058 040e30 016 019 020 020 020 1 Smooth walls A 0 and Re Weh 10 V AH m where Cl is determined from the curve Cl 1 0 or Ar DLO at A002 C00 2 Rough walls A 0 and ReZ 2x10 5 AH where ka and kRe are taken from Table 64 of diagram 61 X is determined by diagrams 22 to 25 v is taken from 13b A is taken from Table 21 225 90 elbow from three elements I Section VI Diagram 615 to 0 02 04 06 08 10 20 30 40 50 60 RDo 0 024 048 070 097 120 235 360 460 600 725 CI 110 095 72 060 042 038 032 038 041 041 041 1 Smooth walls 0 and Re w f 2103 AH where is determined from the curve amf or R Jfx at A002 C fr 002 2 Rough walls A 0and Re 2 x105 where kA and kRe are taken by Table 64 of diagram 61 Saz J IF S is taken from 1 3b I ad 1 is taken from Table 21 90 elbow made from three elements at 24 Section VI welded wih welding seams at Re 105 Diagram 616 J7OJrd Dmm 50 1001 Sol 200 250 10 M IS0 C 08 060 045 038 032 0 030 00 AH as oas 29 is determined from the curve C Domrnm is taken from l3b 50 1 fi M5 AVW O mm 0 226 R Section VI Corrugated bend 725 Re 2106 Sion V1 I Diagram 617 4 v is taken from 13b AHI As taken from the table W0 t Zshaped elbow made from two 300 elbows Section VI Diagram 618 1 Smooth walls 40 and Re hb2105 V 0 0 10 20 30 40 50 60 Do Y lfrP R0De 0 190 374 560 746 930 113 29 Ci 0 015 015 016 016 016 016 where C1 is determined from the curve 41 or f Do D0 Cfr ILDo nat K002 Cfr D0o0 2 Rough walls A 0 and Re2x10 C Aft 2g where kA and kRe are taken from Table 64 of diagram 61 L is determined by diagrams 22 to 25 v is taken from 13b F8 f D A is taken from T able 21 18 J70 Sta Z110 2a 5 o 227 a Section VI Zshaped elbow Re h 10 Diagram 619 4 Dh go Iff perimeter 0 0 04 06 08 10 12 14 16 18 20 66 X1 0 062 090 161 263 361 401 418 422 418 I 24 28 32 40 50 60 70 90 100 cD 4l 365 330 320 308 292 280 270 260 245 239 V4 1 Smooth walls A 0 at any Re where C is determined from the curve Cl 10 C is determined approximately from graph b of diagram 621 0 C f AQN at A002 Cfr 002 Lo 2 Rough walls A 0tentatively where kA is calculated by the following expressions a kA 10 at Re4 104 b kA I 05 10 Aat Re 4 104 and 0001 c kAI5 at Re4 10 and K0001 A is determined from diagrams 22 to 25 v is taken from 13b a A is taken from Table 21A 11 S 1JWLLLULWJ q 2 0 F ar 228 Combined elbow made from two 900 elbows lying in Section VI different planes Re 104 Diagram 620 41e Dh I 7 It perimeter 10 0 04 06 08 10 12 14 16 18 20 CI 115i 240 290 331 344 340 336 328 320 311 10 24 28 32 40 50 60 70 90 1000 Co C 316 318 315 300 289 278 270 250 241 230 1 Smooth walls A 0 at any Re C o H r 29 where C1 is determined from the curve Cl 0 C is determined tentatively from graph b of diagram 621 X 002 L9O o at L002 Cfr D9 2 Rough walls A 0 tentatively y 02 CC1 Cf ig where kA is calculated by the following expressions a kA 10 at Re4 10 4 b kA 1 0 5 10 E at Re 4 10 and 0i0001 c ka z15 at Re4 10 and I X is determined from diagrams 22 to 25i v is taken from l3b A is taken from Table 21 A ii 22 A 1 1a4 711 F 229 ITshaped elbow 1800 with equal inlet and exit sections Section VI FO bo Ret410 D I 0 Re Wh4lDiagram 621 Dh 4P 1 perimeter 1 Smooth walls A 0 at any Re C am Alf CCl Cfr where Cl is determined from the curves C1 of graph a Cfrk ib at ký002 OM 02y C is determined tentatively from the curve C kb of graph b u b1 0 102 104 106 108 1i0 12 114 116 8 120124 SI bchlbo 05 C 1 9 69 61 5k4 1 43142 143 444453 2 bchlbo 7 3 3 Cl1 45136 129 125 124 1 23 j23 123 124 j26j27 32 3 bch b 10 2 113 1o12 12 1o3 114 15 16 23 I 4bchbo 2 0 l 391214 15110 108 1 07 07 106 jo6 106 06107 a 0 25 050 075 20 15 20 30 40 50 60 70 80 C1 110 107 104 100 095 090 083 078 075 072 071 070 2 Rough walls A0tentatively AH where a kA z0 at Re 4 I04 b k 1 05 10 at Re4 104 and 0 o0o00 c karl5 at Re4 104 and A0001 X is determined from diagrams 22 to 25 as a function of Re and A is taken from 13b A A is taken from Table 21 h mlJ Cl 06 0 I 1 II 2 b 5 S 7 230 flshaped elbow 1800 with contracted exit section 1 05 Section VI O Diagram 622 4F D 11 1 0 W perimeter fDh b 10 1 Smooth walls A 0 at any Re and AH 2g where C1 is determined from the curvesC1l 2Of graph a C is determined tentatively from graphc of diagram 621 Cfr bi at 002 C fr 002002 L bo 2 Smooth walls A0 Re2 105 and 10 C hRCC 1 rfr where kR is determined from the curve kRe Re of graph b 3 Rough walls A 0 tentatively 11111W021g khkReC 1 0 where kA and kRe are calculated by the following expressions a kRe 10 for all Re and 1b 10 b hRe is taken from graph b for Re 2 X 105 and 1Ibq 1 0 c kA C 1 0 for Re 4 X10 4 d kA 1 05X103 for Re4x10 4 and 0ýA 0001 7 o ekA z15 for Re 4X104 and A 0001 a 1 XIF ZAP Xl is determined from diagrams 22 to 2 5 v is taken from 13b A A is taken from Table 21A h a 08 10 12 105 1 16 10 20 I0s 24 16 28 I0s kRe 145 134 126 117 110 105 10 IlJb 0 02 1104 06 08 20 22 24 26 28 320 1 odb 05 C 75 52 I 36 I 34 45 60 I 67 1 71 I 73 i 75 f 76 2 ý hbo O7 3 41 581 38 1 241 19 1 22 1 27 1 33 1 37 1 40 1 43 1 47 3 b 1 0 l 55 3 5 21 1 17 19 1 21 1 23 1 24 1 26 1 27 1 27 4 Nb 20 63 42 271211 21 221 22 1 20120 1 18 1 16 b 231 flshaped elbow 1800 with widened exit section b4 Section VI Diagram 623 Dh o I perimeter z 19I 0 02 1 0 4 1 o4 0 08 0 12 14 1 18 1 20 1 bclbo b05 Cl 73 1 66 1 61 1 57 54 1 52 1 51 1 50 1 49 1 49150 2 bhb 07 3 C 39 1 33 I 30 1 29 I 28 1 28 1 28 I 29 I 29 1 30 132 3 b chbo 10 Cl 23 I 21 i 19I 18 I 17 I 17 I 18 1 18 I 19 120121 4 bchbo 20 17 I 14 121 10 I 09 I 08 1 08 I 07 107 I08108 1 Smooth walls A 0 at any Re AN y W2A CAlCfr 2g b b07 y1 4 04 4 s 19 where1 is determined from the curves ft b corresponding to different values ofh C is determined tentatively from graph b of diagram 621 at kzO02 Cf 002 O02 to 2 Rough walls A 0 tentatively Wherekh is calculated by the following expressions a A m 10 at Re 4 10 4 b kA 1 0510 E at Re4 4104 and OA0 001 c ka 15 at Re4 10 4 and 40001 Xis determined from diagrams 22 to 25 is taken from 13b A is taken from Table 21 Dhm A 232 flshaped elbow 1800 with widened exit section 20ion 62 eP Diagram 624 4F Dhwor no perimeter to O0a 041 061 0 101 121 14 1 6 18 20 1 bcfhlbO 05 Cl 84 178 173 168 163 159 156 153 152 150149 2 bcfjbo073 C 4l 139 38 136 135 134 132 131 130 130129 3 bchlb am 10 j 25 J25 1 24 1 23 1 22 1 21 120 120 1 19 1 19 1 19 4 bchbo 20 C 1 12 11r1 I L0 10 109 109 108 108 108 109109 WODh 1 Smooth walls AOat any Re Am ch where C1 is determined tentatively from the curves Cl 11b corresponding to different 76 C is determined from graph b of diagram 621 Cfr i to at A zO002 Cfr ý 002 002 be 2 Rough walls A 0 tentatively c kACC I C fr 2g where kA is calculated by the following expressions a kg 10 at Re 4 104 b ke 1 05 103 at Rc4 104 and 0A0001 c k z15 at Re 4 10 and 1 0001 X is determined from diagrams 22 to 25 v is taken from 13b A A is taken from Table 21 A 5l 1 1 I i s 233 v Ushaped elbow 1800 with contracted exit section o LO5 Section VI FP b00 IDiagram 625 4 Dh Fo 1 perimeter Dh it 41 o 1 o02 04 106 108 110 112 114 116 118120 bch 2 r o7 i 1 os jO7 107 Io6 Io6 io6 0o7 107 j07 3V 1 0 41 18 111 109 108 1 08 1 07 1061 06 0O6 105 4 bth 20 C 211917J514 ICl 4 4 PIChlS weDh 1 1 Smooth walls A 0 at any Re andD0 AH wm mClgl fro where Cl is determined from the curveC1 f to of graph a C is determined from graph b of diagram 621 I at A 002 Cfr 002 002 0 60o 2 Smooth walls A 0 at Re 2x 10 and C03 where kRe is determined tentatively from curve p f Re of graph b 3 Rough walls A O tentatively AH C IO kARCeClCfr where kA and kR are calculated by the following expressions a kRe 10 atany Re and 1o 03 b kRe is determined from graph b for Re 2105 and to 03 c ka 10 for Re 4 104 d kA I 05 10 Wfor Re 4104 and 0 0001 e kA15 for Re 4 104 and 10001 X is determined from diagrams 22 to 25 v is taken from 13b A is taken from Table 21 V JtIi 11 to INa I ii i 14 a Re 1 0 1 1 6 0 20 15 A 0 1 kRe 124 116 11 1 107 L04 102 10 I I Fl 11 1 I iri I IAON Z 4 G af4ire OIw Zif Is5jW ZU7 jt7 Zl5 b 234 0 Ushaped elbow 1800 with equal inlet and exit sections Section VI 1Fl A10 Diagram 626 Dh o 14 perimeter 1 Smooth walls AO at Re wDh 10 am TAIC1 oPI 04 06 o 0io I1 4 1 14 116 1 12o0 I bch1bOO5 C1 45126 119 117 115113 112 111 110109 2 bch h 7 05 Cl 25 115 109 107 105 1o05 04 104 104 103 3 bchboi 0 C1 16 109 105 103 103 103 102 102 102 103 4 bchlbO20 C1 6 11 o0 10 10 7 10 6 10 15 04 104 104 where C1 is determined from the curves C1 II of graph a I 21 C is determined tentatively from graph b of diagram 621 Cfr A atlO00 2 Cfr o002 00212 2 Smooth A 0 and rough A0 walls at any Re AM C i ksReCIl Cfr 2g where kA and ARe are calculated by the following expressions tentatively a kRe 10 at Re210 5 b kReis taken from curve 1 of graph b for Re210 5 and c kRe is taken from curve 2 of graph b for Re 210 5 and a 0do 03 d kA 10 for Re 4 10 e kA1 1510 for Re 4104 and 010001 f k 6 l5 for Re 4 10 and o0001 X is determined from diagrams 22 to 25 v is taken from 13b A is taken from Table 21 A b a Re 0A4 10 08 10 12 10 1 16 105 20 loU 1 24 105 2 10 1 bib0 10 Ldbo 03 kR 124 116 1 1 107 1 104 1 02 10 2 blbo 10 bo03 J35 125 1 1l 1 112 1 107 01 4 10 235 Ushaped elbow 1800 with widened exit section P Ibt 14ScinV Diagramn627 Dhm e ne perimeter 1 Smooth walls A 0 at any Re and 4 05 AH where C is determined from the curves of graph a b o C is determined from graph b of diagram 621 at A 002 Cfr 00 2 O2 2 S mooth w alls A 0 at Re 2 105 and 5 01b 102 104 106 108 110 112 114 116 118 20 1 bchb 05 fkfC 1 C vf Cl 1 2 3112 122 129 119 119 118 118 118sq 2 b 10bo 075 Cl 128 118 1 14I 109 1Io8 18 1o0 o 10 7 107 where kRe is determined tentatively from the curve 3 bRe I Re of graph b 3 Rough walls A O tentatively j 1 9 113 i09107 105 104 103 103 102 102 A 4 bchltbo c 20 W kkftCjC I Cfr l 112 I080 7 106 1 104 104 104 104 2g where k and kRe are calculated by the following expressions 44 a kR 10 at any Re andL05 bT lb d 674O b kReis determined from graph b for Re 2 10 and 2 0 o0 5 2 c kA 10 for Re 4 10 2 d k I 00 10 l forRe 4 10 and 0A0001 e kA z15 for Re 4104 and A0001 LJr1T1TlT I is determined from diagrams 22 to 2 5 v is taken from 13 b P Ais taken from Table 21 h 04 01 Iz to OP 2 a Re 04 105 0810 12105 1610 20105 24105 28105 kRe 124 1A16 111 107 104 102 10 236 Ushaped elbow 1800 with widened exit section Section VI Re Diagram 628 4F 1 Smooth walls A 0 at any Re Dh B e l perimeter AH fe where Clis determined from the curves Cl corresponding to different bcnb6 C is determined tentatively by graph b of diagram 621 at X002 Cfr 0 0 2 00 2 b 2 Rough walls A 0 tentatively 2g where k is calculated by the following expressions a k 10 at Re 4 104 b k I 0510rat Re4 104 and 0 j 0001 c kA l5 at Re 4 104and0001 X is determined from diagrams 22 to 25 V is taken from 13b A is taken from Table 21 A 02 04170b 081 10 121 14 16 J18 20 i bchbo 05 I1 V c 60 o I35 2 25 1 24 1 23 22 21 1 21 20 c TL 2 bchbo 073 20l 1o 16 1 12 1 10 1 09 0 8 08 I08 I09 4 bchbo 2 0 t 10 I 09 I 08 I 07 1 Q 07 i 07 I 08 I 09 I 09 I 09 A 237 Parts made from galvanized sheet for 1 10 Do 100 mm Section VI Re O 1510s Diagram 629 Resistance coe fficient Type Schematic diagram a2a g150 Offset 88190045 Offset 282X90 By pass 4a4X45 v is taken from 13b A 238 Corrugated elbows made from galvanized sheet for Section VI V Dom100ram RemvAhI5 lOs Diagram 630 2 V I i Resistance coefficient Type Schematic diagram Elbow W 45 053 Elbow 082 2A 2X X45o Elbow a 90 133 Gooseneck Ire 28 2 X 450 100 Gooseneck 33 26 2 X 90 330 Resistance coefficient Type Schematic diagram 0 ffset 193 81 90 Offset 8 2XWO 256 By pass 238 414X45 v is taken from 13b 239 90 bend with concentric guide vanes Re A t 10 Section VI v14Diagram 631 F 0b 5 AH from the curve C or approximately by the formula where C is determined 1 646f 004 C tfr 157 P k at X002 0fr 031bo Cw v is determined as C fora bend without vanes from the data of diagram 61 is determined from diagrams 22 to 25 vis taken from 13b The distance between the vanes is determined by the formula ri i26rf I O07b4 R 05 06 071 08 09 10 11 13 15 024 015 012 010 009 008 007 006 007 ClI 072 U0 I 07 09 15 01 240 900 elbow of rectangular section at different ro with airfoil Section VI guide vanes Re 104 Diagram 632 romrzr y ribe 0I1TI02 IO 41O4 105I1O6 1 Onorm C o033 I 023 I 017 I 016 I 017 022 1 031 2 naopt Ci 033 I 023 1 0151 011 1 013 1 019 1030 3 nfilij C1 045 I 033 I 027 I 022 037 f 015 1017 1 Normal number of vanes nnorm 20 1 213 t I 2 Reduced optimum number of vanes n opt 1 4 ol4t 3 Minimum number of vanes n izf0 9 9F ýý Cl t ft yW 2 Cl A 42 where C1 is determined from the curve Cfr I l57rI1 at k002 Cf 002 0 3 1 X is determined from diagrams 22 to 25 v is taken from 13b A is taken from Table 21 For location and design of the varies cf points 33 and 36 of 62 0 U1 aE 41 0J04 45S AS 10 241 900 elbow of rectangular section at different K with Section VI thin guide vanes Vo0 Re FAD 104 Diagram 633 0rmt ýr rlbo 0 005 010 j015 020 0 0 i nnorm 042 1 035 1 030 026 023 I 021 1020 2 nopt C 042 I 035 I03 1024 I 020 I 017 I 014 3 lmin C 057 I 048 I 043 1 039 1 035 I 031 1 028 1 Normal number of vanes n normý 213ýb I 215 1 2 Reduced optimum number of vanes flmad 14 3l4to 3 Minimum number of vanes n min0 9 o0S I Cf r 2g 01 02 o 061 0oo5 am Os A where 1 is determined by the curvesC 1 I tentatively Cfr 157 at X002 C fr 002001 A is determined from diagrams 22 to 25 4 is taken from 13b For location of the vanes cf point 36 of 62 242 900 elbow of rectangular section with thin guide vanes Section VI V950under different conditions Re bi 104 Diagram 634 V Resistance coefficient No Elbow characteristic Schematic diagram t all T90 Sharp inner corner ts0f a 45 normal number 045 1 of vanes at X0002 C047 I SX is determined by diagrams n213 22 to 25 2 The same as in No1 but 2f t C040 UreS0 at 002 C 042 3 The same as in No 1 but reduced optimum number of vanes 038 n 4S1 at K002 C038 4 The same as in No 1 but the inner corner is cut off C 032 1 2k 1 0 25bg at X 002 C m 035 5 Elbow with widening 135 TO018 a 53 normal number of vanes 9 r7 r 040 128K n 3S at 002C043 6 The same as in No5 but reduced mininlUu number of vanes C 060 128A n 09 S at I 002 a 063 v is talck from 1 3 h For location of the vanes cf point 36 of 62 243 900 smooth elbow 02of rectangular section at To05 Section VI with thin guide vanes 4103 Re V 104 Diagram 63 ro Number of vanes optimum opt 1I C1 is determined from the curveC 1 C 0 3I 08 106 1l0 ii2 134 116 316 tXq 2f 2 3 S 052 046 043 042 044 048 052 A is determined from diagrams 22 to 25 Cf v is taken from 13b El 171 90moth lb e02 of rectangular section atl0 Section VI with thin guide vanes iT 107 1Re t 104 Diagram 6S6 Number of vanes optimum hop no TP i Nube o vne otium AH C TjwClCfr 0 where Clis determined from the curve C1 t8 at X A 002 x fr 00 2 0 03 1 7i X is determined from diagrams 22 to 25 v is taken from 1 3h 64 repo 4 A 244 900 elbow of rectangular section at F20 with I Section VI thin guide vanes Re Bb 104 Diagram 637 F Number of vanes optimum h opt 2to 5 Cu C 1 Cfr where C is determined from the curves C1 Cfr b at x zO02 f 002 0031 Cfr A is determined from diagrams 22 to 25 v is taken from 13b O IP7 1 74 1 J 7 I 78ao 82a 1lrbe 02 Atml54 n 5 t 039 I 036 I 0341033 1034103710401 044 2 rbo 05 T 1380 na2 C 032 I 029 I 027 026 1026102510251 025 3 rb 1 0 90 5 C 04 I 026 1 021 J 021 j02503210521 067 245 90 elbow of circular section with airfoil guide vanes Section VI Re V 104 Diagram 638 0 I For the location and design of the vanes cf points 33 and 36 of 62 246 Section Seven STREAM JUNCTIONS AND DIVISIONS Resistance coefficients of wyes tees and crosses 71 LIST OF SYMBOLS Fb F5 areas of the cross section of the branch and the main passage respectively m 2 area of the common channel m 2 Db DR diameters or sides of the cross sections of the branch and the main passage respectively m Dc diameter or side of the common channel m Dh hydraulic diameter of the cross section m a branching angle or divergence angle of the diffuser wb w mean velocities in the branch and the main passage respectively msec Wc mean velocity in the common channel msec Qb Q discharges through the branch and the main passage respectively m 3 sec Qc discharge through the common channel m 3 sec AH pressure loss resistance kgm 2 AHb AH pressure losses resistance in the branch and the main passage respectively kgm 2 resistance coefficient Cb C resistance coefficients of the branch and of the main passage expressed in terms of the respective velocity Ccb resistance coefficients of the branch and the main passage expressed in terms of the velocity in the common channel 72 EXPLANATIONS AND RECOMMENDATIONS 1 Two basic types of wyes are treated in the handbook a wyes in which the sum of the crosssection areas of the branch and the main passage are equal to the cross sections of the common channel FbF F Figure 71 a and b b wyes in which this sum is larger than the area of the common section FbFS Fr with F F Figure 71c 2 Physically each wye is characterized by a branching angle a and ratios of the F b Fb s b cross sections of its three outlets randis The ratios of discharges L and and the corresponding ratios of velocities I and lb may vary in every case All wyes WC Wc can function with the flow directed either toward or away from the main passage Standard wyes are not treated here due to lack of sufficient data 247 ab cc9 e I s S r FIGURE 71 Plan of the junction of two streams a junction of parallel streams Fs Fb Fc bjunction of streams at an angle Fs Fh Pc CjCtionl of streams at an angle Ps b Fc Fs Fc The resistance coefficients of converging wyes are functions of all these parameters The resistance coefficients of diverging wyes of standard shape are functions of the branching angle a and the velocity ratios Ws and wb only Wc wc The resistance coefficient of wyes of rectangular section is almost independent of the side ratio of their cross section 3 The junction of two parallel streams moving at different velocities Figure 71 a is characterized by turbulent mixing of the streams accompanied by pressure losses In the course of this mixing an exchange of momentum takes place between the particles moving at different velocities finally resulting in the equalization of the velocity distributions in the common stream The jet with higher velocity loses a part of its kinetic energy by transmitting it to the slower moving jet The loss in total pressure before and after mixing is always large and positive for the highervelocity jet and increases with an increase in the amount of energy transmitted to the lowervelocity jet Consequently the resistance coefficient which is defined as the ratio of the difference of total pressures to the mean dynamic ipressures in the given section will likewise be always positive As to the lowervelocity jet the energy stored in it increases as a result of mixing The loss in total pressure and the resistance coefficient can therefore also have negative values for the lower velocity jet 4 Generally junctions are more complex than shown in Figure 71 a the branch makes usually a certain angle with the common channel Figure 71 b and c In this case losses due to curving of the stream are added to the losses at mixing These losses are mainly due to stream separation from the inner wall which leads to con traction of the jet at the point of turn and its subsequent expansion Figure 71 b The contraction and expansion of the jet take place after the junction of the two streams and therefore influence the losses in the branch and main passage 5 If the branches are conical instead of cylindrical losses due to the stream expansion in the diffuser part are added to these losses In general the losses in a converging wyes mainly consist of a losses due to turbulent mixing of two streams with different velocities b losses due to the curving of the stream at its passage from the branch infto the common channel c losses due to the stream expansion in the diffuser part Ob 6 The flow pattern in a diverging wye varies with the ratio of velocities or of Qb Ws discharges 715 248 If QbQ a wide eddy zone is formed after the stream entrance into the branch This phenomenon is partially due to the diffuser effect i e to the existence of a considerable positive pressure gradient at the point of stream branching where the total section area increases sharply compared with the area of the common channel This high pressure gradient also produces a partial separation of the stream from the opposite straight wall Figure 72a The two zones of stream separation from the wall create local jet contractions in both branch and main passage followed byan expansion of the stream At QbQs the stream separates even more markedly from the outer wall of the main channel The phenomenon of stream separation from the branch wall also takes place passage Figure 72 b FIGURE 72 Flb patterns in diverging wyes aQbQs bQboQs cQbO At Qb 0 an eddy zone forms atthe branch inlet Figure 72c which causes a local contraction and subsequent expansion of the jet entering the straight passage 7 The losses in adiverging wye usually consist of a shock loss accompanying a sudden expansion at the point of flow branching b losses due to stream curving along the branch and the accompanying shock in the straight passage The resistance coefficient of the straight passage can have a negative value at certain values of the discharges ratio Qb whi ur in this passage This is caused by the branch receiving a larger share of the slowly moving boundary layer than of the highvelocity core at a stream division Hence the energy of unit volume of the medium moving in the main channel will be higher than of unit volume moving in the branch The energy increase in themainpassage is accompanied I 249 by an increase of losses in the branch so that the whole flow will be accompanied by irreversible pressure losses 8 The resistance coefficients of converging wyes of normal shape can be calculated by the formulas obtained by Levin 75 76 and later in a somewhat different form by Taliev 717 Correction coefficients have been introduced in these formulas which bring the theoretical results into agreement with the experimental results of Levin 76 Kinne 722 Petermann 726 and Vogel 728 a Branch gw or Affb Y2 F WS Fb IV 2 A I 2 2 iýCos 01JKb AýFQbFC F c I 2F2 bCos ccs F FTsa Kb 71 72 The value of A for wyes of the type FsFbFc F Fc is taken from Table 71 and the value of Kh is assumed to be zero the value of A for wyes of the type FsFhFC is taken as unity and the value of Kb from Table 72 I ABLE 71 a a06O0 Fb 002I304 06 I08 I10 A 10 b a90 A 101 075 07006 jo60 ABLE 72 PbIFe 010 020 033 05 Kb Kb Kb Kb Kb Kb Kb K 150 0 0 0 0 0 014 0 040 30 0 0 0 0 0 017 0 035 45 0 005 0 014 0 014 0 030 600 0 0 0 0 0 010 010 025 900 0 0 010 0 020 0 025 0 b Constantsection main passage CC I i 2 F 2w Co s 2g AHS F 2 2 V PC b2 o ig 73 74 or 250 w i The value of K for wyes of the type FsFbFC FF is taken as zero the value of K for wyes of the type FsFbF is taken from Table 72 c Conical main passage Here the resistance coefficient Cd of the diffuser part is added to the values Cs obtained by 73 or 74 HI X I0b 5 Fl where ns F area ratio of the diffuser portion of the passage Yexp coefficient of shock determined from the data of diagrams 52 to 54 Cfr friction coefficient of conical part determined from the data of the same diagrams 9 The resistance coefficient of diverging wyes of normal shape can be calculated by the following formulas of Levin 77 and Taliev 717 which contain correction coefficients obtained from the comparison with the experimental data of Levin 77 Kinne 722 Petermann 726 and Vogel 728 a Branch Ab I2 2 m 76 2S or llb 2 bFc 2 Qb Fc b F cb y A I 2cosJ a 77 IQ Fb F 2g where according to Levins data Kb a sin j is the jet contraction coefficient PIX according to Levin The value of b for wyes of the type FSFbFC 1F is assumed to be zero and the value of A as 10 for fb 08 and as roughly 09 for Ob 08 For wyes of the type FsFbF A 10 and the value of Kb is taken from Table 73 251 T AB3LE 73 go 150 300 45W 600 90N Kb 004 016 036 064 10 b Constantsection main passage For wyes of the type FsFbFC F F within the limits O Sc WCC curves Cs of diagram 723 c Conical main passage In this case the resistance coefficient Cd calculated by 75 is added to the values cs obtained by formula 78 or by diagram 723 The recommended formulas and the corresponding values of the resistance coefficients given in section VII can be used for all values of Reynolds number Re m 1O4 10 Since the resistance coefficient of diverging wyes of normal shape is independent of the area ratios Fand generalized curves can be plotted for this coefficient as c urveso ofSjý of diara 723 Web a fncionofor which is impossible in respect to or This iswhy the re sistance coefficients are in some cases given in this section as cb and Cs although most curves are given as cnicandlcna g In The resistance coefficients of w5es are often expressed through the mean velocity in the corresponding branch These resistance coefficients are connected with the resistance coefficients expressed through the velocity in the common channel by the fol lowing exp res sions ASb hh cb 79 a fucto of oFwihi mosil nrsett r hsi h h e 252 4 and All cS 710 2 Qb 2 F 710 12 The resistance of wyes of normal shape can be considerably reduced by rounding the junction between the branch and the main passage With converging wyes only the outside corner has to be rounded r Figure 73 On the other hand with diverging wyes both corners have to be rounded r Figure 73 which makes the flow more stable and reduced the possibility of stream separation near the inner corner r lost t FIGURE 73 Improved Y FIGURE 74 Y with smooth bend A very efficient method for reducing resistance of both converging and diverging wyes is the use of a diffuser in the branch Here the losses are reduced by reducing the flow velocity in the diverging section and reducing the true branch angle of the turn a a Figure 73 Together the rounding of corners and widening of the branch will give a still larger reduction of the branch resistance A minimum resistance is achieved in wyes where the branch is smoothly bent Figure 74 such branches with small branch angles should be used wherever possible 13 In gasheating and water lines the pipes are screwed into wyes or tees of larger diameter so that the inner surface of the pipe does not coincide with the inner surface of the fitting and forms an annularprotuberance Figure 75 which increases the re sistance of the fitting a b FIGURE 75 Annular protuberance FIGURE 76 Equilateral in a standard tee tee with partition a welded tee b tee with screwed pipes The values of the resistance coefficients of a number of threaded malleableiron tees are given in diagrams 716 and 7 25 253 14 In the case of tees which are used for joining two opposite currents converging tees Figure 76 the resistance coefficients of the two branches are practically equal When a partition is installed at the junction of a tee the two flows are independent of each other before converging into a common channel This junction is followed by the usual turbulent mixing of two streams moving at different velocities Here the losses in the tee are made up of a the loss at mixing and b the loss at the 900 turn The resistance coefficient of the branch through which the lowervelocity stream moves can have a negative value just as with a converging wye due to the additional energy from the highervelocity stream Without a partition the flow pattern is less clearly defined The pressure drop before and after the stream junction mainly reflects the losses common to both branches These losses are positive at any ratio n and are approximately equal to the losses in an expanding elbow The resistance coefficient of each branch of the tee before the junction can be calculated by the following formula proposed by Levin 710 Ccbý Hb I3Fc 2 QD 2Qb 1 2g 15 If the tee is used for stream division the conditions of flow in it are approximately the same as in an ordinary turn The losses in a diverging tee can therefore be approximately determined from the data for elbows with different ratios The resistance coefficient of a diverging tee can also be determined by the following formula proposed by Levin 710 AWb 12b cb 1 k 712 2g where ks 15 for standard threaded malleableiron tees k03 for welded tees 16 The resistance of a tee can be decreased considerably by making it with smooth bends 17 Atbranching angles 90the tee acquires the shape of a Y cf diagram 736 The resistance coefficient of such true Yjoints with F2F at junctions can be calculated by the following formula proposed by Lewin P 710 C SQb 091I cos2 Q 4 Qb Cosz 4 cos a 402 05 coO a 713 254 The resistance coeffieient of the same Yjoints at stream division can be calculated tentatively from diagram 722 as the resistance coefficient of the branch of an ordinary wye of the type FsFbFC 1 8 The flow pattern in crosses is basically similar to the flow pattern in single wyes and tees The resistance coefficients of double wyes of area F F at stream junction converg ing double wyes cf diagrams 731 to 735 can be calculated approximately by the following formulas proposed by Levin 78 and 79 a One of the branches No 1 A i b P 2 Q 2 b b fQIb2 r Q2h2 I j L 2 Cos 714 Fi eQ1bRmb Fib h 1 t The resistance coefficient of the other branch No 2 is obtained by interchanging the subscripts 1 and 2 b The main passage Q h 2 S Q s 2 IQ s2 Q2 F c s1 i 2 cos 715 7j o 75V25 Q 19 The following formulas are recommended for calculating the resistance co efficient of welded converging crosses in cylindrical manifolds for steam water etc Levin 78 79 a One of the branches No 1 AH I 5 b Ft C2 16 h CI CtQQhiI 2g Q FJ bc Q T b The main passage I Q 2 T 717 C f 10 2QQ2 0 o75o25 255 For standard crosses made of malleable cast iron and with Qe 07 the following magnitude is added to the values obtained for cs ACS L 0 718 Qqi 20 The resistance coefficients of double wyes at stream division are determined tentatively as for single diverging wyes from diagrams 721 to 723 tAH 21 The coefficient of local resistance cs 7 of the part of a header between two Wb side openings Figure 77 is a functiont of the velocities ratio f and the ratio of the pressures H7st and ot i2 wherelt static pressure in section 11 Htot total pressure in the same section This coefficient is also a function of the sides ratio I of the pipe section The values of Ccs for these passages determined on the basis of Konokotins ex perimental data 74 are given in diagram 738 22 When several branches start from the same header Figure 78 and the distances between them are larger than the header width the resistance coefficient of each branch can be calculated as for a single wye b Is WIfb abf FIGURE 77 Side openingsin aheader FIGURE 78 Header aconstant section header hbconverging section header 23 The uniform distributionof the flow to the separate branches of a header is en sured either by making its cross section constant Figure 78a and of area Fhe 3s where FSF is total area of all branches or by contracting it in such a way that the stream velocity remains constant along the header cf Taliev 718 A constant velocity header can be achieved as shown in Figure 78 b Here the resistance of the branches turns out to be considerably higher than in a header of constant section 723 For the method of determination of the pressures in such pipes cf M aksimov 711 256 0 24 It is advisable to design the transitions between the exit openings of the header and the branches perpendicular to it by means of the diagrams given in Figure 79 These transitions are of a simple design and have minimum resistance coefficients 723 They can be adopted as standard AHb 25 The resistance coefficient of the ith branch Clb 2I b of a header with transi 2g2g Wjb tions made according to Figure 79 is a function of the ratio of velocities f only it is practically independent of Reynolds number for Rel10 4 of the sides ratio of the header for 05A10 and of the areas ratio Pb bC Streamflow direction in a header a b c d FIGURE 79 Transitions of the branches of a header a and bside branches c and dupper or lower branch The resistance coefficient of a branch at the side is lower than that of a branch at top or bottom since in the latter case the stream makes two consecutive 90 turns in two mutually perpendicular directions Figure 78 257 73 LIST OF DIAGRAMS FOR THE RESISTANCE COEFFICIENTS OF SECTION VII Source Diagram Nt Diagram description Sore number Nt 71 Converging wye of type F FbFc Fs F a 30 Branch Main passage of the same Converging wye of type Fs Fb F Fs F a 45 Branch Main passage of the same Converging wye of type Fs Fb F F F a 60 Branch Main passage of the same Convergingtee oftype F5 Fb Fe Fs Fc a 90 Converging wye of type Fs Fb a 15 Converging wye of type Fs F a 30 Converging wye of type F b F a 45 Converging wye of type Fs Fb b F a 60 Converging tee of type Fs Fb CF a 90 Improvedshape converging wye of type Fs Fb F6 Fs Fe a 45 Improvedshape converging wye of type Fs FbF Fs P F 60 ImP rovedshape converging tee of type Fs FbF4 Fs F at 90 Standard converging threaded malleable iron tee of type Fs Fb Fc F Fc t 90 Circularsection converging wye with smooth side bend RlDb 20 of type Fs Fb b F a 12 to 15 Branch Main passage of the same Rectangularsection converging wye of type Fb Fs F smooth rlbb 10 a 96 Branch Main passage of the same Diverging wye of type Fs Fb F Fs F Branch a 090 Diverging wye of typeFs F4 F Branch a 090 Levin 75 76 Taliev 717 The same Petermann 726 Kinne 722 Vogel 728 Zusmanovich 72 Averyanov 71 Taliev and Tatarchuk 716 Levin 77 The sanie 72 73 74 75 76 77 78 79 710 711 712 713 714 715 716 717 718 719 720 721 722 Calculating formulas The same Calculating foimulas refined by Kinnes expeiiinents 722 The same Calculating formulas refined by Petermanns experiments 726 The same Calculating formulas refined by Vogels experiments 728 Calculating formulas refined by Levins experiments 76 The same Experimental data The same Calculating formula correction co efficient based on Kinnes 722 Petermanns 726 and Vogels 728 experiments Calculating formula correction co efficient based on Levins experi ients 77 258 continued D ia gram Note Diagram description Source numbr Diverging wye of type FsFb F0 and Fs Fb F Main passage a O90 Improvedshape diverging wye of typeFs FbFc Fs F Standard threaded malleableiron diverging tee of type FFbF FsFC a 90 Rectangular smooth ribs 10 diverging wye of type Fs FbFP u 90 Branch Main passage of same Asymmetrical converging wye of type Fs Fst F with smooth bends RID 20 W 900 Symmetrical tee a 90 Symmetrical wye dovetail a 90 Double wye of type Fib F2 Fs F a 15 Double wye of type Fib a Fsb Fs F0 Double wye of type Fib Fgf F F a 450 Double wye of type Fib F2b Fs F a 60 Cross of type F 3s F2b F1 a 90 Wye of type F 2 Fs Header with transition stretches Passage through a side opening of a header pipe of constant cross section Passage through a side opening of a header pipe of constant cross section Levin 77 Kinne 722 Petermann 726 and Vogel 728 Zusmanovich 72 Taliev and Tatarchuk 716 The same Franke 720 Levin710 ldelchik Franke 720 Taliev and Tatarchuk 716 Levin 78 79 The same Levin 710 Konzo Gilman loll andMartin 723 Konokotin 74 The same 723 724 725 726 727 728 729 730 7 31 732 733 734 735 736 737 738 739 Calculating formula correction cocffi cient based on Levins experiments 77 Experimental data I he same Calculating formulas Experimental data The same Calculating formulas and experiments The same Experimental data The same a 259 74 DIAGRAMS OF RESISTANCE COEFFICIENTS Section VII Converging wye of typeFsFbFz Fs Fc a 300 Branch Diagram 71 lllk Values of Ccb Fb 01 02 03 04 06 08 10 0 100 100 100 100 100 100 100 01 021 046 057 060 062 063 063 02 310 037 006 020 028 030 035 03 760 150 050 020 005 008 010 04 135 295 115 059 026 018 016 05 212 458 178 097 044 036 027 06 304 642 260 137 064 046 031 07 413 850 340 177 076 050 040 08 538 115 422 214 085 053 045 09 580 142 530 258 089 052 040 10 837 173 633 292 089 039 027 H b b L N Ccb O2 CF fg 21 oQ 2 74 tc Sý Qb is determined from the curves ýcb I ý corresponding to different Fb FC 2Zb b p 260 Converging wye of type FsbFP F Fs 30 Main passage Section VII Diagram 72 77 w Values of s Pb Qb 77 01 02 b3 04 06 08 10 0 00 0 0 0 0 0 0 0A 002 011 013 015 016 017 017 02 033 001 013 019 024 027 029 03 110 025 001 010 022 030 035 04 215 075 030 005 017 026 036 05 360 143 070 035 000 021 032 06 540 235 125 070 020 006 025 07 760 340 195 120 050 015 010 08 101 461 274 182 090 043 015 09 130 602 370 255 140 080 045 10 163 770 475 335 190 117 075 k s 1 1 7 a Q f is determined from the curves c s b F corresponding to different Lb S s c Cs 2 261 Convergingwye FsFbF F F a 450 Branch Section VII Diagram 73 WY AHb Qb Fc 2 Qb lb b E Q 1II 21 Q yW2 kQFb 14 Qb2 is determined from the curves Cb I corresponding to different PC AHf b c b 2 F 2 2b f b Values of cb 01 02 03 04 08 04 10 0 100 100 100 100 100 100 100 01 024 045 056 059 061 062 062 02 315 054 002 017 026 028 029 03 800 164 060 030 008 000 003 04 140 315 130 072 035 025 021 05 219 500 210 118 060 045 040 06 316 690 297 165 085 060 053 07 429 920 390 215 102 070 060 08 559 124 490 266 120 079 066 09 706 154 620 320 130 080 064 10 869 189 740 371 142 080 059 262 ConvergingwyeoftypebeFs 5 FsF 450 Main passage Diagramn VII i Digram74 R Ut Xs 71 141101 Values of Ccs 0 01 02 03 04 05 06 07 08 09 10 0 005 020 076 165 277 430 605 810 100 132 0 012 017 0o13 050 100 I 70 260 356 475 610 0014 022 008 012 049 087 140 210 280 370 00 16 027 020 008 013 045 085 139 90 255 0017 027 028 026 016 004 025 055 088 135 0 017 029 032 036 030 020 008 017 040 077 0017 031 040 041 040 033 025 018 042 sF 11 Qb is determined from the curves 4cs f corresponding to different T C s A cs 71 1 21 Q 0 263 Convergingwye of type FsFbF FsF a 600 Branch Section VII Diagram 75 Ut I Isr C Fe Values of 4cb Pb Qb Te Q c 0 01 02 03 04 06 ý 08 I 10 0 100 100 100 100 100 100 100 01 026 042 054 058 061 062 062 02 335 055 003 013 023 026 026 03 820 185 075 040 010 00001 04 147 350 155 092 045 035 028 05 230 550 240 144 078 058 050 06 331 7790 350 205 108 080 068 07 449 100 460 270 140 098 084 08 585 137 580 332 164 112 092 09 979 172 765 405 192 120 091 10 910 210 970 470 211 135 100 S 4 AffbQbF c CC 77 is determined from the curves Qbý 64 so 8 Og corresponding to different Lb Fc Alib tc b g Qc F0 P3 0 7 6 as ouiE 32 f8 08 0 0 08 264 Converging wye of type FbFs Fe Fs FC a 600 Mainpassage Section VII Diagram 76 uiý rs a 7Av4 Values of Fb 01 02 03 04 06 08 10 0 0 0 0 0 0 0 0 01 009 014 016 017 017 018 018 02 000 016 023 026 029 031 032 03 040 006 022 030 032 041 042 04 100 016 011 024 037 044 048 05 175 050 008 013 033 044 050 06 280 095 035 010 025 040 048 07 400 155 070 030 008 028 042 08 544 224 117 064 011 016 032 09 720 F308 170 102 038 008 018 10 900 400 230 150 068 028 000 ACc s Qb F b 1 Q Fb Qcb 2g is determined from the curves Cc corresponding to different T C sA CcIs 2 265 Converging tee of type Fb FtF F Fý 900 Section VII Diagram 77 s Ve t Le C H alb Tm fb Cc b Qc F Tbý cb p2 4 A1 06 a QbQc 0 0 1 0 2 03 0 05 066 107 0 10 0 Values of Ccb Ob Fe 01 02 03 04 06 0h 10 0 100 100 100 100 1O0 100 1oo 01 040 037 051 054 059 060 061 02 380 072 017 003 017 022 010 03 920 227 100 058 027 015 011 04 163 430 206 130 075 055 044 05 255 675 323 206 120 089 077 06 367 970 470 298 168 125 104 07 429 130 630 390 220 160 130 08 649 169 792 492 270 192 156 09 820 212 970 610 320 225 180 10 101 260 119 725 380 257 200 1 Branch 29 where gc bis determined from the curves s tiI FCS at different on graph a Fb A is taken from Table 74 at different b TABLE 74 Fb 002 0304 06 08 10 A 100 075 070 065 060 2 Main passage Arts Qb QbA 2g is determined bythe curve Fb practically true for all values of Cs Cc Alf 2 Q qrý a tI 010l1610271 038104610531057105910601 P 591055 meH T CCW j b 266 Section VII Converging wye of type FsFb F a 150 Diagram 78 TABLE 75 FbFc Ks 002 0 033 014 050 040 I B1ranch cbý I ri 2 194 29 is determined from the curves Ccb corresponding to different PC AHb Cc b Cb b tQb P 2 Main passage Fcs Wf Q 1 2g 2 c I i 94 2 Ks is determined from the curves Cs i corresponding to different Fb K is taken from Table 75 I Cs C 2 I QIP FI 2g C QFs Fbt QbQc 0 1 003 J 005 1 010 1 02 1 0 o 04 1 05 1 06 0 08 110 Values of cb 006 112 070 020 184 992 230 410 643 010 122 100 072 001 280 717 13 11 206 297 020 150 140 122 084 002 120 255 420 612 820 107 033 200 180 171I 140 067 016 042 105 167 230 295 420 050 300 280 260 224 156 100 040 002 040 066 093 114 Values of cs 006 000 006 004 013 095 250 460 750 010 001 010 0A12 002 036 120 2 50 410 612 020 006 015 020 022 005 028 089 166 263 1384 522 033 040 042 045 047 042 024 008 052 125 180 260 466 050 140 L 140 139 337 124 101 078 043 010 082 108 246 267 Section VII Convergingwye of type FbFbFC a 30S Diagram 79 cfc TABLE 76 1 Branch Aib fQb la F Q Aff FC 2ýc b c Q 2g is determined from the curve s Cc b Q corresponding 0 Fb to different Cs Afb kb 2 Main passage cs 1 to diflerent bk o0 Ks is taken from Table 76 C s b Y Q I 0f QbIQc 0 0 3 005 01 02 1 03 04 j 05 j 06 07 08 10 Values of tcb T 006 213 00710301182 1011 233 415 652 I 010 122 100 076 002 288 I 734 134 21 1 294 I I 020 1 50 1 35 122 084 005 140 I 270 446 648 870 114 17 3 033 2001 180 I 170 I 140 072 I 012 052 120 189 256 I 330 I 480 050 300 280 i2601224 144 1091 036 014 056 084 118 153 Values of Ccs cs 4l 006 0 10 020 033 050 0 001 006 042 140 006 004 010 081 210 407 660 010 008 004 033 105 2 14 360 010 I 013 016 006 024 073 140 045 1 048 051 052 032 007 032 140 240 136 126 109 086 053 540 230 082 015 334 359 864 147 2819 400 052 s2o82 2o7 f I 4 9 268 Convergingwye of type Fs FbFl a 450 Section VII Diagram 710 SS F TABLE 77 Pb 010 005 020 014 033 014 050 030 1 Branch A I QbN Fe QbV Fc IQ b is determined from the curves ccbht k corresponding Fb to different F C UCcbcs I A I7 I S03 g s8 6 06 Ccbl MZS L e SHb Cc QbFc Qcb 2 Main passage 29 Q IC 2 1 141 fb is determined from the curves Cc SI corresponding to different Fb K is taken from Table 77 All QbI 1c 1 I IS I Fb QObb 0 003 1 0056 01 02 1 03 1 04 1 05 06 1 07 0 0 Values of c b 006 1112 070 020 182 103 238 424 643 010 I122 100 078 006 300 I764 139 220 319 020 I150 140 125 085 012 142 300 486 705 950 124 033 I 200 182 169 138 066 010 070 148 224 310 395 576 050 300 280 260 224 150 0L85 0 24 030 079 126 160 218 Values of Cc 006 I000 005 005 005 059 165 321 513 o10 I 006 010 0 12 011 015 I 071 155 271 373 020 I 020 025 030 030 026 004 033 086 152 240 342 033 1 037 042 045 048 050 040 020 012 050 101 160 310 050 130 130 130 127 12001 110 090 061 022 020 068 152 269 Section VII Converging wye of type FsFb FC a 60 Diagram 711 1 Branch AHII lbF F h Cchb 27p QcQ FhQC 2g is determined from the curves Cb colt espolldilg Fb ý to different 7 C Kb is taken from Table 78 AHb 4cb Cb Q F a Wb 2 Main passage A c Qb PjQ Q QC is determined trom the curves cs j corresponding F C to different fr Ks is taken from Table 78 4 CsS w 15 c s I 0 QbIQc 0 0 00 101 02 1 03 1 04 1 05 061 07 08 110 Values of ýcb 006 112 072 020 200 106 245 435 680 010 122 100 068 010 318 801 146 230 331 020 150 125 119 083 0120 152 330 540 780 105 137 033 200 181 169 137 067 009 091 180 273 370 470 660 050 300 280 260 213 138 068 002 060 118 172 222 310 Values of C 006 000 005 005 003 032 110 203 342 010 001 006 009 010 003 038 096 175 275 020 006 010 014 019 020 009 014 050 095 150 220 033 033 039 041 I 045 I 049 045 034 016 010 047 085 190 050 1 125 125 125 1 231 JJ7 107 090 075 048 022 005 078 270 Section VII Converging wye of type FbF P Diagram 712 1 lABLE 7 9 1 Branch AHb cb 1 Q6 FC e Q 2f Is Kb 80 CcbCcs 7 405 a10le42 72 C 1 pOJ1 0300 4 22S fl I A Ce s 411 is determined from the curves Ccbt1 Q1 fb corresponding to different X Kb istaken from Table 7 9 b b Pot 79 QbFb 2 Main passage AHs 2jr is determined from the curves Ccb t corresponding to different Fb C Affs ks Csf 2 Q I 2g FbF OblQC bFC 0 003 1 005 1 1 0 T7 04 J05 106 1 07 108110 Values of 4cb 006 112 075 020 206 112 250 462 725 010 122 100 075 020 358 891 162 255 367 020 1 40 125 110 068 050 213 420 670 970 131 170 033 180 178 150 120 045 056 159 270 405 542 698 104 050 275 255 233 196 115 0i35 4042 125 205 280 365 525 Values of ýcs o06 002 005 008 008 010 004 008 I 010 020 I I I 020 008 012 018 025 034 I 032 I 033 045 050 1 052 059 066 064 062 I 058 050 100 104 106 116 1 25 I128 122 110 088 070 271 Section VII ImprovedshapeconvergingwyeoftypeFsFbF F Fe 450 Diagram 713 No I r r No 2 02 No3 i80 Values of 9cb NoI O 2 1 02 j a 80 b 5b 0122 034 1 0 I10 122T 034 01 000 047062 062 004 058 03 430 030017 017 180 000 06 195 210022 022 050 090 10 537 540 038 038 225 210 C WI4 1 1 Branch Affb Ccb is determined from the curves t 2 Fb for different on graph a C Q7 b AfHb Ccb 2 c h 2 Main lassage AM s is determined from the curves Ccs for different b on graph h FC All5 CCs ýW I Values of Ccs No 1 0 102 QhQc 0 22 034 10 10 0122 034 01 0101 010 014 014 010 010 03 0050 000 019 018 036 009 06 320 066 006 003 220 040 10 970 290 058 061 710195 42 a LI U b 272 Section VII Improved shape converging wye of typeFsFF F F a 6 Diagram 714 r Nol 01 Db N o 2 0 2 No3 o Values of c1 No I r 0 2 r 02 3 88 QC 0122 034 120 2hF 0 0122 034 01 000 043060 060 050056 03 550 042014 016 140 000 06 219 230030 026 750 087 10 600 618 053 050 211 2 OD 7iv 1 Branch tcb e ýIl is determined from the curves c 29 for different on graph a Athb Ccb b Qb Lc 2 Main passage c is determined from the curves Qcb 2g for different pon graph b CS W ls Lb Values of ýcs No I fbL J 5 3S QQC 0122 034 10 0t22 034 01 010 015 013 013 015 015 03 010 019 023 023 000 025 06 145 025014 013 078 000 10 614 I65030j 035 310075 Rc b 01 I II 13 I I I No ft 3 2 I1 I ýeltoNoIOjY 0 a CO 14N 7S I 4 gNofji5J I I I l FIN i C V A 273 Section VII Improvedshape converging tee of type FS bFCFs P5 a 90 Diagram 715 No1 01 Db TI r No2 5b 02 No 3 88 0 7 1 wFe C9f Values of ch No 0L 1 2LP 2I 8 0 0122 034 10 10 0122 0D4 01 050 o036060 064 050 043 03 460 054 0101 015 3241049 06 236 262043 031 192 220 30 711 087 071 620 538 P 1 Branch AHb cb 7 is determined from the curves Ccb 2g for different Lb on graph a Af Cc b 2 Main passage Ccs is determined from the curves Ccs 2g for different f on graph b Values of Ccs No 1K 01 2 T 0 QhQc SPC 10 10 01 012 008 03 0 29 021 06 036 025 10 035 017 Q b b ANS Cc 274 Iff Section VII Standard converging threaded malleableiron tee of type FsFbFc Fs F 900 Diagram 716 Ws fsP cF 77 1 Branch Cc b is determined from the curves c b Lb for different s AHb Cc b kQoFb 2 Main passage Ail5 Ccs To is determined from the curve Ccs C rs Qs C8 QbtQc FbIPc 01 02 03 04 05 06 07 08 09 10 Values of Cb 009 050 297 990 197 324 488 665 869 110 136 019 053 053 214 423 730 114 156 203 258 318 027 069 000 111 218 376 590 838 113 146 184 035 065 009 059 131 224 352 520 728 923 122 044 080 027 026 084 159 266 400 573 740 912 055 083 048 000 053 115 189 292 400 536 660 10 065 1 040 024 010 050 083 113 147 186 230 Values of Cc s A t l I I I I I I I FbFc 070 064 060 065 075 085 092 096 099 100 4 275 Circularsection converging wye with smooth side bend Section VII t 2 of type PsFb F c a 12 to 15 B ranch 17 b c Diagram 71 AHb 29 is determined from the curves Cc b for different Akb 9b b Qbe QbtQc 01 015 1 02 I 03 1 04 1 05 1 o00 07 1 08 09 10 Values of cb 01 120 290 02 036 060 240 03 048 050 140 222 04 024 044 109 168 06 010 040 092 140 06 044 002 040 070 07 037 006 040 056 08 028 012 040 052 09 060 020 016 039 276 Section VII Circularsection converging wye with smooth side bend 2 FsFbFc 12 to 15 Straight passage Diagram 718 AHs CC s 70 is determined from the curves for different Fb AHs cS QYQ 014 015 02 025 02 I1 A 05 1 06 I 0 I S 09 Values of cs 01 016 010 006 002 004 02 016 010 006 000 03 026 016 006 002 0o4 030 016 000 024 05 040 030 000 044 06 060 003 094 07 090 6037 148 08 160 000 09 060 120 04s 0 02 03 P a1 04 j 08 l 1 0 277 Section VII Rectangularsection converging wye of type Fs FbF smooth ribb 1 0 900 Branch Diagram 719 Dig am 7 1 AHb 23 is determined from the curves cb for different Fb Fb s F ars Qcb bb Ob 4 if Values of Ccb FbIFs Fs PC rbpF01 Q2 0 3 QbYO7 J 0 9 00 4 0 5 0 6 8 025 100 025 050 000 050 120 220 370 580 840 114 140 033 075 025 200 120 040040 160 300 480 680 890 110 130 050 1 00 050 100 050 020 000 025 045 070 100 150 200 270 067 075 050 170 100 060020010 030 060 100 145 200 260 100 050 050 300 215 145095050 000 040 080 130 190 280 100 100 100 100 060 030 010 0 04 013 021 029 036 042 050 133 075 100 180 120 080040020 000 016 024 032 038 040 200 050 1 100 300 210 140090050020 000 020 025 030 040 1 ZcJ 1 Cc b A1I 1 I I I I I Pzs azf I a3a 5 InX a I I 7 tUJ1L25 t iooii I I W 7MO I 1a II II I 1 7 l 9 GS t 0 Liz Ir IVV 4 at 278 a 278 R Section VII Circularsection converging wye with smooth side bend Y2 FsFbF 12 to 15 Straight passage Diagram 718 Als 5cs 7 is determined from the curves Cest Qb for different Fb rts i c IT T o2 s I PbFC 0 0o5 0 02 03 1 0 5 0 6 0 I S 09 Values of ýcs 01 016 010 006 002 004 02 016 010 0 06 000 03 026 016 006 002 0 4 030 016 000 024 0o5 W 40 030 000 0o44 06 060 003094 07 090 037148 08 160 000 09 060 120 16 08 04 0 08 IT 08b 07 Q 277 Section VII Rectangularsection converging wye of type Fs FbFc smooth rlbb 10 90 Branch Diagram 719 4v Ab icb A b 22 Twc is determined from the curves Cbt Qb for different Fb Fb AH s cb C b Y2 OhFb b 2g Q Id Valdes of ýcb PbIFs P Fc tblFc Qb QC 0 01 02 03 04 05 06 07 08 09 10 025 100 025 100 050 000 050 120 220 370 580 840 114 140 033 075 025 200 120 040040 160 300 480 680 890 110 130 050 1 00 050 100 050 020 000 025 045 070 100 150 200 270 067 075 050 170 100 060020010 030 060 100 145 200 260 100 050 050 300 215 145095050 000 040 080 130 190 280 100 100 100 100 060 030010004 013 021 029 036 042 050 133 075 100 380 120 080 040 0201 000 016 024 032 038 040 200 050 100 300 210 1400 900 50 020 000 020 025 030 040 Z 6 tz 4 0 04 2 c b I I A 1 1 1 i i i zFsL I Fe x i b 02S a25 9175 a50 I I V 1 RJ2 l A l 5f 16 0 04 I 0 10OJO j i j i 2 04 50 071 09 03 1 A 278 Rectangular section converging wye of typeFFbFl smooth Section VII rlb 10 g 90 Main passage Diagram 720 c s s 29 is determined from the curvesC fbfor different Pb an s and K Afl cc Qb Fe 12 Values of Ccs Pb As Fb QjQ 71 FC YC 0 01 02 03 o4 05 06 07 08 09 10 033 075 025 000 030 030 0o20010 045 092 145 200 260 30 050 100 050 000 017 016 010 060 008 018 027 037 046 055 067 075 050 000 027 035 032 025 012 003 023 042 058 070 100 050 050 110 115 110 090 065 035 000 040 080 130 180 108 100 100 000 018 024 027 026 023 018 010 000 012 025 133 075 100 005 075 036 038 035 027 018 005 008 022 036 200 050 100 050 080 087 080 068 055 040 025 008 010 030 71075 1 075 050 I007 f 0 000360 279 hb No3 060 and a 900 at 23 2b b 1b b hb height of the branch he height of the common channel AHb Ccu b I Wb Qb Fc Vec Qc Fb No2 a90 and hl 10 pto O2 AHlb Ccb A 034 Z AdVc b 2g jb for where b is determined from the curves cb I f different a A10 for 2b08 ccb 26 Fi I 20 06 04 Ob Ak 09 for O0U Values of Cc wCv 15 30 45 60 h SIt23 kAM s NcO o 10 10 10 10 10 10 01 092 094 097 10 101 10 02 065 070 075 084 1104 101 04 038 046 060 076 116 105 06 020 031 050 065 135 115 08 009 025 051 080 164 132 10 007 027 058 100 200 145 12 012 036 074 123 244 160 14 024 070 098 154 296 177 16 046 080 130 198 354 195 20 110 152 216 300 460 245 26 275 323 410 515 776 30 720 740 780 810 900 40 141 142 148 150 160 50 232 235 238 240 250 60 342 345 350 350 360 80 620 627 630 630 640 10 980 983 986 990 300 Wr b 280 Section VII Diverging wye of type FsFbF a 0900 Branch Diagram 722 as Cc I 2cosa 22 where 4bis taken from Table 710 TABLE 710 15 30 M 60 90 Kb 004 016 036 064 LOD Ecb is determined from the curves Ccb b for different t Values of Ccb mb 01 02 03 1 Q4 05 1 06 1 08 110 12 1 14 16 18 20 15 081 065 051 038 028 019 006 003 006 013 035 063 098 30 084 069 056 044 034 026 016 011 013 023 037 060 089 45 087 074 063 054 045 038 028 023 022 028 038 053 073 60 090 082 079 066 059 053 043 036 032 031 033 037 044 90 100 100 A00 100 100 100 100 100 100 100 100 100 100 281 Diverging wye of type FFbF and FsFbFc 090 Section VII Main passage Diagram 723 Nol F Fb F No 1 5 we C s No 2 lk We i No FsPbFc td 4 CcH is determined from the curves cs If 3 AHL ccsc Values of Ccs No1 No2 159o i56 90o SC F S IF 010 010 004 05 06 07 0 0 040 100 100 100 100 100 100 01 032 081 081 081 081 081 081 02 026 064 064 064 064 064 064 03 020 050 050 052 052 050 050 04 015 036 036 040 038 037 036 05 010 025 025 030 028 026 025 06 006 016 016 023 020 018 016 08 002 004 004 016 012 007 004 10 000 000 000 020 010 005 000 12 007 007 036 021 014 0 07 14 039 039 078 059 049 16 090 090 136 115 18 178 178 243 20 320 320 400 16 282 Improved shape diverging wye of type F Fb F Fýs Fe Section VII Diagram 724 6 Nol 0I Db No2 r NoA r 8 1 Branch A Hb Cc b A is determined from thlie curves Cccmh l affb Cc0 bNb Y ticf 1 a45 Values of cb No Ib r201 2 2 1 Q37QC 0122 034 1 0 10 01221 034 01 040 062 077 077 040 062 03 190 035 056 056 090 035 06 960 090 032 032 540 060 10 306 335 032 032 174 200 283 Section VII Improvedshape divergingwye of type F FbFc F FcBranchcontd Diagram 724 1 13 ranch 2 a 60 3 a 90 Values of cb FbIFc 0122 034 1 10 1 01221 031 01 090 077 084 084 070 067 03 270 060 067 067 130 044 06 120 1 10 053 053 540 068 10 367 316 062 062 166 185 Values of Ccb 4cb l j No30J22 N No2 I t 4 r IJo 0 02 0q 06 08 to 02 a A 458 to A 2 Main passage 4 c is taken from diagram 723 No 1 2s 284 Standard threaded malleableiron diverging tee of type Section VII Fs Fbp Fs Pc 900 Diagram 725 a a4e 1 Branch AHb To is determined from the curves ýcbI Qb for different PC Ab Cc b an CCb 2 Main passage Ais Cc s N is determined from the curve Cc s S for all QVC Fc Cc b Cc s alls Ccs I QbyIFa F FC 1 0 Q c QsQ 0 1 F 2 o3 1 0 4 1 05 0 o1 071 06 I 91 0 Values of Ccb 009 280 450 600 788 940 111 130 158 200 247 019 141 200 250 320 397 495 650 845 108 133 027 137 181 230 283 340 407 480 600 718 890 035 110 154 190 235 273 322 380 432 528 653 044 122 145 167 189 211 238 258 304 384 475 055 109 120 140 159 165 177 194 220 268 330 100 090 100 113 120 140 150 160 180 2061 20 values of Ccs 070 1 064 1 060 057 105 1 1049 1055 1 6F I I I I I I1 0 285 Section VII Rectangular section smooth rbs 1O diverging wye of type FsFbF St V a 90 Branch Diagram 726 1b hHb c bmj is determined from the curves Ccb for different Fi and Ph s p AK5 OM s F Values of 4c b Fb P s Fb QblI Ts IF FI 1 02 03 1 0 05 1 0 1 07 08 1 0 10 025 100 025 080 055 050 060 085 120 180 310 435 600 670 033 075 025 050 035 035 050 080 130 200 280 375 600 650 050 100 050 080 062 048 040 040 048 060 078 108 150 200 067 075 050 070 052 040 032 030 034 044 062 092 138 200 100 050 050 055 044 038 038 041 052 068 092 121 157 200 100 100 100 078 067 055 046 037 032 029 029 030 037 050 133 075 100 078 070 060 051 042 034 028 026 026 029 037 200 050 100 065 060 052 043 033 024 017 015 017 021 025 s C OA o25 900 050 67 050 100 050 S C 08 2 100 0 0 42 03 1q 0 06 A 07 0 8 t9 1o 3 286 Section VII Rectangularsection smooth rbbio diverging wye of type FI FbFS a 9 0 0 Main passage Diagram 727 j b AI1s is determined from the curves c s for different Ls and s ut t F I II IF Q Values of Cc Pb L F b Qblll S I F Fi 02 1 03 I04 5 o6 1 OT7 08 0 9 1 10 025 100 025 004 001 003 001 005 013 021 029 038 046 054 033 075 025 020 008 000 002 001 002 008 016 024 034 045 050 100 050 005 003 006 005 000 006 012 019 027 035 043 067 075 050 020 004 002 004 003 001 004 012 023 037 050 100 050 050 100 072 048 028 013 005 004 009 018 030 050 100 100 100 005 002 004 004 001 006 013 022 030 038 045 133 075 100 020 010 001 003 003 001 003 010 020 030 042 200 050 100 095 062 038 023 013 008 005 006 010 020 040 287 Section VII Asymmetrical converging wye of type Fs FstFc with smooth SectionVI bends 2R 2 90 Diagram 728 De70 W No 1 Sidebranch edge slightly rounded mOI0 No 2 Smooth sidebranch R 2 I Branch Aub cb 0 is determined from the curve Ccb nI hHb Ccb Cbbb fQN 2 Main passage AHs C 5 is determined from the broken curve Cr5 Hs c s Cs c y2g Qj 24 Qo Qe 0 01 1 02 I 03 1 04 1 05 06 07 108 I 09 110 No 1 cb 10801059 0350 15 0021018 031 040 054 1 070T 090 011 0151 019 0221 024 o 024 023 021 020 019 017 No 2 C cb 060 1040 127 014 002 005 012 015 1020 1024 027 J028 j0301 0291 0281 025 020 015 010 005 1002 008 5 288 Section VII Symmetrical tee s 900 Diagram 729 Partition KWfbFfb Junction Division Ccb I I V rAf 6 2 1 Junction of streams a without partition nb Y a tQb 2 gQb 2g Q b Fib is determined from the curves Cb for different AH bIb lc b C 72 IQIbF For the second side branch replace the subscript 1 by 2 b with partition icbis determined from the brokencurve CIcb 1 2 Division of a stream Ccb C W where k 55 for standard threaded malleableiron tees k P 03 for welded tees Values of Ccb Fi b QbIQc F 0 010 1 o2 030 040 0 050 1060 07o 080 090 1 10 a Without partition 025 170 127 9380 69254 50 54 692 932 127 170 050 500 392 308 248 212 200 212 248 308 392 500 075 277 230 192 166 150 145 150 166 192 230 277 10 200 173 152 137 128 125 128 137 152 173 200 b W Oh partition 10 I0325l24o1151 1o8oI 0 10751 145 1215 28513501 415 289 Section VII Symmetrical wye dovetail a 90 Diagram 730 No 1 Circular section R 20 No2 Rectangular sectioný 15 Junction Division 9 I et U 09 No 1 Circular section lb CIcb is determined 29 a at junction by the curve b at division by Table 711 AHI b CIcb For the second branch replace subscript 1 by 2 For a rectangular section cf Table 712 TABLE 711 PC 05 Oc 05 050 075 10 15 20 Ctb 110 060 040 0225 020 TABLE 712 Qlb 0 Fb050 1 0 Junction CIcb 023 007 Division tcb 030 025 a No2 Rectangular section tc Hi b Hcb T 2 is determined by Table 712 2g w 290 Section VII Double wye of type Fib FsbFs FF 150 Diagram 731 1 Junction of streams converging double Y a branch hHib lb Fl P Y Qib x c w Q x 19 Ib i S IQ iQ b Oh k b FT th iqa N d 46 0 Ps r 48 is determined from the curves CIcb for different Fib FE For the second branch interchange subscripts 1 and 2 b main passage I QIsD QQ Ccs es C Q Q 2g VC7 Q t b Q 1931 V is determined froin the curves C I for different Fib 2 Division of a stream diverging double wye CIcband Ccs are determined tentatively by diagrams 721 and 723 No 1 as for diverging wyes 291L S Section VII Doubl e wye of type Fib FsbFs Ps Fe a 15 continued Diagram 731 Q2 b QlbIQcQs MQe 0 0 01 02 03 04 05 06 07 08 09 10 T 02 C 05 10 037 046 148 269 407 562 Ccb 10 10 029 043 123 180 281 20 10 032 031 113 Ccs 05 and 20 437 293 204 144 108 058 022 003 016 014 0 10 384 293 213 144 089 045 013 008 017 014 0 Fib c 0 4 05 10 050 005 034 065 090 104 Ccb 10 10 039 006 031 035 014 20 10 027 010 065 cs 05 and 20 170 119 076 040 012 008 021 027 025 016 0 10 142 096 058 026 002 015 026 029 026 016 0 Fibp06 05 10 051 011 021 042 055 053 Ccb 10 10 039 005 040 031 009 20 10 022 008 018 05 and 20 081 047 019 004 020 030 036 035 029 017 0 10 061 031 005 013 027 035 039 037 029 017 0 Fib 05 10 051 012 020 039 049 037 Ccb 10 10 038 009 036 044 028 20 10 018 027 019 05 and 20 035 7011 010 026 036 042 043 039 031 018 0 10 021 002ý 019 033 041 045 045 341 031 018 0 v J 292 Section VII Double wye of type Fib F2b F F 30 Diagram 732 1 Junction of streams converging double wyc a branch CAHIb 29 I Qb Fc 2 8 b X d j Q jIb 411b J J 2 I 2b 41bb A is determined from the curves Clcbf L QI2b for different ib F For the second branch interchange subscripts 1 and 2 b main passage AH 5js sV cs C05 02 Q s 2gO75O25 1 7 3 QsF N Qb R T Qb2 Q is determined from the curves Ccsf fQs L lb different Fi r Qb2b for 41 2 Division of a stream diverging double wye cband Ccs are determined tentatively by diagrams 721 and 723 No 1 as for diverging wyes 293 Section VII Double wye of type Fib F2h Fs Fe a 300 continued Diagram 732 ub QIbIQe QsQc Q1ib Fib 02 05 10 036 051 159 289 438 610 Ccb 10 10 027 051 141 212 291 20 10 027 011 072 Cc s 05 and 20 381 251 181 120 086 044 013 008 018 014 0 10 334 253 181 120 071 032 005 012 018 014 0 Fib b04 Fe 05 0 049 003 040 075 106 144 Ccb 10 10 038 010 040 051 034 20 10 025 001 042 cs 05 and 02 142 097 058 026 002 015 026 030 026 017 0 10 116 076 048 014 007 021 030 031 027 017 0 Fib 05 10 051 010 025 050 065 068 cb 10 10 038 008 045 042 025 20 10 021 015 008 Ccs 05 and 20 062 032 007 013 027 035 039 037 029 017 0 10 045 018 004 021 033 039 041 039 030 018 0 Fib 05 10 051 011 022 043 055 055 048 Ccb 10 10 037 010 040 051 038 20 10 017 031 028 05 and 20 003 021 034 045 050 052 049 043 032 018 0 C 10 013 029 041 049 054 054 051 044 032 018 0 v 294 Section VII Double wye of type Fib b FSF 450 Diagram 733 1 Junction of streams converging double wye a branch AHb Qib c 8 Q bY 12 4 1 Qb QcbV b Q LiQb QibN is determined from the curves ctb for different Fib For the second branch interchange subscripts 1 and 2 4 07C C Z 4 DI I 00 b main passage Qs CcsI 2 s Q a s Q Q VO W QIo 2c9 Q o Y 075 025 e b Q 1 t is determined from the curves ICs iQ 9bfor different Is lb Q lb f r d ff r n Fib 2 Division of a stream diverging double wye 4cband cs are determined tentatively by diagrams 721 723No 1 as for diverging wyes 295 Section VII Double wye of type FibF2 b F F 450 continued Diagram 733 Q2b QIbQc QsIQc Qb0 01 02 03 04 05 06 07 0 09 1 Fib 2 05 10 036 059 177 320 488 679 Ccb 10 10 024 063 170 264 373 20 10 019 021 004 05 and 20 292 187 129 080 056 023 001 016 022 015 0 10 254 1 87 130 080 042 012 008 020 022 015 0 Fib 704 PC 05 10 048 002 058 092 131 163 Ccb 10 10 036 017 055 072 078 20 10 018 016 006 05 and 20 098 061 030 005 014 026 033 034 028 017 0 CS 10 077 044 016 005 021 031 036 035 029 017 0 Fib Fc 06 05 10 050 007 031 060 082 092 Ccb 10 10 037 012 055 060 052 20 10 018 026 016 Ccs 05 and 20 032 008 011 027 037 043 044 040 031 018 0 10 018 004 021 034 042 046 046 041 031 018 0 Fib 05 10 051 009 025 050 065 064 Ccb 10 10 037 013 046 061 054 20 0 015 038 042 05 and 20 011 036 046 053 057 056 052 044 033 018 0 10 029 042 051 057 059 058 054 045 033 018 0 ID iU 296 Section VII Double wye of type Fib F1b Fs Fe a 600 1 Junction of streams converging double wye a branch AHflb Ql F Qlbý cb b LI IL 8 29 Qc Obl O bQrbY 4 Q2b QIb 1Q Q QIQýF is determined from the curves Ccb f b for different Fbb PC For the second branch interchange subscripts I and 2 b main passage Qs AHs aQb QC t YWQC Q QN is determined from the curves Cc s 1 Q b for different Qb CFe 2 Division of a stream diverging double wye Ccband Ccs are determined tentatively by diagrams 721 and 723 No 1 as for diverging wyes 297 Section VII Double wyeof type Fib F 2b Fs Fe a 600 continued Diagram 734 4 Fib T02 05 10 031 059 200 362 554 772 Ccb 10 10 020 080 207 330 477 20 10 009 062 097 Cc 05 and 20 177 102 064 030 015 006 020 026 026 016 0 Cs 10 150 1103 064 030 1005 013 024 029 026 016 0 05 10 047 006 060 112 163 210 Ccb 10 10 034 025 073 110 131 20 10 015 027 041 05 and 20 040 014 007 024 035 041 042 039 030 018 0 CcS 10 025 002 016 031 040 044 045 040 031 018 0 Fib06 05 10 050 004 038 074 103 123 Cc b 10 10 036 018 067 082 087 20 10 015 040 047 CCs 05 and 20 006 023 036 046 051 052 05 043 032 018 0 10 016 032 043 051 055 055 051 044 033 018 0 Fib 05 10 050 007 030 058 079 088 Ccb 10 10 036 016 053 074 075 20 10 013 046 061 Ccs 05 and 20 044 054 060 065 065 062 056 047 034 018 0 10 050 059 064 067 067 063 057 047 034 018 0 U 298 C Cross of type Fib PF 900 Section VII Diagram 735 1 Junction of streams converging cross anch AHlb QbFQIb Cfcb 14 V 8 Qv ýFlb 2g is determined from the curves 4Icb t b for different Ftb For the second branch interchange subscripts 1 and 2 b main passage I Qs V 2 0 0759 4 Qs is determined from the curves Qs for ttb ditferent Qs For standard malleableiron crosses at 07 hits Qs Cs W c 2S I j 2 Division of a stream diverging cross a csand cb are determined tentatively by diagrams721 and 723 No 1 as for diverging wyes 299 Section VII Cross of typeFlhF21 FF a 900 clontinued Diagram 735 Fib 02 05 085 010 109 272 477 725 101 Ccc b 10 085 5 135 312 500 740 20 j085 031 177 337 Flb04 PC 05 085 029 034 103 177 256 337 1 CCb 10 085 014 060 133 205 20 085 012 102 168 Fib 086 0 08 03 102 2 12 0 21 Ccb 10 085 018 046I 102 150I 185 1 I I I I 20 085 009 o 88 137 I I I Fib 06 Fc 05 085 033 023 061 102 138 26131 Ccb 10 085 018 0416 091 153 154 1 I I 20 085 008 083 126 1 I Fib 10 Fe 05 085 034 013 056 093 125 168 cb 10 085 019 039 086 121 140 20 085 0087 081 121 Fib Q2b 112 5 03 8 0056 2r a025 13 0 Qlý 300 Section VII Wye of type F 2F Diagram 736 1 Junction of streams converging wye s b rI 1 Qi Q a a 15 b 73 07uQ 37I 264 b 30 CIcbýHr 6 025 Q j 3 I S230 2g C a45 Cicb L 5 61b0 5 0 bb0 Q 2 Q K Q W C 4 2021b 180L Q 2 Division diverging wye AHib 4icbý is determined tentatively by diagram 723 as for an ordinary wye of type Y9 FF Fb Values of CIcb QabIQe 0 010 020 030 040 050 060 070 080 090 10 15 256 189 130 077 030 010 041 067 085 097 104 30 205 151 100 053 010 028 069 091 109 137 155 45 130 093 055 016 020 056 092 126 161 195 230 100 1000 do U q 0 6 08 fo 20 30 301 Section VII Header with transition stretches Diagram 737 AHb oib is determined from the curves b where wII1 s mean velocity in the header before the Ith branch 404 06 08 10 20 30 40 50 Stream direction in the header a U 1 Branch at side L Cib 430 160 088 060 024 020 019 018 a I Brac a2 Branch at top or bottom 1 lranch at side 1 Cib 300 180 143 092 090 112 167 d 2 Branch at top or bottom Dimensions of the different headers h height of the header section Header D A Iffy A B L R r a 0609h 7D D 113D h 1 15125h 0 30045h 115h 0609h 0lh 6 c 0609h 17D D 02D d 1 15125h 0 35045h 115125h 0609h 0609h 0304h 28 20 0 8 b 10 2 5 20 24 28 12 35 9 f5 f 8 S A 302 Passage through a side opening of a header pipe of Section VII constant cross section Diagram 738 collecting converging pipe a distributing diverging pipe AH esL resistance coefficient of the transition between 2g two openings is determined from the curves Wcs e corresponding to different and different Nt where 2g where st static pressure in section 1I Values of Ccs imb 06 o 8 10 1 12 1 14 16 1 18 1 20 1 25 3 1 40 50 alb 10 5 098 096 091 084 074 056 038 016 15 093 096 092 088 082 074 052 028 30 100 102 098 096 094 090 083 074 050 022 50 102 102 101 100 098 096 092 084 068 051 ab 20 5 115 010 104 093 078 060 040 020 5 120 116 102 102 094 086 065 044 30 136 130 124 118 112 107 094 080 052 025 50 140 136 131 126 116 104 093 071 052 ab 30 5 121 110 098 083 064 045 020 15 134 125 116 107 098 089 064 039 30 146 140 134 127 122 117 110 086 057 028 50 152 146 141 136 131 125 112 100 075 055 303 Section VII Passage through a side opening of a header pipe of constant cross section Diagram 739 POOLP AH S resistance coefficient of the transition 2g between two openings is determined from the curves Ccs C corresponding to diffeient 7F and diffeient o 1 whereutt total pressure in section 11 29 hQ v2 a22 NI 0 as2 0 1 02 ot 02 03 I 03 0 f L Values of Ob tot G 06 06 Io0 12 14 1 16 1 18 20 1 25 130 40 8 0 alb 10 5 014 007 004 002 000 15 037 025 020 017 014 012 010 006 003 30 059 052 046 042 037 034 031 028 022 018 011 005 50 057 052 048 045 042 039 033 029 021 016 alb 20 15 30 50 014 058 007 004 002 001 000 035 025 020 016 014 012 010 007 005 002 050 045 040 037 033 030 028 022 018 010 005 056 051 047 044 042 039 037 031 028 021 016 ab 30 15 005 0 0 003 006 009 011 013 017 30 0O0015 011 0OSl 005 003 000005009015020 50 027022 019 0151 013 010 007 002 00000508 4 is as6 08 1O 3 304 A Section Eight FLOW PAST OBSTRUCTIONS UNIFORMLY DISTRIBUTED OVER CONDUIT CROSS SECTIONS Resistance coefficients of grids screens pipe bundles packings etc 81 LIST OF SYMBOLS FP F3 flow area of the obstruction crosssection and area of the conduit section before the obstruction respectively m2 2 Fg area of the obstruction front m2 area of one opening of the grid or screen inm cross section coefficient io perimeter of the section m De conduitsection diameter m Dh hydraulic diameter of the conduit m do diameter of the section of a perforatedplate orifice m dh hydraulic diameter of the orifices of an obstruction or of the pores of a layer of loose or bulk material etc m din dout inner and outer diameter of the tubes of a bundle of rings etc m dgr diameter of a spherical grain m d bar thickness m a width of the gap of a bar grate radius of the orifices of a disk plate m I depth of the orifices of a grid wall thickness at the place of the orifice of the gaps of a bar grate m 1 thickness of a porous layer total length of a transverse bundle of tubes of a packing of plates m S S vertical and horizontal distances between the axes of adjacent bars of a grate tubes in a bundle etc and also between the orifices of a perforated plate m S diagonal distances between the orifices of a perforated plate m 2 angle of attack of the bar in a bar grate angle of inclination of the bar of a bar grate of the tubes of a tube bundle toward the stream and also of the orifices in the case of their checker board arrangement in a perforated plate W w mean velocities of the stream in the gap of the obstruction grid grate screen bundle of tubes layer etc and in the conduit in front of the obstruction respectively msec Woin Woex mean stream velocities in the gap at the inlet of the obstruction and at the exit from it msec WIre Worn mean stream velocities before the obstruction and in its cross section 4dependent on the arithmeticmean stream temperature along this obstruction inmsec AH pressure loss resistance kgm 2 T specific gravity in kgm 3 of the flowing medium in any section Tin specific gravity in the inlet sectionof the obstruction Tex specific gravity in the exit section of the obstruction 305 Tm specific gravity dependent on the arithmeticmean temperature To specific gravity at t 0C t temperature of the flowing medium in any section 0 C tin temperature in the inlet section of the obstruction C tex temperature in the exit section of the obstruction C tm arithmeticmean temperature over the entire depth of the obstruction bundle layer etc C a jetcontraction coefficient at any area ratio F F 6 jetcontraction coefficient of a sharpedged orifice at F 0 porosity percentage of pores free volume of a porous medium resistance coefficient of the obstruction At additional resistance coefficient allowing for the pressure loss at the change of stream velocity as a result of a change in its specific gravity with temperature 2 friction coefficient of the conduit orifice or thickness of the layer depends on Reynolds number and relative roughness for a conduit Re Rem Reynolds number and average Reynolds number obtained from the arithmeticmean temperature of the stream along the obstruction M Mach number 82 EXPLANATIONS AND RECOMMENDATIONS 1 Grids screens layers cloths checkerboards etc made from Raschig rings bulk material or arrays of tubes all represent obstructions distributed uniformly over a conduit section 2 A plane grid placed in a straight pipe has the same resistance effect as an orifice plate the stream contracts during its passage through the grid orifices and its exit velocity is higher than its inlet velocity Losses result which are connected both with the entrance to an orifice and with the sudden expansion at its exit Figu 81 A 77r I I hsp a b lt FIGURE 81 Pattern of flow through FIGURE 82 Icsigning a perforated grid FIGURE 83 Screen plates il a grid or screen aorifices in vertical columns borifices staggered a rectification column 306 The resistance coefficient of a plane thinwalled grid is a function of its cross section coefficient f g Fg grid frontal area the shape of its orifice edges and the Reynolds number Re ao It is calculated by the same formulas as V a restrictor ie by formulas 424 and 426 to 430 respectively 3 The stream velocity in the narrowest section of the jets passing through the grid can turn out to be very high at small values of 7 even at low inlet velocities and in some cases approaches the velocity of sound Under such conditions the resistance coefficient of the grid becomes a function of the Mach number M This is expressed by the formula 81 2g where kM is the corrective coefficient for the influence of the Mach number and is determined on the basis of the data of 859 this coefficient has been plotted in diagram 8 7 C is determined as in the case M 0 ie by the formulas given in Section IV 4 The following relationships between the number of orifices z their transverse S and longitudinal S pitches the orifice diameter d0 and the crosssection co efficient of the grid f are usefulwhen designing perforated grids 1 number of orifices 1 g 82 2 distance between the orifices when these are a arranged in vertical columns Figure 82 a 0 785d S 283 s2T and 0785d4 2S 0 84 where 83 is used when the pitch S is known and formula 84 when the pitch S is known in the particular case Slsy S 89d 85 307 b staggered at an angle 0 Figure 82b S 125dYtg 0 86 and s 0625d 87 ITtgo In the particular case of equal distances between the orifices in the vertical and diagonal directions S1S 030P it follows s1 o95d 88 and s 0o82d 89 In the case SS we obtain once more formula 85 5 The resistance coefficients of screens are calculated by the following formula cf 819 and 820 C w k 1 F0 810 Here k 13 according to Adamovs data for screens made from circular metal wire not perfectly clean but with normal surface state neither rusty nor dusty k 10 for new wire screens and k0 21 for silkthread screens according to Khanzhonkovs data 854 The resistance coefficient of circularwire screens is a function of the Reynolds number for Re 400 the resistance coefficient of silkthread screens isafunctionoftheReynolds number for Re 0 M 150 See diagram 86 The influence of the Reynolds number can be allowed for by the formula C Re kRec 811 where C is determined by formula 810 kRe is determined from diagram 86 as a func tion of the Reynolds number At small values of the crosssection coefficient the velocity in the screen orifices can approach the velocity of sound The influence of the Mach number M is allowed a 308 for here by the formula cM AHke 812 where kM is the corrective coefficient allowing for the influence of the Mach number its value has beenplotted indiagram88 on the basis of Cornell s experimental data 859 6 The installation of two screens close to each other theoretically should not lead to an increase in resistance since if the wires of the two screens are accurately super posed the result is equivalent to one screen of doubled wire thickness in the stream direction Actually however the superposition is never quite so accurate and the result is always a certain decrease of crosssection area as compared to that of a single screen It follows that the resistance will increase but rarely by a factor of two When the two screens are however installed at a distance from each other larger than 15 wire diameters the resistance is doubled Therefore in practical calculations the total resistance of screens mounted in series can be considered as equal to the sum of the resistance coefficients of the separate screens S 813 where z is the number of screens 7 When grids or screens are used as bubbling plates in apparatus where a process of mass exchange takes place rectification and sorption columns gas moisteners etc Figure 83 their resistance depends upon two factors One is the type of work of the plate dry wetted by the motion of a liquid column with or without bubbling and the other is the physical properties of the working media and plate dimensions 8 The resistance coefficient of a dry plate is determined from the data given under points 2 and 5 as for an ordinary grid or screen The resistance of a wetted plate with small orifices is higher than the resistance of a dry plate since a liquid film forms in the orifices whose tearing requires the ex penditure of a certain amount of energy by the fluid stream passing through the orifices The resistance coefficient of a wetted plate with small orifices can be calculated by the following formula proposed by Usyukin and Aksel rod 850 2 2 104 sa0 814 Cdr gUo W 2g 2g where Cdr resistance coefficient of a dry plate determined from diagrams 81 to 86 as C for an ordinary grid a surfacetension coefficient of a liquid at the boundary between the gaseous and liquid phases kgm Yg specific gravity of the gas kgm 2 a radius of a circular orifice or width of a slit in the plate m Under normal operating conditions the resistance coefficient of a plate with bubbling can be calculated by another formula proposed by the same authors 210 AH IF 2 7ý 815 2g 2g 2g 2g 309 where y and yi are the specific gravities of water and the working liquid kgm 3 hs pI Iare height and length of the spilling partition of the plate m 9 The resistance coefficient of bubbling plates without special spilling devices can be calculated with sufficient accuracy for technical calculations by the following formula proposed by Dilman Darovskikh Aerov and Akselrod 810 4 C AH 2C FF0 2 I 4ý 816 where I is the fraction of the cross section of the plate slots through which the liquid flows down this is calculated by the following formula from the same authors 0 Cdr 05 817 05 where G0 LO mass flow per unit area of gas and liquid respectively kgm 2 p1 is the discharge coefficient of the fluid through the slot orifice of the plate 10 Just as for ordinary thickened grids the total losses through bar gratings of different bar cross sections cf diagrams 89 and 810 are comprised of entrance losses frictional losses and losses with sudden expansion at the exit from the section between the bars in the grating The resistance coefficient of gratings at 5 and 05 can d S be determined by Kirschmers formula 861 C Pk sin O 818 where is the coefficient of bar shape determined from Table 82 of diagram 89 k S 4 819 8 is the angle of inclination of the bar toward the stream The resistance coefficient of gratings can be determined approximately at any value of the ratio and any relative grating thickness by the formula Sa 0 4t sin 0 820 2g 310 where P is the coefficient of bar shape determined from Table 82 of diagram 89 on the basis of Kirschmers data 861 Eis the resistance coefficient of an ordinary grid or orifice plate with thickedged orifices determined by formula 427 or from the graph of diagram 84 a S I are gap width distance between the axes of adjacent bars and bar thickness in the stream direction m 11 The resistance coefficient of a bar grating of arbitrary bar cross section placecA immediately behind a stream turn at an angle of attack a is determined for L 05 Si from the relation cf Spandler 862 C AH 0821 2g where a is a coefficient depending almost entirely on the angle of attack a and de determined for given bar shape from graph a diagram 810 0 is acoefficient depending on the angle of attack a and the crosssection coefficient and is determined from graph b diagram 810 12 The resistance coefficients of bar gratings used in hydro structures turn out to be higher than the ones determined by these formulas due to fouling and to design peculiarities of the gratings Accordingly it is recommended cf Dulnev 811 to introduce a correction coefficient c into formulas 818 820 and 821 whose value is to be determined as a function of the nature and amount of flotsam contained in the water method of cleaning the grating possibility of deposition of silt before the grating etc In the case of mechanical cleaning of the gratings C 1113 and in the case of manual cleaning c 1520 In order to allow for design peculiarities the same author recommends the intro duction into the formulas of an additional corrective coefficient C 1C 1 822 where L internal height of the grating m A total height of the transverse elements Ahzdz m hand z are height and number of intermediate support bars d and z are diameter and number of bracing elements 13 The tube bundles of heat exchangers are laid out either in a parallel or in a stag gered arrangement In the first instance the following pattern of flow is observed cf Abramovich 81 Jets flow out of the space between the tubes of the first row and enter the space between the rows Figure 84 Here further massesfrom the shaded regions are mixed with the main stream core Upon reaching the second row of tubes the jets divide The main core passes past the second row of tubes while the added masses form a closed stream circulation or eddy zone in the shaded regions The pattern of flow in the spaces between the succeeding rows is similar to the one just described Thus the pressure losses in an array of tubes are similarto losses in a free jet Actually the flow bccomes turbulcni after passing the first row of tubes and the conditions of flow past the succeeding rows arc somewhat altered as a result 311 7 7 a b FIGURE 84 Arrangement of tubes a vertical columns b staggered 14 The resistance coefficient of a bundle of staggered tubes including thelosses at inlet and exit canbe calculated at 3 10Rem10s by the following formulas proposed by MochanandRevzin 841 1 S 2 0 and 014 tdout 17 out s2 dout 32 23 OmW S dout dout 2g 2S 20 and 014 ou 17 2 dout gS2 d 0 u AH 2 Re e 2 7z1 824 tV mO2 MMz0 3 L 10 and 17 Std u 52 2g dout S dout H 044 otou 1 ReOv z1 825 Tmm m where 2g 273 Im 6 W0rn 1 WOin 07F73 8in6 tif tex 827 2 t 828 1 e Wmdout 829 v is determined by 13 b for the arithmeticmean temperature tm 15 The resistance coefficient of a bundle of vertically arranged tubes including the losses at inlet and exit can be calculated at 3 10 Rem 10 by the following formulas q 312 proposed by Mochan and Revzin 841h SI Sa 1 dout t AH S tdout 02 S 02 2 152 o z 830 2g 2 d00 dut Al 068 0s 5 02 a l 0 2 s do u t 0 9 o e S S s d j o83o m2o 032 Z m e udtt 2gM If the pitch varies within the limits of the bundle the resistance is calculated by its mean value 16 If heat exchange takes place in a tube bundle it is necessary to add to values of C obtained by formulas 823 to 825 830 and 831 a term AC to allow for the pressure loss accompanying change in rate of flow of the stream within the bundle and which is caused by a change in the specific gravity of the working medium cf Mikheev 840 A x tin 832 273tm A is positive in the case of heating and negative in the case of cooling 17 When the flow is obliquely directed toward the tube bundle the conditions of flow past the pipes are improved and its resistance is smaller cf Kazakevich 824 The resistance reduction ratio the coefficient of stream direction is a function both of the angle of inclination 0 and of the other parameters of the bundle For practical calculations however the influence of other parameters can be neglected and the mean value of q can be considered constant for a given inclination angle These mean values of j are 1 Vertical columns 2 Staggered 0 60 4 082 0 60 4 080 S450 5 054 0 45 057 0 z 30 030 6 30 4i034 18 Ribbed or finned tubes are frequently used to increase the surface of heating or cooling and streamlined tubes in order to decrease the resistance of the tube bundle to cross flow Data for the determination of the resistance coefficients of such tubes in bundles are given in diagrams 813 and 814 19 Three main flow states exist in the case of stream passage through porous media molecular laminar and turbulent The state of flow is molecular when the pore dimensions are equivalent to the freepath length of the molecules of the order of tenths of a micron Laminar flow is subject to the PoiseuilleHagen law which can be written in the case of a porous medium in the form sd2AH 833 UP j 3 t2 V 313 or in Darcys form Wa All 834 where K isthe seepage coefficient Y is the permeability this magnitude is constant for a given porous medium and does not depend on the nature of the flowing medium It coefficient of twisting of the pores dh 4 hydraulic diameter 0 3 of the pores m a porosity free volume fraction S specific surface of the porous medium m 2m 3 t0 layer thickness m ltr true length of the pores m 71 dynamic viscosity kgX secm 2 20 A distinctive feature of porous media is the gradual transition from laminar to turbulent flow starting at low values of Reynolds number and extending over a wide range of values of it The smooth character of the transition is explained by the twisting of the pores the contractions and expansions and also by the roughness of the porous surface which contribute to formation of eddies and stream disturbances It is also helped by a gradual propagation of turbulence from large pores toward the smaller ones which is connected with the distribution of the different sizes of pores in the media 21 Porous media can be classified into three main groups 1 bonded or cemented media such as porous ceramics porous metal 2 loose or bulk media such as powders various bulk materials packings made from regular geometric shapes spheres cylinders rings 3 regular media such as grid screen or chord packings sieves tubes corrugated strips etc 22 The porosity and magnitude of the gaps crosssection coefficient in a layer made from identical spherical bodies are independent of the grain diameter they are a function of the mutual disposition of the grains ie of the angle 0 Figure 85 c 1 3 835 6i cosO V1 2cose and 4sin 0 where e porosity m 3m 3 The extreme values of 0 are equal to 60 and 900 The values of the theoretical porosity a and off in this range of values of 6 are given in Table 81 FIGURE 85 Arrangement of spheri cal bodies in a layer 314 TABLE 81 W W02 167 j111 W MW 67210 1 0170 7128P 7403 J 210 I Mea I WOO a 0259 026 028 030 032 034 036 038 040 042 044 046 0476 f 00931 00977 01045 01155 01266 01337 01491 01605 01719 01832 01946j 02057 02146 The value of a for bodies of irregular shape is determined experimentally The value of Fcan be expressed as a function of the porosity by the following approximate formula proposed by Bernshtein Pomerantsev and Shagalova 88 Tf095 75o 837 23 The resistance coefficient of both a loose layer of granular bodies and of cemented porous media of granular material of constant diameter d with relative layer 1 thickness Kr can be calculated by the following formula proposed by Bernshtein Pomerantsev and Shagalova 8 8 C AHT3 o3 kl 2 L 838 y 71 A2 eReO7I dg dgr dgr where I is the friction coefficient ofalayer thickness equal to the grain diameter gr k 153 839 Re 3O 03 840 e dh 045 wldgr 841 dh 0423 dgr 842 dt is the hydraulic diameter of the narrowest interval between spheres m dgr is the grain sphere diameter m 1 layer thickness m 24 The resistance coefficient of a layer made from bodies of any regular shape except those listed in diagram 816 can be calculated by the following formula of Bernshtein Pomerantsev and Shagalova 88 A 53 15 15 1 kV 843 wr 12 5Re 7 5 1 2g where Re and dh are determined by formulas 841 and 842 315 25 The resistance coefficient of the materials listed in diagram 816 and of bonded porous media made from bodies of irregular shape is calculated by the formula Aff I 0 844 wdh where according to the data of Ishkin and Kaganer 823at Rehh3 180 845 Reh and at Re3 1L64 7 846 Reh R eo The value of dh here is taken from the data of diagram 816 26 The resistance of regular porous media such as Raschig rings packed in regular rows cf diagram 820 and of chord packing from wooden laths laid in parallel cf diagram 821 is mainly determined by the frictional pressurelosses in the absence of wetting the liquid The resistance coefficient of such packing can be calculated by 844 where accordingto Zhavoronkovs data 812 1 312 847 for 04 10 Re h 8 I and I 01 const 848 wd h 1 4c forRe8103 Here Reil d is the hydraulic diameter of the gap between the rings m S is the specific surface of ailll rings m 2 m3 27 The resistancb of Raschig rinigs in a staggered arrangement cf diagram 820 and of chord packing placed crosswi I c 0f diagram 321 is determined in the absence of wetting by the liquid boilt by the frictional losses and by the losses accompanying the sudden contraction and xpalsion of the stream at the places of inter section of the packing I tic rasoi fur the sCpMattc trattl Oft 0fthe11 11 3Ud Is IUC to HtIh ir orsitv it Ho t s h i clh orreC Lty dcterntl cd Zhau voron kovs ti pxcriu vns iS 2 Also eithler 1hC sizC ol O1W bodice is solmcti iws iorwim or it is impossibic to determine it Formtulas 15 anld 1 j M for I il e with thie i a s of g I il ic crigmal rcfer nIccs 316 dout 28 The resistance coefficient of ceramic Raschig rings of diameter ratio 712 and In relative height 1l0 laid in a staggered pattern can be determined by 844 where dout according to Zhavoronkov 812 S92 849 ReO37 for 04 103 Reh 6 10 1 and 1 037 const 850 for Reh 6 l03 Formulas 849 and 850 can be extended with a certain approximation to rings of other dimensions 29 The resistance coefficient of chord packings laid crosswise is calculated by 844 where according to Zhavoronkov 812 36 k851 for 04 101Reh6 l10 and const 852 for Reh610 where k and A are taken as functions of the grid geometry cf diagram 821 30 The resistance to the motion of a gas stream in a wetted packing is consider ably larger than in a dry packing The increase in the resistance is due both to the reduction of the free crosssection area by the liquid stream and to the bubbling of the gas through the liquid retained in the stagnant zones of the packing The influence of the intensity of wetting on the resistance increases with the decrease of the size of the elements in the packing Three states of flow are observed in the case of gas motion by a countercurrent through a wetted packing a stable where the liquid flows down completely b un stable in which there occurs at first a retention of the liquid and c a reverse motion of the liquid leading to flooding and ejection of the liquid from the packing together with the gas Retention of and flooding by the liquid occur at a velocity of the gas stream which is the lower the larger the intensity of wetting Aof the packing cf Zhavoronkov 812 31 The resistance coefficient of a wetted packing ordered or disordered up to the beginning of the retention of the liquid ie at a velocitywAW11i can be approxi mately calculated for A 50m 3 m 2Xhour by the following simplified formula based on Zhavoronkovs data 812 C dr tA 853 Y g 317 where Cdr resistance coefficient of a dry packing determined as C from 838 to 852 A is the intensity of wettingof the packing by the liquid m 3m 2 Xhour I is a co efficient allowing for the influence of the type of packing on the resistance increase as a result of the wetting it is given in diagram 821 for different types of packing wilim is the limiting velocity of the gas stream in the free section of the apparatus before the packing at which the retention of the liquid starts the values of Wlhim are given in diagrams 816 820 and 821 32 The resistance of packings can increase sharply by a factor of two to three or more if the gas passing through them is impure this should he taken into account in the hydraulic calculation 33 The resistance coefficient of regenerative packings serving for heat recovery in heating and other systems depends on the type of packing Formulas for calculating the resistance coefficients of such packings are given in diagram 822 34 Where the gas temperature changes as a result of its passage through the packing the additional term 832 should be included in the formula for the resistance coefficient Al 854 where C is determined by formulas 838 to 852 273tm tin texI m 273 ti in 2 273 Womdh WImdh l Reg where v is takencf 13 b as a function of the arithmeticmean temperature týn 318 83 LIST OF THE DIAGRAMS OF RESISTANCE SECTION VIII COEFFICIENTS OF Noof Diagram description Source idiagran 1 Note Plane grid perforated sheet with sharpedged orifices Ldh 00 015 Re10 Plane grid perforated sheet with sharpedged orifices ildh 00 015 Re1O Grid with orifice edges beveled facing the flow or made from angle iron Re10 4 rhickened grid perforateu plate or laths Iidh 0 015 Grid with roundedorifice edges Re10 3 Screens Grids with sharpedged inlet in the orifice of a wall of arbitrary thickness at high stream velocities large Mach numbers Grids with orifice edges beveled or rounded and screens at high stream velocities large Mach numbers Bar grating with an angle of approach ac 0 Re104 Bar grating with an angle of approach a 0 and 05 Re1O4 Bundle of circular tubes in vertical columns 3X1 0Rem 1 5O Bundle of staggered circular tubes 3X1 0 3 Rem 105 Bundle of ribbed tubes air heater Bundles of tubes of different crosssection shapes Recuperators air heaters Packing material deposited at random loose layers from bodies of irregular shape at given dh dry and wetted Packing material deposited at random loose layers from bodies of irregular shape at given dgr ldelchik 819 820 822 The same Adamov Idelchik 819 Khanzhonkov 854 Cornell 859 The same Dulnev 811ldelchik 819 Kirschmer 861 Spandler 862 The same Mochan and Revzina 841 The same Antufev and Beletskii 84 Timofeev and Karasina 848 Shcherbakov and Zhirnov858 Antufev and Beletskii Sknar Telegina 84 Tulin 849 Kuznetsov and Shcherbakov 830 Shcherbakov and Zhirnov 858 lshkin and Kaganer 823 Zhavoronkov 812 The same 81 82 83 84 85 86 87 88 89 810 811 812 813 814 815 816 817 Calculating formula and partially experillicilts The same Calculating formula Experimental data and calculating formula The same Screens experimental data grids approximately Experimental data calculating formula as for an ordinary grid The same Calculating formulas based on experimental data The same la 319 continued lIagrai ironNoof Nt Diagram description Source dia gramNote Packings loose layer of spherical granular 8ernshtein Pomerantsev and 818 Calculating formulas based on bodies or porous cemented layer from Shagalova 88 experimental data granular material constant diameter Packings bonded porous medium non Ishkin and Kaganer823 819 The same gran ular Packings ceramic Raschig rings Zhavoronkov 812 820 Out z01 dry or wetted Packings of wooden laths dry or wetted The same 821 Regenerator checkerwork of furnaces Linchevskii 836 822 41p i4 4 320 84 DIAGRAMS OF RESISTANCE COEFFICIENTS Plane grid perforated sheet with sharpedged orifices Section VIII 0 001s Re 105 Diagram 81 Grid is determined from the curve F f or from the table 21 003 004 005 006 008 010 012 014 OAtS j016 020 C1 7000 31 l 16701 105170 40 2516 1 60655 EJ 406 320 268 223 182 1156 131 116 955 2 66 j4 Tl 050 1 052 10855 060 1 065 1070 1075 1080 10115 1 0900 6 1 10 4140 1348 I 285 I 200 1 141 1097 o 1 065 1 042 I25 01 o 05 10 5 41I 9 I 065 I 042 I 025I 013 I 005 I000 C 0 fffftJ fa 111111 X 4V 41 057 02 02 UT dh T0 4f perimeter dh U fo orifice area F0 total flow area of grid v is taken from 13 b al A2i ii j ON 08 U7 0L 321 Plane grid perforated sheet with sharpedged orifices Section VIII tdj C 0015 Re 2 Diagram 8 2 dh V 0 Grid AN e FiI j capproxim ately 2g where C is determined from the curves f Re for different Ton graph a oRe is determined from eOR 1e on grapha I 0707 1 VT is determinated from the curve C on graph b a 201 f4f fer 5 d0 Re 125101 410 1610 10 I 210 0 10 2I 0 41 1 10 24IP 1P 2a14P I10 se 034jos 10710110421046 j053 1059 06410741 j94j6 77 Values of 0 194 138 114 089 069 064 039 030 022 015 011 004 001 0 02 178 136 105 085 067 057 036 026 020 013 009 003 001 0 03 157 116 088 075 057 043 030 022 017 010 007 002 001 0 04 135 099 079 057 040 028 019 014 010 006 004 002 001 0 05 110 075 055 034 019 012 007 005 003 002 001 0o1 001 0 06 085 056 030 019 010 006 003 002 001 001 0 0 0 0 07 058 037 023 Oi11 006 003 002 001 0 0 0 0 0 0 08 040 024 013 006 003 002 001 0 0 0 0 0 0 0 09 020 013 008 003 001 0 0 0 0 0 0 0 0 0 095 003 003 002 0 0 0 0 0 0 0 0 0 0 0 107A nI 4y dh j T1 perimeters F is taken from 13 b V a a sag2 7 I0 42p5 a W 8 tO t6 1 2 10 0 av f 2 43 e 41 s A0 48 Is to b r F o0 1 01 0 2 1 314 1 05 06 07 1 08 09 1 10 CO 1 171 1167 11631 159115511501145113911321122110 322 V 322 Grid with orifice edges beveled facing the flow or made Section VIII from angle iron ReO Diagram 83 Corners Grid H il 1 2 2g where V f is taken from the table or more accurately from graph a of diagram 412 The values of c are determined from the curves or taken from the table v is taken from 13 b Values of C oh02 1 o04 006 1d 1 oo 1 015 0o2 0 025 030o 040 050 060 1 0 0 0o 00 1 0 001 046 6800 1650 710 386 238 968 495 286 179 790 384 192 092 040 012 0 002 042 6540 1590 683 371 230 932 477 275 172 760 368 183 088 038 012 0 003 038 6310 1530 657 357 220 894 457 264 165 725 350 172 083 035 011 0 004 035 6130 1480 636 345 214 865 442 256 158 700 336 167 080 034 010 0 006 029 5750 1385 600 323 200 800 412 234 146 685 308 153 073 030 009 0 008 023 5300 1275 549 298 184 743 378 218 135 592 280 137 064 027 008 0 012 016 4730 1 140 490 265 164 660 335 192 119 518 244 118 055 022 006 0 016 013 4460 1080 462 251 154 620 316 181 112 480 228 110 050 020 005 0 r Uperimeter F 323 Section VIII Thickened grid perforated plate or laths 0oi5 Sion VaII Diagram 84 Grid zit dh I o perimeter no Re 10 05V where c is takenfrom the table or more accurately fromthegraphofdiagram 411 05 tV1 1 7 Ir A A is determined from diagrams 21 to 25 as a function of Re and A D11 At 002 the values of C are determined from the curves f corresponding todifferent I or from the table v is taken from 13 b Ais taken from Table 21 2 Re 0 approximately 2e where is determined as at Re105 and 7IRe cf diagram 82 324 Section VIII Thickened grid perforated plate or laths 001o continued h Diagram 84 Values of 4 002 004 6o o08 1010 015 0 A 0o30 i Ioo 040 0Io Ioo 1 I 1 0 135 7000 1670 730 400 245 960 515 300 182 825 400 200 097 042 013 0 02 122 6600 1600 687 374 230 940 480 280 174 7 70 375 187 091 040 013 001 04 110 6310 1530 660 356 221 890 460 265 166 740 360 180 088 039 013 001 06 084 5700 1380 590 322 199 810 420 240 150 660 320 160 080 036 013 001 08 042 4680 1130 486 264 164 660 340 196 122 550 270 1 34 066 031 012 002 10 024 4260 1030 443 240 149 600 310 178 I11I 500 240 120 061 029 011 002 14 010 3930 950 408 221 137 556 284 164 103 460 225 115 058 028 011 003 20 002 3770 910 391 212 134 530 274 158 990 440 220 113 058 028 012 004 30 0 3765 913 392 214 132 535 275 159 100 450 224 117 061 031 015 006 40 0 3775 930 400 215 132 538 277 16 2 100 460 225 120 064 035 016 006 50 0 3850 136 400 220 133 555 285 165 105 475 240 128 069 U37 019 010 60 0 3870 940 400 222 133 558 285 166 105 480 242 132 070 040 021 012 70 0 4000 950 405 230 135 559 290 170 109 500 2 50 138 074 043 023 014 80 0 4000 965 410 236 137 560 300 172 111 510 258 145 080 045 025 016 90 0 4080 985 420 240 140 570 300 174 114 530 262 150 082 050 028 018 10 0 4110 1000 430 245 146 597 310 182 115 540 280 157 089 053 032 020 c 0 4 z jM 4 N wJ21 r I I F F F I I F I I N m sm 4 10 W a I 96 4V I U I 4 4 4 4 4 4 4 4 4 A 4 I 4 J I I 4 I IH fir1 h u I 2 3 7 8 to y 325 Gwh3 Section VIII Grid with rounded orifice edges Re 3101 Diagram 85 14t II TIF where C is taken from the table or more accurately from graph b of diagram 412 The values of t are determined from the curves C 1 corresponding to different W or from the table dh 41o Us perimeter F Values of j 0 2 004 006 008 010 015 o o20 02 301 035 040 o 045 050 o ý oOo C 070 075o 080 0o o 10 001 044 6620 1600 690 375232 940 480 277 173 110 770 560 370 265 184 125 090 060 038 01 12 0 002 0376200 1500 p642 348216 876 445 258 161 107 710 500 348 233 169 1lt8 082 056 034 010 0 003 031 5850 1400 600327201 820 420 242 149 950 656 450 320 222 155 110 075 050 031 009 0 004 0265510 1 330 570 310192 775 390 227 141 900 619 420 300 200 145 095 070 045 029 6i08 0 006 0195000 1 200 1518 278 173 699 365 203 125 800 550 400 260 172 127 085 060 040 024 007 0 008 0154550 1 100 437 255158 636 322 185 114 750 500 340 230 152 113 078 053 034 021 006 0 012 009 3860 928 398 216 133 535 270 156 930 650 416 300 190 124 089 060 040 027 016 004 0 016 003 3320 797 340 184 113 454 230 129 1790 530 340 220 160 100 070 050 032 026 012 003 0 I 326 Section VIII Screens Diagram 86 F F I Screen r 1 Wire 2 Silk threads 1 Circular metal wire 745 to 11T 1 o M Mw 7 Aw MW 5 W S W N 1 b Re 40 1 So I 12 1 30 W1 0 kRe 1 161051 1 01 I00 1101 i01 1 103 140 1149 I 70 a Re wma 400 C 131 ii Iisdetermined from graph a b Re 400 AH CR I kftt 2g where kRe is determined from graph b C is determined as for Re400 In the case of z rows of successively installed screens AHC or XCRe 2 Silk threads Cs i 62Cw 2g 0 100 z100 XI U SM c I i 6 4 Zone A 4 2 0 4 5 507 41 0S t J I II I I I Zone I I I I1 glA lFH a where Cw is determined as C for circular metal wires ARe is determined from graph c v is taken from 13 b V 47 Oz 4 044d 6U 45 7 90 601 71 a 0osj o10 0151 0 2D 025 o301035 0401 645j 050 os 05 L60 0651 0701 075j 0so 090 100 36382 34 70100 6201I1301220165 1 26 097 075 058 1044 032 0141 000 C 6 2 3 4 1 0 o LV2 0 301 22 327 Section VIII Grids with sharpedged inlet inIhe orifice of a wall of arbitrary thickness at high slream velocities large Mach numbers Diagram 87 f A a1 a1Qf where ill CM C is determined as at s 0 from diagrams 81 82 and 84 kM is determined approximately from the curves Im nof M corresponding to different T a Mach number in front of the grid a n sound velocity msec Values of kM 0 1 05 010 1 015 1o02D I oM 1 030 I o03 o4 OAS o50 o55 060 0 6 5 02 100 109 130 03 100 103 113 151 04 100 100 103 114 141 05 100 100 100 103 110 127 185 06 100 100 100 100 104 112 130 177 07 100 100 100 100 103 108 116 135 168 08 100 100 100 100 101 103 107 112 120 137 163 201 09 100 100 100 100 100 100 102 104 107 113 121 133 150 175 M I db 02 0 ap M 01 WI 2 02J O QX O WS GO W5 Q Q W P A 328 Section VIII Grids with orifice edges beveled or rounded and screens at high stream velocities large Mach numbers Diagram 88 C is determined as for M 0 from diagrams 83 or 86 where ký is determined from the curves ký f M cor responding to different 7 tentatively in the case of grids Mach number in front of the screen a sound velocity msec Values of hý 0 10 1 015 035 1 0 065 W 4 065 035 100 101 104 112 130 040 100 100 102 110 125 155 045 100 100 101 107 119 140 182 050 100 100 100 104 113 130 164 055 100 100 100 100 104 117 142 193 060 100 100 100 100 102 111 132 168 065 100 100 100 100 101 107 122 147 190 070 100 100 100 100 100 105 116 133 160 212 075 100 100 100 100 100 103 112 123 142 173 240 080 100 100 100 100 100 101 106 115 128 149 181 085 100 100 100 100 100 100 100 101 108 120 140 180 271 090 100 100 100 100 100 100 100 100 100 101 108 132 175 265 oil U j ll j o oos ow s ezo wv6 ass oo05 00F W 329 Section VIII Bar grating with an angle of approach a 0 Re 10 Diagram 89 Section 11 Shape of grating bars IqI 21W4 luý 7 I Cleani graling of scrCeLI a 5 and 05 I j lkz sin O 2g where is taken from Table 82 St kl 1 3 is determined from the curve k a I a0 b any I and any j AH YwI is taken from Table 2 is determined from diagýam 84 as C for a thickened grid TABLE 82 Type of bar 1 2 3 4 5 7 p 234 177 177 100 087 071 1 p 10 076 076 043 037 030 074 a p va 04 I lf IA Zone A r 2 Clogged grating where e 11 to 13 in the case of mechanical cleaning of the grating c 15 to 20 in the case of manual cleaning of the grating 3 Grating with additional frame C cf c c where c A2 0L ae 0708 hz W hdz 2 total height of the rrasverse 05 0 0Z7 0A8 0 elements z 1 number of intermediate support S bars z2 number of bracing elements L in ternal height of the grating v is taken from 13 b I i ilii I I I I 1 I P i o al Q Qv 04 v5 06 a 47 08 Os to 4k 330 Bar grating with an angle of approach az0 and ý05 Section VIII R 0 D t WG10 Diagram 810 AH 01 alas where as is determined froiu graph a 02 is determined from graph h v is taken from 13 b Values of No 0 5 D0 15 20 1 251 3 40 50 6 1 100 100 100 100 100 100 100 100 100 100 2 076 065 058 054 052 051 052 058 063 062 3 076 060 055 051 049 048 049 057 064 066 4 043 037 034 032 030 029 030 036 047 052 5 037 037 038 040 042 044 047 056 067 072 6 030 024 020 017 016 015 016 025 037 043 8 100 108 113 118 12 125 128 133 131 120 9 100 106 110 115 118 122 125 130 122 100 10 100 100 100 101 102 103 105 110 104 082 11 100 104 107 109 110 111 110 107 100 092 Shape of grating bars No No S 6 Values of a 1 0 15 10 1151 20 12 130 14 150 1 6 050 234 240 248 257 268 280 295 365 400 470 055 175 180 185 190 200 210 225 268 355 450 060 135 138 142 148 155 165 179 219 300 435 065 100 105 108 112 120 130 140 177 256 425 070 078 080 085 089 095 105 117 152 230 410 075 060 062 065 070 075 085 095 130 205 390 080 037 040 045 050 055 064 075 106 175 370 085 024 025 030 036 042 050 060 088 140 350 b 331 Section V111 w Bundle of circular tubes in vertical columns 31PRe f2aut106 III V Diagram B11 AhI i e PL OX An C ý m ARez At 29 S1 S2 1 a S our dout A a1b a 5 S dot02 is determined from the curve Sj out a S dout of graph b i1 ksoutl b uof graph b m 02 is determined from the curve TABLE 83 Rem is determined from the curve RemIRe at S out 10 on graph c Sa dout 2 at St s Out cout A c1bC C Sdoi 70 9 is determined from the curve c Sdou d on graph a 02 M saou Rem is determined from the curves Rem s tRe for different S du Sz dout on graph c is taken from Table 183 as a function of 0 I a o ut 01 02 04 06 08 10 12 16 20 24 28 32 36 40 42 Sg dour a 240 210 182 170 158 152 146 138 132 128 123 120 118 115 114 C1 153 072 041 030 024 021 017 015 014 014 332 A Section VIII Bundle of ribbed tubes air heater Diagram 813 Bundle characteristic Resistance coefficient C n Tilo 29 t I Vertical columns of cast iron tubes with circular ribs 3000Re 25 000 287046 h1 h 2 4 h d 0 d 4out u 2to0 L12 totz lRe12 At 14t02 to 03 dto dout S 2 to4 dont z 4 to 6 The same with square ribs and 033 t O z Re Mg to ut Yi 2ni t jfl t cx 70 R2 3 tlfl I2 WO WO in 2731i z number of transverse rows of tubes in1 8he bundle is taken from u h as a fuSsction of t m For fouled bundles Cf 12 1 335 Section VIII Bundles of tubes of different crosssection shapes Diagram 814 Staggered finned tubes is taken from diagram 812 If the fins reduce the gap between the tubesworn is replaced by WS dout tWom o S douT6 V Oval tubes in vertical columns 10K W nmdout 10Re 310 C 0059z 031 A Staggered oval tubes 10 Re 310 C o20z 014 ACt Dropshaped tubes tin tex Ysn Eex R I0Re d ý3 10 V 4 012z 0016 M v is taken from 13 b 14 336 r0utSection V11I Bundle of circular tubes in vertical columns 310Remi 10 continued Diagram 811 Values of Re Re S dOut t dout 310 3 410 3 610 3 810 3 10 4 210 4 4104 6 04 9104 10 020 019 018 017 016 014 012 011 010 14 044 043 041 040 039 036 034 032 031 18 061 060 059 057 056 054 052 051 050 22 072 071 070 069 068 066 065 064 063 26 079 078 078 077 076 075 073 072 071 30 084 083 083 082 081 080 080 079 078 34 087 087 086 086 085 084 083 083 082 38 090 U 6 189 088 088 087 087 086 086 42 0 2 031 091 090 090 089 089 088 088 rex tin iI ex 2 273t0 2 1 2 TII Ill WoIlf I0 ill 273 t tif z number of transvcrse rows of tubes in thi bunhdle v takun frorn 13 h as a function of I For fouled indles f o5 IA Out ut it 16 444u1 ozat C 333 wd Section VIII Bundle of staggered circular tubes 3108 Rem mnut 10i m VDiagram 8 12 C mAHm WeA0e7 z1 2g S Sdout 1 at 20 and 014 u7 17 out S out 2 at So 20 and 0 14 St S dou 17 A 32 3 ato 10 and 17 ot 52 out Sdot ISt dout A 044 S i dout is determined from the curve A 02 on graph a 2 Out Remis determined from the curve Rein Re m on graph b is taken from Table 84 as a function of 0 5ex fin I tin tex 102 273t m t 2 0045 m i 2 73 t m m W0 m Oin 273 tin I A1 TABLE 84 0 30 45 60 90 49 034 057 080 10 t100 II 16 20 L4 Z6 12 36 0 4 4 8 42 a S1 dout S dout 17 18 20 24 28 32 36 40 44 48 52 A 320 343 396 506 634 770 932 110 128 147 169 z number of transverse rows of tubes in the bundle V is taken from 13 b as a fuction of tm For fouled bundles Cf I3 oil 007 Jd 680 2 4 8 tO p b 334 I Section VIII Bundles of tubes of different crosssection shapes continued Darm81 Bundle characteristic Scheme Resistance coefficient C TmO m 2a Staggered Elesko 10Rem mdout410 type tubes W 1e 046zA4 tin 5 t ex nvTin rex 32dot out Tubes with wire ribbing We fe a Re 650 to 6 0OO Wfin Dex 024 1 5 doujO ftin texPP x32e hk7 kW SRe6000 S 5t0 o36 h5 odoJ 10 0 1 to 03 h 08 to 25 dour t T 1 4 to 22 Belt wire d05toO7 mm a4to5 mm h7to9 mm 2ex tin tin tex 70273tm 2 7 3 t m tm 2 7m t m w Owoin273 tin z number of transverse rows inthe bundle v is taken from 13b as a function of tmI For foamed bundles C f 12 to 3ý ql 337 Section VIII Recuperators air heatersDiga 85 ar tPsitance coefficient C an Characteristic Till 0 1 Ribbed castiron air heaters recuperators dh 00425 m 1 As measured inside the pipes air flowj 2 As measured outside the pipes gas flow Ribbed toothed air heaters recuperators 1 As measured inside the pipes air flow WO mdh a Re 10 2 As b Re 10 h 2 As measureda oeutsidel the pipes gas flow 1 2 116z0JRe 2 A b Re 10 C 04 0334z AC tex A in AIRA R A1on 103 1Cti 2 mm0in2t 1f 273 z ibbeoohef trarsverse r cus uf t os recupirators Sis takei from 13a as a function ofW 0 For fouled pipes os t p2tof3 338 Packing material deposited at random loose layers from Section V111 bodies of irregular shape at given dh dry and wetted continued Diagram 816 I TABILE 86 Type of material d11 m mm 3 m K 3 rn m2n 3m Andesite lumps 432 mm 00333 0565 68 Circular gravel 42rm 00193 0388 80 Catalyst for ammonia synthesis 61mm 000194 0465 960 Catalyst for CO conversion made in 115x6mm tablets 00033 0380 460 Vanadium sulfuricacid catalyst made in 11x65mm tablets 000415 0430 415 Iron rings 35x35x25mm 00372 0830 147 50X50x5 mm 0036 0970 104 Ceramic rings l5xl5x2mm 00085 0700 330 25x25x3 mm 00145 0740 204 34x35x4 mm 00225 0780 140 50x5Ox5mm 00360 0785 88 Porcelain rings 8x8x15mm 00045 0640 570 Ceramic saddleshaped lements125mm 07100760 The same 25mm 0710 TABLE 85 ms m A m hm m2xhr Ise 0 00 5 08 10 07 25 06 50 05 1 Dry packing C W2l Xh Cdc Ati d Im Im dh 29 ReM mdh I a Re 3 180 xRh is determined from the curve A f Re b 3 Re 1000 164h 768 164 h6 is determined from X I Re Reh R 0h1 2 Wetted packing tentatively At A50 wlWjlim Sdh30 to 35mm T m QCdr looAAb 2g A intensity of wetting by liquid in 2 hr Wilim is taken from Table 85 dhandeare taken from Table 86 tex tin an cf 2 273 diana 8 7mn trilSin wland v cf diagram 815 it 339 Packing material deposited at random loose layers from bodies of irregular shape at given dl dry and wetted continued Section VIII Diagram 8116 Ile A A 5101 1 1110 ý 1 510 2 3 I I 4 3600 1800 360 180 1 90 Re 10 15 20 25 30 35 Re 243 224 168 137 120 107 990 90 100 150 200 250 300 350 652 627 562 512 484 465 449 600 700 800 900 1000 407 397 396 381 374 Re U 4 340 Packing material deposited at random loose layers from Section VIII bodies of irregular shape at given dgr Diagram 817 tin I e 7j tex Ain X C f Ad ACtCdr AC 7TmWlm g 29 75 15 where W Ret I is determined from the curve f Re of graph a 153 k13is determined from the curve k 1slof graph b 142 0 45 w md Re dgr mean diameter of body grain m a porosity freevolume fraction m3 m 3 taken from Table 87 v is taken from 13b as a function of tM 2 tex tin jtill ex Act2 2 7 3 tm tn 2 To 273n t 7m t m W 1 In Wi m 2 73 tin TABLE 87 Type of material 91 3 mm In m Anthracite 12 0485 35 0466 57 0466 712 0457 1218 0465 1825 0475 Agglomerate 1020 0480 2030 0488 from rotating furnace 3050 0490 Alumina 13 0500 35 0500 I 910 0520 Soil 0517 0355 0600 0343 0715 0352 0800 0378 0915 0394 110 0401 I 122 0397 145 0400 181 0395 Coke 1030 0435 I 2050 045 I 3050 047 68 0513 Longflame gas coal 57 0466 57 0500 712 0466 128 0466 Silica gel KSM 35 0490 Shale 712 0575 1825 0575 Hard coal 46 0488 57 0442 712 0447 1218 0460 341 Section VIII Packing material deposited at random loose layers from bodies of irregular shape at given dgr continued Diagram 817 Re 1103 5103 1102 110 110 510 1 2 3 4 5 75424 15212 7601 1567 7935 1725 910 492 346 262 22 Re 6 7 8 9 10 210 310 410 5410 610 710 196 174 157 143 132 810 622 525 462 420 385 Re 810 910 102 2102 310 4 102 5102 6102 7102 910 103 A 370 340 325 244 211 194 182 174 168 159 155 I a 6 I at 020 025 030 k 1330 520 238 k 045 050 055 A 443 278 188 040 698 070 683 or 0 43 04 h 45 as 0 p 342 Packing loose layer of spherical granular bodies or porous ScinVI 2g ýA F 0 30 3 where layr ro grnu7 03 is determined from the curve vi n 7e x Re of graph a k is determined from the curve k Ia of graph b 045 Usdgr ReT dgr diameter of bodygrain m a porosity freevolume fraction m3 m 3 61 cosOp 2cosO is determined from Table 88 A t ex fin Ar 2 7 3 t m fin ex YTo tin 2 Tm tm 2 73 m W m W273 tin v is taken from 13b as a function of tm TABLE 88 60 60 64 68 72 76 80 84 90 a 0260 03201 0365104051 0435 0455 0470 0476 020 025 030 035 040 045 050 055 060 065 070 k 1330 520 238 128 698 443 278 188 131 945 638 41 343 Section VIII Packing loose layer of spherical granular bodies or porous cemented layer from granular material constant diameter contd Diagram 818 Re 1103 510 1102 5102 110 510 1 2 3 4 5 A 30320 6125 3064 634 313 652 333 172 117 893 730 Re 6 7 8 9 10 210 310 410 510 610 710 620 5 05 475 430 390 217 157 128 110 091 088 Re 810 910 102 2102 3102 4102 5102 6102 7102 8102 103 081 071 072 052 046 042 040 038 037 036 035 4 I IA a L I 4 Q b Ib w Ity 4 344 Packing bonded porous medium nongranular I Dection VIII iagram 819 YIm m 273tm WI mWU273 t in v is taken from 13b as a function of tm Tmml 1 dh ea 2g smrdh 1 a Re 180 x is determined from the curve AI Re b Re3 164 768 is determined from Reh Reo0 11 curve IL f Rex dh and a are taken from Table 89 2 t ex stin tin t ex 273 2m m 2 3 4 5 6 615 479 397 337 40 45 50 60 107 990 924 870 830 762 250 300 350 400 450 500 484 1465 449 437 429 421 Re 600 700 800 900 1000 140 397 1 396 374 TABLE 89 Type of porous dh m3 m3 medium Firebrick 00000072 0157 0 0000400 0430 0000130 0435 Diatoma ceous earth 00000550 0485 00000850 0443 00001150 0461 00002050 0426 Quartz 00000570 0361 00000950 0502 Glass 00000041 0230 00000680 0296 00000180 0271 00000210 0267 00000710 0263 Coal 00000061 0198 00001270 0203 345 lout2 Section VIII Packing ceramicRaschig rings Idiot dry or wetted Diagram 820 No I Rings in vcrtical columns 1 Dry packing S 00000 F0000 tin 000 tex pooo0rex j00000 No 2 Rings staggered i10 aout SinI rdI ex r8E88 00r TABLE 810 A Ilim m 3m 2 hr rnsec 010 20 1525 15 3050 10 T2 1 1 7mm dh No 1 a 04l10 Re 8I0 312 A 3 Re0 375is determined as a function of Re by curveNo 1 b Re 810 1010 coast No2 a04103Re61O S 92 is determined as a function of Re by curve No 2 Re 0at b ReO 6c108 1 034 const 91 11 TABLE 811 A OIUim m3 m 2 hr rmsec 010 1520 3050 15 12 08 TABLE 81S dout ahd m mm h M go 2mm 50 0027 073 136 185 108 80 0036 072 139 193 100 0048 072 139 193 150 0075 072 139 193 200 0100 072 139 193 2 Wetted packingtentatively A X I 004 A A1 where A intensity of wetting by the liquid mamI hr WilimiS taken from Tables 810 and 811 tex tin t in ex AC 2 273tm tm 2 Y rn 273 i Y t 1M 273m m In m W2jtin v is taken as a function of im from 13 b dh and gare taken from Table 812 Re 1410216102 181021 10 311510 3 210 2 410 31610 38 103 No I A 033 1028 1025 10231 020 1018 1014 1012 1011 No 2 A 1 098104 1075 1070 060 1053 I041o 361o34 45 346 S Section VIII Packing of wooden laths dry or wetted Diagram 821 No 1 Chords placed in parallel lg av jex 4i No 2 Chords placed crosswise tin 7in 1 Dry packing Tmnlm A dh1e2 29 No a 4102Re 10 312 31R2O is determined as a function of Re by curve 1 b Re 104 X 010 Const N 2 a4102 Re v 4 1W kt is determined as a function of Re by thecurves for grids of the corresponding number h is taken from Table 813 b Re 104 k X is taken from Table 813 TABILE 813 No of dM a0 h tirrn dhj all I T grid t1nM HI I m m Ill 72 2113 1 10 10 100 22 002 2 055 182 331 100 44 014 2 10 10 50 22 0022 055 182 331 100 57 018 1 10 20 100 41 0041 068 147 210 66 67 021 1 10 30 100 1063 0 063 0 77 130 169 49 85 026 347 Packing of wpoden laths dry or wetted continued Iction VIII Diagram 821 2 Wetted packing tentatively A 50 iv CWjlim AH 2g where A intensity of wettingby the liquid in1 m 2 004 for No I and 006 for No 2 WilimiS taken from Table 814 tex fin tin e 273 tm t f 2 2 7 3 tm Tm m I W mWl 273tj 273 dh and e are taken from Table 813 v is taken from l3b as a function oftir ITABLE 814 A in3n 2 hr 010 1025 2550 No I WIlIm nsec 20 15 10 No 2 wlim 10ScC 10 0 7 05 348 Section Regenerator checkerwork of furnaces Vill Diagram 822 Simple Siemens checker work 0114 dh Siemens checkerwork 1 57 a Omdh a Re Iv 70D Checkerwork of Stal proekt design 1400 10 A b Re 700 C 24o A Fencetype checker work of V F Grum Grzhimailos system a Re 2 d 00h W 4 400 at Re b Re 1000 3 ReO 3oa1 tex ti t in t To 7 sz tm WomWOin 273t v is taken from 13b as a function oft 349 Section Nine STREAM FLOW THROUGH PIPE FITTINGS AND LABYRINTH SEALS Resistance coefficients of throttles valves labyrinths etc 91 LIST OF SYMBOLS F crosssection area of the inlet the throttling device or of the gap of the labyrlnh m2 Ino section perimeter m h crosssection area of the labyrinth chamber m 2 D diameter of the passage crosssection of the throttling device m Dh hydraulic diameter of the passage h lift of the gate or valve m hch height of the labyrinth chamber m I length of the labyrinth gap m S length of the free jet length of the labyrinth chamber m so halfwidth of the gap for a labyrinth with double grooves or width of the jetfor a labyrinth with one groove m as width or halfwidth of the free jet at the chamber end m we mean stream velocity in the passage crosssection of a throttling device inthe gap of a labyrinth and in a complex fitting msec P0 absolute pressure before the throttling device kgm 2 p absolute pressure after the throttling device kgm 2 A pressure loss resistance kgm 2 resistance coefficient 92 EXPLANATIONS AND RECOMMENDATIONS 1 The resistance coefficient of throttling and control devices is a function of their design and the shapesof the inside of the body which determines the stream flow the uniformity of the section etc The quality of finish of the inside of the body also in fluences the resistance coefficientk 2 The design length of some tyjes of globe and gate valves does not vary in proportion to their flow section and therefore a complete geometrical similitude is not preserved when the diameter of this section is varied Further the relative roughness of the casting increases with the decrease of its size As a result the resistance of some globe valves and gate valves varies withthe flow cross section diameter the resistance co efficient C of globe valves of large dimensions increases with the flow cross section diameter while in globe valves of small dimensions it increases with the decrease of the diameter 3 The resistance of gate valves is similar to the resistance of restrictors in which a sudden stream contraction is followed by a sudden expansion Figure 91 a The phenomenon in butterfly valves taps faucets and globe valves is more complex 350 Figure 91 bc and d abrupt and complex variations of direction being added to the sudden contractions and expansions This results in local velocity increases stream separations and consequently eddy formations which increase the resistance of these elements I 3 b a d t FIGURE 91 Flow pattern in throttling and control devices a gate valve bbutterfly valve cdisk valve dglobe vaIves The resistance of each type of throttling device depends largely on the position of the shutoff member In order to reduce the size of a gate valve and the magnitude of forces and torques necessary to control it the flow section in the valve body is usually contracted This contraction is usually symmetrical in the case of onesided direction of stream motion it can however be made asymmetrical cf Gurevich 96 The contraction of the passage increases the resistance coefficient of the gate valve The best design for minimizing fluid resistance is that of a straightway globe valve The resistance coefficient of straightway globe valves depends largelyon the Reynolds number Re At small values of Re Z decreases rapidly with the increase of Re V passes through a minimum at Re 5X10 4 then increases slowly with the further increase of Re until finally it becomes constant and independent of Re 6 The resistance coefficient of a straightway globe valve as a function of the valve liftD can be determined by the following formulas proposed by Murin 912 351 a at Do 38amm All 0084 91 C n 128 Oyl b at D 200mm aH 051 92 29 Do at full opening of the valve within the limits D 25 to 200 mm AH 52 3 7 The resistance coefficient of certain types of valves can be determined by the following formulas proposed by Bach 918 a disk valve without bottom guides within the limits 01 4 025 and 0 D 025 C 055 4 L T 94 99 1I where bd width of fhe disk flange m b disk valve with bottom guides within the limits 0 125 ho 025 andOl do 025 Do Do t vd173 Tl08 to100554 b 0I 1 a a 2h 95 2Dg where Sc1 width of the guide shoulder cf diagram 914 i is the number of guide ribs c conical valve with flat seat within the limits 01 025 and for 01 204 96 d conical valve with conical seat within the limits 0125 04 a 06 0156 y 19 352 e spherical valve with spherical seal within the limits 01 025 01 4 014 C 27 89 8 Since the motion of a gas through throttling devices is accompanied by large pressure losses the density of the gas will vary considerably when determining the re i sistancge of the device This should be taken into account by the formula cf Gurevich 96 in o kgM 2 99 where w0in is the mean stream velocity before the throttling device at a pressure p m sec Yin is the specific gravity of the gas before the throttling device kgmr3 k c is the correction for the gas compressibility depending on the ratio 9 between the absolute pressures before pA and after the throttling device 1910 Pe PA The following values are obtained for the correction a atE09 or AHOlp PO kc a i0 b at PI orI Pecr NP P c Po k i kc 0 2 911 PO or approximately cf Aronovich 93 1 l 912 10465 where is the critical ratio of the pressures before and after the throttling device at PO cr c r which the stream velocity in the narrow section becomes equal to the local velocity of sound in the case of air and a biatomic gas p 053 and 1 047 cr c r The magnitudes AH LI and kc are calculated by the method of successive approximation 9 The resistance coefficient of a ringseal gate in a spillway is independent of the tailwater level h Figure 92 a i e it is identical in the cases of discharge 353 into the atmosphere and discharge under water cf Rolle 914 When the ring seal gate is placed in a stilling chamber which ensures the reliable dissipation of the kinetic energy of the stream in the tailwater Figure 92 b its resistance coefficient varies somewhat cf diagrams 917 and 918 a b FIGURE 92 Ringseal gate in a spillway a gate design b flow pattern 10 In a labyrinth seal with the intermediate baffles located at one side and on one level the stream passage is straight The stream contracts on entering the first gap WFigure 93a just As in the case of entrance in a straight channel mounted flush iin the wall or in the caselof passage through an orifice in a thin wall It then expands on entering the labyrinth chamber and due to turbulent mixing additional fluid is en trained When the dimensions of the chamber are sufficiently large relative to the gaplsize a core ofconstant mass separates from the jet at the chamber end and con tracting enters thesecond gap The attached masses of the surrounding medium separate from the Stream core at the chamber end and move with a circulatory motion in the chamber until they become once more mixed with the jet Since the constant core possesses a high kinetic energy before entering the second gap there is less contraction than at the entrance to the first gap 11 The resistance of the labyrinth cell Figure 93a is due to the frictional losses in the gap and the energy losses in the constantmass core The latter are made up of two parts the difference betweenlthe energy stored in theý constantmass core at the beginning and end of the cell and the loss at the inlet of the next gap In the case of relatively small chamber dimensions fulfilling the inequality ch 5 the jet issuing fromrthe gap into the chamber will fill the entire section The resistance in this case is made up of 1 the frictional losses in the gap 2 the losses at sjudden 354 expansion 3 the losses at entering the following gap according to Abramovichs data 91 as 24 as S 1 913 where at is the coefficient of stream turbulence taken here as 01 Ia N U 9n a o 12 n theFGUR 93 Floawnt patears with labrinthsnestgee rrneet baffles and with large chamber dimensions between the baffles the stream is directed toward the labyrinth protuberance after the compression in the gap Figure 9 3 b Here it i s deflected through 90 and flows in a straight line up to the lower wall of the chamber It then circulates in the chamber and flows toward the second gap along the second channel The flowing stream entrains stationary masses from the surrounding space causing a motion of these masses and the formation of eddy zones The existence of protuberances between the labyrinth baffles lengthens the path of the free jet which contributes to the dissipation of its energy Labyrinths with curved flow are more effective since the length of the jet path in them and correspondingly the resistance are considerably larger than in labyrinths with straight stream passage 13 The resistance coefficients of labyrinths with oblong gaps are calculated by the following formulas obtained by the author 99 a at AH z a C f 914 2g where at b are coefficients depending on the relative length of the labyrinth cell and de aermined fromthe resofsime labph babrinth is the friction coefficient therfloingd streamtentorrinsstatdionaryph massesafrom the9 surroudin spcecauin 355 of the gap I is the friction coefficient of unit relative length of the gap determined by the data of diagrams 21 to 25 C is a coefficient by which allowance is made for the influence of the shape of the inlet edge of the gap it is determined from the data of diagrams 33 and 36 asa function of the degree to which the inlet edge is rounded or beveled b at chs to 8o I zab f 915 where FF9F9i6 14 The resistance coefficient of combshaped labyrinths is calculated by a different set of formulas 99 a hC s a at aH zC t d 9 18 740 2g where cd are coefficients depending on the relative length S18 of the labyrinth chamber and determined from the corresponding graphs of diagram 920 h c h 6 s b at h AH d 919 where c I 0707 i O 920 c o d 8I 0707V I 921 a 15 The flow pattern in complex fittings of conduits in which sharp turns sudden expansions and contractions bypasses etc follow each other at a very short distance cf diagrams 923 to 925 is similar to curved channels restrictors and labyrinth seals with wide gaps 356 When calculating the resistance of such complex fittings it is necessary to allow for interaction of the separate elements in each fitting which considerably increases the total resistance above the sum of the resistances of the separate elements sometimes by a factor ot three and more 16 If a complex fitting is used as labyrinth seal its resistance is useful since it makes operation more efficient a higher resistance decreases the entry of air through it Where the complexity of the fitting is necessitated by the limited size of the in stallations however the resistance is harmful and should be reduced The losses in such fittings can be considerably reduced by enlarging certain cross sections The installation of guide vanes at sharpcornered turns is a very efficient method of de creasing the resistance cf S62 and what is more does not necessitate alterations of the dimensions of the fitting The resistance is also reduced considerably when the corners are rounded The installation of fairings is very useful in the case of obstruction of irregular shape placed in the stream 357 93 LIST OF THE DIAGRAMS OF RESISTANCE COEFFICIENTS OF SECTION IX No of liagram description Source diagram Note Gate valve ldelchik 98 91 Calculated by the formula for restrictors Weisbach 922 experimental data Wedgetype gate valve Idelchik 92 According to the authors exerdiments Gate valve with symmetric contraction Gurevich 96 93 Experimental data Butterflv valve Weisbach 922 94 The same Stopcockk The same 95 Standard globe valve with dividing walls Bach 918 Erlich 9171 96 Ypattern Kosva globe valve The same 97 Directflow globe valve Murin 912 98 Various globe valves and gate valves Bach 918 Erlich 917 99 Flap Aronovich and Slobodkin 910 94 Doubleseat control valves Gurevich 96 911 Formula given by the author Check valve and suction valve with screen Kuznetsov and Rudomino 912 Tentatively 911 Frenkel 916 Disk valve without bottom guides Bach q181Frenkel 913 Approximate formulas 19161 Disk valve with bottom guids The same 914 The same Conical valve on conical seat 915 Conical valve on flat seat add ball valve on 916 spherical seat Ringseal gate free Rolle 914 917 Experimental data Ringseal gate in a chamber The same 918 Labyrinth seal with increased gap Idelchik 999 919 Calculatingformulas Combtype labyrinth seal The same 920 Various expansion joints 921 Tentatively Coils Aronov 92 922 Experimental data Complex passage from one vlume to another ldelchik 923 The same through a 90 elbow Complex passage from one vblume to another 924 through an oblong 180 elbow Complex passage from one vblume to another 925 through different labyrinth seals 358 94 DIAGRAMS OF THE RESISTANCE COEFFICIENTS Section IX Cate valve Diagram 91 1 Cylindrical pipe A is determined from the curves t h JL z 1Zone A 2 Rectangular pipe 1 1 Z 5l N n hDb 0 010 0125 02 03 04 05 06 07 08 09 10 1 Cylindrical pipe F 0 01 025 038 050 061 071 081 090 096 10 1978 350 100 460 206 098 044 017 006 0 2 Rectangular pipe 0I1 193 445 17H 1812 402 1208 095 039 009 0 359 Wedgtye gae vlveDiagram 92 h 1M031 04 05 06 107oa I 1 C 300 220 120o530280150 0801030 J015 zo I z 241 Zone A l e is determ ined i from the curve CI k B 7 1 g0 0 0 40 to Section IX Gate valve with symmetric contraction iarm O is taken from thle table 7 2 067 067 075 080 L 250 168 133 150 145 180 060 039 W 14 360 Section IX Butterfly valve Diagram 94 I is determined from the curves Too Wr a P 5 10 6 2 25GI 130 4 50160165 70 0 1 Cylindrical pipe 10241052 090 154 251 1 391 1 108 pe326 118 2 Rectangular pipe F 091 083 074 066 058 050 036 4 028 045 077 134 216 354 930 023 013 906 249 17743 18 368 12 1 2 fie too 80 o I I Zone A Ii Ad 7 14 1r PI4 I ZoneA I LA iLl 0 a t0 30 40 so 60 361 Stopcock Section IX Diagram 95 AH AH is determined from the curves 8 1 Cylindrical pipe 10 is 20 25 30 35 40 45 5W 55 67 F9 093 085 077 069 060 052 044 035 027 019 011 0 005 031 088 184 345 615 112 207 410 953 275 oo 2 Rectangular pipe 5 to Is 20 25 30 31 40 451 0 60 N 093 085 077 069 061 053 046 038 031 025 014 0 005 029 075 156 310 547 968 173 312 526 206 362 I I Section IX Standard globe valve with dividing walls I Diagram 96 I Dividing walls at an angle of 45 2 Verticaldividing walls 1 Dividing walls at an angle of 45 Dmm 13 IN 1 40 1 1 I S I M I M 3 0818 149D 14I00 141lA 7 1 4A01550 2 Vertical dividing walls FO C 159 105 930 860 760 690 top I f is determined from the curves C I D J e t ion mm Ypattern Kosva globe valve Seciagra 97 AH d 1 With 30 contraction of the seat section is determined from the curve C f D and fromidretoofaow e Is in direction of arrow a Table 91 DOmml 60 IO 100 ISO I o 250 3M 3M C 270 240 220 L86 165 150 140 130 a4 1 2 With full seat section TABLE 91 D inches I flow along t flow along arrow a arrow b mm Ix JO Z mm 1 180 170 1 4 200 190 12 170 160 363 Directflow globe valve Section IX ý Diagrarn 98 1 Re WO 310 V A Incomplete opening a Do38mm and 02Ba0 AMl 0084 I I2 8 is determined frOm grph a D b DO 200mm and 02 10 AM 051 Al 0 is determined from graph a o B Full opening for diameters Dmm25to 2150mm AM 52 is determined from graph b 2 Re 3J10 C kft where kR is determined from graph c v is taken from 13b I 1 1 DminI 25 1 38 1 50 165 1 751 100 1125 1150I1200I1250 C 114010807310650601050046104210361032 02 03 104 105 106 107 108 10 112 114 CD 38mm 1204401260120011701501136111 09 85 4D 200mm 130580 320 200 140 100 080 050 040 036 Re 05 1 1 e 10i I a U V 364 Various gl obe valves and gate valves Section IX Diagram 99 Valve type Sectional view Resistance coefficient C Reytype globe valve 34 2 Forged globe valve C78 wF Wedgetype gate valve Cm 02 Steam gate valve with lever gate 075 Conduittype gate valve D T7 12 14 18 C 03 07 22 365 i Section IX Flap Diagram 910 035 1003 is determined from curve C fO 6 p a Fgj I I 120 25 30 35 40 45 50 55 60 65 70 75 117 123 132 146 166 195 114 120 130 142 162 190 4 j j 000 k I0 Ii X IV 50 w 70 366 Doubleseat control valves Section IX r vDiagram 911 C AH is determined from the cuirves fA for different D I nm OI 01 F 03 04 05 06 07 01 0f 10 D 25 mm 1 700 220 5 1 740 1 560 1 460 1400 360 13o 0 320 D 50 mm 0 17001 225 1301 900 1675 1560 1 495 1 450 1410i 4oo Do 80 mm C 1700 1230 135 9801 8001 700 I 630 1 580 15401 525 Do 100mm 7070 235 I140 1105 8501 7501 680 1 620 16001 580 D15ISmm C 700 1 24 1 145 I 110 1 900 1 800 1740 1 680 16501630 C N ýmm 1mm 367 Check valve and suction valve with screen DSection IX I Diagram 912 1 Check valve 2 Suction valve with screen A9 Domm 40 70 100 200 300 500 750 1 Check valve 00 I 13 14 I15 I 19121 25 29 050 2 Suction valve with screen Ž is determined from the curves C D 0mm 12 85 70 47 1 3 1 25 16 WO Diskvvalve without bottom guides Section IX I Diagram 913 bd 10 1 0 1 01 016 018 020 022 024 025 L all 0105 012 014 0 S063 071 079 087 095 103 111 115 AH C s p where a 055 4 d01 i is determined from graph a 21 aal 4 V 421 41 ir W4 419 4W ex h is determined from graph b This formula is valid for 010 012 014 016 018 020 022 024 025 01 5 025 01 1 025 155 108 790 605 478 387 320 269 248 a II 368 s vSection IX Disk valve with bottom guides Diagram 914 W 1 010 012 014 016 018 020 022 024 1025 ae 055 063 0711079 087 095 1031111 115 a F I oI 00310841085o81io0 8 080 0 1 082 0831 4 08 0 70 1 160 1 148 1 IM 1 123 1 114 1 102 1 092 1 080 i i I i I B i where a 055 4 d 01 is determined from graph a 7 is determined from graph b 1 73 it is determined from graph c I number of guides Fp r free flow area The formula is valid for S bd o 25 o25 ojob o 25 Do 0125 1014 1 16 018 1 01 o22 0 24102 111 18 1 675 1535 1433 1358 1300I 277 to u014 ci qi4 ax c azz VZA ON2 369 Conca vlv oncoicl ea Section IX Cnia alv on onial eatDiagram 915 Q I L SAH C0o6 015 Vt is determined from the curve h8 The formula is valid for 0 125 2 0 4D 4 hD 010 015 020 025 030 035 040 6 t4i at WIdl 4MO QJ 41V I 156 727 435 300 227 182 154 Conical valve onflat seat and ball valve on spherical seat Seciagra IX 1 Conical valve 2 Ball valve h 010 012 014 016 018 020 022 024 025 p 800 666 571 500 444 400 363 333 320 140 973 715 546 432 L 290 243 224 AN 2g 08hO is determined fromn curve Ff ýID 014 P3 hlDO2 is determined from curve P hDo The formula is valid for h bd 0 2 OI 370 Ringseal gate free Section IX I Diagram 917 C is determined from curve C nie 710 where n is the degree of gate opening Ringseal gate inma chamber I Section IX Diagram 9ý18 is determined from curve C I nal 2g where n is the degree of gate opening 16 371 Labyrinth seal with increased gap ScDiagram 919X Dh O 0 perimeter hch as z aa gb gfr 2 hchh a ft AN 2 1 CzOsCbBCfr where ar o and b are determined from graph a al 0 andb F are determined from graph b C is determined asC from diagram 33 at r800 V05 X is determined from diagrams 21 to 2 5 z is the number of cells of the labyrinth Dh is the hydraulic diameter of the gap Fqisthe area of the gap section TFch is the area of the chamber cross section a sx L a I 0 0 0 5 015 008 10 028 016 20 053 031 30 065 040 40 073 047 50 078 052 60 082 055 70 084 058 80 087 059 90 087 061 100 087 063 FeIh I I0 1011 021 03 o4 0o5 o6 I o7I o08 09 1I a i 10 081 064 049 036 025 016 0 04 001 0 110 090 080 070 060 050 040 030 020 010 1 0 4 a 372 N I Section IX Combtype labyrinth seal I Diagram 920 1140 W FE UV F Fch hch s LH zcd hch fis a Am zc 2 d here C f and duf d re determined from graph a d 30707 iVF re determined from graph b is the number of ceils of the abyrinth a si o Ci E 0 0 100 5 032 131 10 063 162 20 124 196 30 160 210 40 178 219 50 192 226 60 202 232 70 210 236 80 216 240 90 220 242 100 226 1 246 b FFch 0 01 02 03 04 05 06 07 08 09 10 C 292 250 205 167 132 100 072 047 027 011 0 da 292 281 268 254 239 225 209 192 173 150 10 373 t Coils Section IX oisDiagram 922 is determined from diagram 63 M S Section IX Complex passage from one volume to another through a 900 elbow Diagram 923 Resistance coefficient c AH Elbow characteristic View m With cutoff inlet exit stretch without Cin M 48 vanes Section II ex 237 Exit The same but with vanes Ct nQ 28 23 ex With inlet exit stretch of length Is a Section 11 rin 43 without vanes 1Iniet C ex a37 Exit in23 The same but with vanes tina Cex a17 375 Complex pasage from one volume to another through an Section IX oblong 180 elbow Diagram 924 C is determined from the curves C b 1 With baffle L 10 bj 02 04 108 12 16 20 24 26 1 Inlet S 73 46 143 4 3 143 I43 44 4 4 2 Exit 113 T 6 68 66 163 61 60o 59 2 Without baffle blee 05 06 08 10 1 14 1 Inlet 2 80 58 44 36 32 2 Exit 120 101 74 57 46b 141 a b 376 Complex passage from one volume to another through different Section IX labyrinth seals Diagram 925 1 Short 180 elbow Section 11 Ib L41 2 Hood with threesided inlet or exit Section II LI 3 Hood with straight stretch at the inlet or exit Section II Ut 0 J gojInlet I 9E 377 Complex passage from one volume to another through different Section IX labyrinth seals continued Diagram 925 is determined from the curves Wi or ch 7W 4e 1 Short 180 elbow S 05 06 08 110 12 1 4 1 Inlet 1110 190 67 5 I 49 5 2 Exit S 172 145 102 1 7 58 51 2 Hood with threesided inlet or exit ba 08 02 04 06 08 10 1 Inlet 1133 1124 1 62 57 156 55 2 Exit i 142 1139 1 94 80 75 70 5 3 Hood with straight stretch at the inlet or exit 011 05 06 08 1101 12 114 1 Inlet C 1135 1120 1 90 174 166 1 59 2 Exit C 1130 1117 1 95 18o0 71 1 63 fo INN 8I m US4 AD 118 Lo 1 378 Section Ten FLOW PAST OBSTRUCTIONS IN A CONDUIT Resistance coefficients of stretches with projections trusses girders andother obstructions 101 LIST OF SYMBOLS F area of the conduit cross section before the obstruction m 2 S maximum cross section of a body ie area of the projection of an obstruc tion in the pipe cross section mi2 HI perimeter of the section of the pipe or of the mine shaft excavation m Do diameter or side of the conduit cross section m dm characteristic dimension of the maximum cross section of the obstruction m 4F Dh hydraulic diameter of the conduit cross section m I total length of the pipe stretch m i 1 body length in the direction normal to the flow and the distance between adjacent obstructions arranged in a row m dm relative distance between adjacent obstructions arranged in a row I chord of the obstruction profile m it I relative length of obstruction w mean stream velocity in the conduit before the obstruction msec AH pressure loss kgmi2 coefficient of local resistance of the obstruction in the conduit c drag coefficient of the obstruction ap aerodynamic resistance coefficient of the mine shaft or excavation kg sec2 m 4 Re Reynolds number of the conduit Re Reynolds number of the obstruction 102 EXPLANATIONS AND RECOMMENDATIONS 1 The resistance of conduit stretches containing obstructions is made up the re sistance of the stretch proper and the resistance of the obstruction tsum I Stwo 9 101 where s is the resistance coefficient of the stretch in the case of a straight stretch ýst fr C is the local resistance coefficient of the object placed in the conduit 379 2 The coefficient of local resistance of a single object in a conduit is expressed as the drag coefficienit of the object by the following formula obtained by the author 105 3 3 6 0 oDýls mV FeI 102 2Cg ft Sm3PM3 where c d 103 SSm Wcdm c is the drag coefficient of the object depending on its shape Reynolds number Re and other parameters and is determined from the data of diagrams 101 to 1013 Pd drag force Sm midsection of the object m2 dm is the diameter or maximum width of its midsection m y distance of the center of gravity of an object from the channel axis m kJ Wax is the ratio of the maximum stream velocity in the free conduit wO to the mean velocity over its section it is a function of the exponent m cf 101 and is given in Table 101 m is a number depending on Reynolds number ReLot the V conduit at steady velocity profile it is given in Table 101 g is a corrective coef ficient allowing for the influence of the shape and the mutual disposition of the geparate objects for smooth objects 10 TABLE 101 Re 4103 25104 210s 610O 310 m 5 6 7 8 9 10 k 132 126 123 120 117 115 At Re6X 105 m is practically equal to 9 in that case k 117 and kk3 16 This Sm value of k is true for objects of very small ratio of the midsection to pipe sdction in the case of thr eedimensional flow Th value of k d Sm flow hevalu of kdecreases with the increase of and tends toward unity The values of k given in the diagrams of this section have been approximated to allow for this fact 3 The drag coefficient of oblong objects is determined by two factors the frictional and the form resistances This latter is a result of the stream separation from the objects surface and of the subsequent formation of eddies The magnitude of these two te sistance components and their ratio are a function of the body configuration and Its position in the stream the roughness of its surface and Reynolds number In the case of nonstreamlined bodies the frictional resistance is very small compared with1 the 380 total drag In the case of streamlined shapes the frictional resistance and the form resistance are of comparable values 4 The dependence of the drag coefficient of shapes such as a sphere cylinder etc on the Reynolds number is very complex Figure 10 1 The value of c is maximum at very small values of Re decreasing with the increase of Re passes through a first minimum at a value of Re 2 to 5X103 then increases somewhat and remains constant up to R 1 to 2 X 10 5 the critical Reynolds number It then drops sharply to a second minimum Re 510 5 and increases negligibly to Re 106 where it becomes fairly constant FIGURE 101 number Drag coefficient of a sphere as a function of Reynolds 5 The flow pattern past spheres and cylinders is characterized by the absence of eddies at small values of Re Figure 102a The flow is purely laminar and the resistance of the body is determined entirely by the viscosity forces With the increase of the value of Re the influence of the inertia forces begins to be felt leading to the separation of the stream from the rear of the object Figure 102 b The stream separation here is due to the same causes as in flow in a diffuser i e to the increase of the pressure along the stream resulting from the decrease of velocity 52 Therefore at moderate values of Re when the boundary layer is still laminar and is characterized by a linear distribution of the velocities giving a maximum thickness the stream separation from the surface of the sphere or cylinder starts almost at its widest section Figure 103 a With the further increase of Re the flow in the boundary layer passes from laminar to turbulent This is accompanied by a decrease of the boundary layer thickness and by an increased fullness of the velocity profile in the detached stream which causes it to adhere again to the spherical surface Since the inertia forces continue 381 to increase with the increase of Re the flow will separate once more after this ad herence however this will be a turbulent separation taking place farther downstream beyond the widest section of the sphere As a result the eddy zone behind the sphere will be much narrower than with laminar separation Figure 103b aai b b D FIGURE 102 Pattern of flow FIGURE 103 Pattern of flow past a sphere past a sphere alaminar boundary layer bturbulent a laminar flow without stream boundary layer separation bflow with stream separation 6 Transition of flow in the boundary layer from laminar to turbulent takes place at the critical value of Re at which the value of c starts to drop sharply The thickness of thezoneof separation becomes a minimum at Re 5X 105 where c reaches the second minimum The further small increase of c is probably explained by the state of the spherical surface which starts to influence the resistance by the considerable decrease of boundary layer thickness at high values of Re 7 An artificial mixing of a stream impinging on a streamlined body has the same effect as a natural mixing caused by the simple increase of Re The critical region in which a sharp dropof c is observed is shifted toward smaller values of Re The value of c of nonstreamlined bodies does not materially vary with Re and the degree of mixing of the stream This may be seen from the instant the inertial forces exceed the viscous tforces since the separation point for nonstreamlined bodies ýs the same as for sharp corners 8 The drag coefficient of a cylinder and other oblong bodies is a function of the rlative length tL and inpreases with it dm i i 9 When se eraliobjects are located in the same section of the pipe the total co efficient of local resistance of these objects is calculated by the formula 3 2y C F I D 104 SIV20 2g 382 where i is the ordinal number of the object of the given complex n is total number of objects in the complex 10 The total drag of two identical objects placed one behind the other in the stream direction is not equal to twice the drag of a single object the drag coefficient of each of these objects and their total drag coefficient will be a function of the relative distance 7Ld between them 11 In the case of two cylinders place closed to each other in the stream flow the rear cylinder will be completely immersed in the eddy zone created by the front one Figure 104 and will not exert any drag The rarefaction behind the first cylinder will be larger than the rarefaction behind the second and the resulting pressure gradient will cause the appearance of a force opposing the stream flow This will cause the value of c for the rear cylinder to be negative and the total drag coefficient of the two cylinders will be smaller than the drag coefficient of the first cylinder alone The effect ofsuction of the rear cylinder toward the first one decreases with the increase of the distance between them however since the rear cylinder remains in the strongly mixed and slower I zone ft of the first cylinder its drag coefficient slowly approaches but remains lower than the value of C corresponding to an isolated cylinder even with the increase of 1 A lower value of is obtained not only for cylinders but also for any bodies located in the aerodynamic shadow of another body 12 The mean value of the drag coefficient cm of a body placed in a longitudinal row of more than two bodies is smaller than the mean arithmetic value of cm of a couple of bodies since the drag coefficient of each of the rear bodies is considerably smaller than the drag coefficient of the first body 13 If several groups of bodies arranged in longitudinal rows are placed in a pipe the coefficient of local resistance of a pipe stretch equal to one hydraulic diameter is calculated by the following formula 105 3 AHi 2y I H k CX I X 0 105 TR Sm 2h 0 EikD I where i is the ordinal number of a body in a given complex or the ordinal number of a given longitudinal row of several bodies n is the total number of longitudinal rows C is the drag coefficient of a single body belonging to the ith row determined as a function of the body profile shape the Reynolds number Re and other parameters by the data of diagrams 101 to 1013 FIGURE 104 Flow past two FIGURE 105 Profile of a cylinders placed close together streamlined body 383 14 The coefficient of fluid resistance of all the bodies contained in the entire stretch considered will be equal to AH 1 L 106 The friction coefficient of a straight pipe stretch of the same length is All L 10 7 Hence AM L C In f 108 where fris friction coefficient of unit pipe length determined as A from the data of diagrams 21 to 25 15 An important factor influencing the drag coefficient of a body is the shape df its profile The more streamlined the body the smalleris the stream separationand forma tion of eddies and therefore the smaller is the drag coefficient Streamlined bodies should thus be used wherevei possible The streamlined shape is characterized by a smoothly rounded nose and a taipering tail Figure 105 The sharper the c6ntraction of the profile beyond the midsection the earlier will the separation occur upstream and the more intense will be the formation of eddies behind the body A correct selection of the tail profile can lead to a considerable shift of the beginning of separati6n toward the trailing edge of the body or even to the avoidance of separation altogether 16 The values of the dimensionless coordinates of several streamlined profiles are given in Table 102 TABLE 102 0 005 010 020 03 04 05 06 07 08 09 095 10 27 Profile No 1 dm 01 0528 0720 0917 0987 100 0960 0860 0738 0568 0340 0195 0 Profile No 2 rO008 0490 0750 0960 100 0980 0930 0840 0ý720 0560 0370 010 drn Profile No 3 2Y 0 0530 0720 0940 100 0995 0940 0860 0910 0520 0300 0 dm o is the radius of curvatureiof the profile nose and tail 17 Elliptical cylinders and circular cylinders with tail fairings likewise belong to the category of streamlined bodies The drag coefficient of these bodies is higher than that of bodies shaped according to the data of Table 102 In view of their great simplicity however they are frequently used in practice 384 18 The drag coefficient of systems of interconnected bodies such as beams or trusses is a function of their cross section shape the method of connecting the beams the direction of impinging stream and Reynolds number The influence of the direction of the impinging stream for such a system is more complex than for a single body since here the rear elements are oriented differently in relation to the aerodynamic shadow of the front elements Figure 106 a FIGURE 106 Pattern of stream flow past truss systems 19 The coefficient of local resistance of a truss placed in a pipe is approximately determined by the formula 7W2O I 15c 19 I 1 FF3 109 385 where in the given case F yr filling ratio of the pipe section by the truss elements n filhing coefficient of the truss proper s c drag coefficient of the truss at given Reynolds number Re and given angle a of the impinging stream it is determined by the formula cf Khanzhonkovs paper 106 e c 6 1010 where ce is the drag coefficient of the truss at a 0 and Re Re C is the drag coefficient of the truss at a 0 land the given Re e is the drag coefficient of the truss at the given a and the value of Re at which the relationship efa was obtained 20 The calculations of mine shafts and excavations are based on the dimensional coefficient of aerodynamic resistance expressed by the following formula through the coefficient of local resistance 1 a I kgsec2 m 1011 P28 4 The resistance of the mine excavation is expressed by the following formula through the coefficient ap 24L Q TIl AH4a a TL kg 2 o 1012 386 t 103 LIST OF THE DIAGRAMS OF RESISTANCE COEFFICIENTS OF SECTION X Diagram description Source Diagram Note number Single smooth cylinder placed in a pipe Plane 1012 101 Caccording to the experimental parallel flow data of the authors calculating formula according to the authors recommendations Single stay rods and braces placed in a Kuznetsov 103 Flaksbart 102 pipe Planeparallel flow 10131 Chesalov 108 Yurev and Lesnikova 109 Hiitte 1015 Single rolled sections placed in a pipe 1012 Skochinskii Kseno 103 The same Planeparallel flow fontova Kharev and Idelchik 105 Sphere placed in a pipe Threedimensional 1012 Hiitte 1015 104 flow Smooth elliptical cylinder placed singly in The same 105 a pipe Threedimensional flow Single bodies of different shapes placed in 106 a pipe Threedimensional flow Single ellipsoid placed in a pipe Three 107 dimensional flow Circular cylinders placed in pairs in a pipe Kuznetsov 104 108 Planeparallel flow Re10 5 Circular plates placed in pairs in a pipe 1012 Hfitte 1015 109 Threedimensional flow Rolled sections arranged in a row in a pipe Skochinskii Ksenofontova 1010 Planeparallel flow Kharev and Idelchik 105 Pipe reinforced by various stay rods and The same 1011 braces across the section Triangular truss placed in a pipe Plane Khanzhonkov 106 1012 parallel flow Square truss placed in a pipe Plane The same 1013 parallel flow 387 104 DIAGRAMS OF THE RESISTANCE COEFFICIENTS Section X Single smooth cylinder placed in a pipe Planeparallel flow Diagram 101 m dmli Sm Ali 2 dLsj 1a0IIKcII r2gi where C is taken from the curve c I4 4 drn v is taken from 13 b Re 01 05 10 5 110 510 110 1 2 03 103 10 4 510 4 o0 10 210 13105 1410 51510 1610 5171 810 8 IC 1 Small turbulence cZ159o01225110o0145012651165111o 1201ooi 090 11051125 25 1120 1110 108010601032I03010321035 2 Large turbulence C1 lI I1112109510901105125112010401031 I I 388 Single sta rosadbae lcdi appPae eto Sl where cr and t are taken from the tables given here v is taken from 13 b 389 Single rolled sections placed in a pipe Planeparallel flow I Section X Diagram 103 WT ýddT 0If Sm r where ce and c are taken from the table correspo mg to the given profile for the indicated angle a 15 i a 390 Sphere placed in a pipe Threedimensional flow DSection X I Diagramn 104 Smm 4 Sm I o 2 where c is taken from the curve cx Re wedm 1 is taken from 13 b Re 05 10 5 10 510 102 5102 103 5103 104 c 750 300 900 4001 175 100 061 048 038 040 Re 104 2105 3105 41056105 7 10s 5 106 C 049 050 049 040 018 020 020 021 022 391 Smooth elliptical cylinder placed in a pipe Section X Threedimensional flow Diagram 105 Sm S where c is taken from the curves c tRej corresponding to different Idin Re i w is taken from 13 b Re 3104 4104 5104 6104 7104 8104 9104 10 5 Idn 2 5 Cz 038 031 026 I 0m22 1 0185 016 014 013 lldmr 30 c 0o32 026 022 1 01 1o016 014 0l 12 011l Ildmn 35 c 02 02 02 o 1 018 1 016 01 o 6 12 0 1 ldm 40 Ij2L12 18 016 015 014 j013 013 392 Section X Single bodies of different shapes placed in a pipe Threedimensional flow Diagram 106 Sm 2 where c and t are taken from the tables given here N v is taken from 13 b Type View Drag coefficient s Convex hemisphere dm c 034 tml5 Concave hemisphere S dM2 C 133 m925 Smooth cylinder axis parallel t0 1 2 1 3 1 4 1 5 6 7 to direction of Iflow C 091 085 085 087 090 095 099 sm 4 M 15 dm Smooth cylinder axis perpendi dM 0 0025 010 020 050 10 cular to direction of flow Smi di Wedm 8 120 098 082 074 068 063 R e 88 1041 V It ag 12 Cone SM d 505 4 CZ 30 50 Square beam a 0 10 20 30 40 50 d 5 CX 158 112 080 087 089 090 15 393 Single ellipsoid placed in a pipe Threedimensional flow Section X Diagram 107 Jmr9n n Sm Elongated ellipsoid rl where ex is taken from the curves c 5 atCRdfor the different Flattened ellipsoids a att e ne d elhip so zi y v is taken from 13 b Re 2110 i 10 2105 310 5 4105 51O 610O5 47 1 Elongated ellipsoid tdm 59 4 I032 1022 10101 0051006 1 007 10o51 008 4 2 Flattened ellipsoid tdm 43 94 5 I62105910581 0571031100 Diagram 106 continued Type D View Drag coefficient c Rectangular plate II f Sm 41 jdn 0 005 010 020 025 035 050 10 cZ 200 140 129 121 119 117 111 110 15 D 0 01 02 03 04 05 Washer IC 110 114 115 118 120 L22 01 07 081 09 jio Cm DdI 125 140 1 178 192 200 W 5 a 394 Circular cylinders placed in pairs in a pipe Plane parallel Section X flow Re 10 Diagram 10 8 Smm d41 sin a4 tot s4 V W 40 50 89 I I 5hm10 t15120 2 30 40 50 10 120 30 50 100 Cot 060 060 076 110 144 150 152 162 j182 192 20 206 Sm I H 0 i 15C t F 1 2y 3 where cxtot is taken from the curve Cx tot U L i istaken from 13b Section X Circular plates placed in pairs in a pipe Three dimensional flow Diagram 109 VWm Sm Sr F M 2Y Cxtot 7O 2 to0 10 11s 04 08 8 10515 0 MI 5 folio where ot is taken from the curves cx toti tot 0 025 05 075 10 125 15 175 20 215 30 CZ tot 222 180 140 118 098 084 080 088 105 130 152 395 Section X Rolled sections arranged in a row in a pipe Planeparallel flow Diagram 1010 Smm D4F 4 UIT perimeter llilll lllli lllll Sm L A H 1 1 I 1 3 2 y 3u TAS L I A ý I D1 If L where c 1 is taken from the curves c j 1 for the different sections is taken from the table for each section X is taken from diagrams 21 to 25 dm 4Er0 j2 r jej dm T 12 0 5 10 too Section No 1 g15 Section No2 va15 0 1017 08 1045 106 1o71 1080 10851088 o Section No 3 c 10 cS 0 1 011 1o12 1012 1012 1012 1o12 0121012 1012 Section No4 4 qI 0 C 0 1 17 10 2 1037 1043 I046 1047 10471047 0o47 Section No5 c 10 CA I 0o17 1026 1o30 1o30 1o30 1o030 03o301030 030 I 396 396 Pipe reinforced by various stay rods and braces across the section Section X SDiagram 1011 Dh no pipe perimeter 1 g CWO LIT xi dm Dh Dho 2g rr YLbI¼F where i ordinal number of the reinforcement Czu is taken as cfor the given section as a function of I11d from diagrams 101 to 10 10 I is determined from diagrams 21 to 25 tj is determined as a function of the section shape a for ordinary rolled sections plates with frontal impingement of the streafn f etc by the curve b for cylinders and streamlined sections qt 1w0 dmI 2 1 6 a 1 10 20 30 40 50 60 80 100 100 135 70 210 240 260 260 2501230 210 190 175 155 145 397 Triangular truss placed in a pipe Planeparallel flow Section X I Diagram 1012 SM 0 where Co CX c is taken from the curves c a of graph a obtained for Wodm cO is taken from thz curves cm fRe of graph b obtaicu for a 0 cx0 is taken from graph a for aO0 v is takenftwm 13 b Go 1 1W0 10 20o 250 3W 35 400 45 50r 6I0 Truss No 1 C 3 132 13 137 125I 113 1 100 1 115 125 139 142 140 Truss No 2 C 152 152 149 143 135 1130 1132 J142 153 158 158 Truss No 3 C 157 157 154 147 139 1135 1 137 146 157 160 155 W elded truss without cross SNo 1 stays V 0183 Welded lattice truss with cross No 2 stays IP 0230 Lattice truss with cross stays and No 3 corner plates f 0241 U L I i I I I JI i I I 1 iII 1 1 1 1 i 1 iI ii AF j a a do u 5 5 5 5 Re 0510 0610 08101 1010 1210 1510 1610 j Truss No 1 CX0 165 163 161 1 158 1z55 150 Truss No 2 Cr 165 163 160j 155 150 140 I 135 Truss No 3 C 155 I 150 1 141 132 117 1112 4 398 Square truss placed in a pipe Planeparallel flow 0 5 10 15 20 30 35 40 45 Cistknfoth Truss No 1 wodm c 1 135114 115 1178 1 1791 17811671154 1150 Re is take frm Truss No 2 fCo is taken from the Cxs1 150 1160 1178 1193 11951 195 1193 1183 1181 for a fm CAo is taken from gra Truss No 3 Sm b11 cl 149 156 1173 1189 119311931 191 180 1177 FO F 6 is taken from 1 Truss No 4 cI 1591168 1188 1203 12051203 1199 1190 1188 Section X Diagram 1013 Sm F1 where curves C6 a of graph a obtained for curves co Re of graph b obtained ph a for aa 0 3 b Welded lattice Lattice truss llItruss without U withcross cross stays No 3 stays and 0183 spheres J fY 0249 Welded lattice Lattice truss 2 IA trus withW ith cross tA russswthy No 4 stays and V 0230 9 1corner plates o 0 C0 0 C Truss No 1 1155 11501144113811301122 Truss No 2 Co01 80 1 1 717o1165116 11541 Truss No 3 cO 172 1 168 11641159 11551151 1146 Truss No 4 ool 184 177 1 17331170116811661 18AS 399 Section Eleven FOP Fex r F0 F o r i l Dor r R D Re STREAM DISCHARGE FROM PIPES AND CHANNELS Resistance coefficients of exit stretches 111 LIST OF SYMBOLS area of narrowest and exit sections respectively m 2 total flow area and frontal area respectively of the grid washer screen m 2 free area of one orifice of the grid screen m 2 perimeter of the orifice section m area ratio diameter and radius of narrowest section of the exit or of the initial section of the free jet nozzle m diameter of the orifices of the grid washer m Dor 4F 4t h I 81 0 We ws wor All hydraulic diameters of the conduit grid washer or screen m sides of narrowest rectangular section of the exit m width of gaps between the louver slats m halfwidth of the initial section of a planeparallel free jet m distancebetween the discharge orifice of the exit and the baffle m dejpth of the orifice or length of the exit stretch of a bend or elbow m diffuser length m free jet length m cdntral angle of divergence of the diffuser or angle of the edges of the grid orifice and also halfangle of divergence of the free jet mean velocity in narrowest and exit sections of the conduit msec mean velocity in the openings of the grid msec total pressure losses or resistance in the exit stretch kgm 2 resistance coefficient of the exit stretch kiheticenergy coefficient 112 EXPLANATIONS AND RECOMMENDATIONS 1 When a strearn flows out from a pipe independent of the exit conditions the kinetic energy of thecdischarged jetis always lost to the pipe in general it follows that the exit losses will be a All AHt Aldy 11 1 The resistance coefficient of the discharge in terms of the velocity in the narrow section t 400 will be equal to AH Afft d tT YOO Csttd 112 In general the velocity distribution at the exit is not uniform and therefore the dynamic pressure is determined on the basis of the specified distribution Ay L d 113 Fex and tdndyf dP d 71 N 114 7Fex Fe w n We where n is the expansion ratio of the exit stretch and N e dFis the ex Fi h kineticenergy coefficient of the stream in the exit stretch x 2 In the case of free discharge into a large volume from a constantsection straight conduit the total losses reduce to the loss of dynamic pressure at the exit since F F n the total resistance coefficient will be AH AHdYnN 115 2g 2g The coefficient Nis a function of the velocity distribution at the exit and is larger than unity except for a uniform distribution where it equals unity 3 In the case of an exponential velocity distribution at the exit cf points 6 to 9 of 42 Wa 116 where Wwax is the velocity at the given point and maximum velocity over the section respectively msec R is the radius of the section m y is the distance from the conduit axis m m I is an exponent the resistance coefficients of the discharge from conduits with circular and square sections are calculated by the following formula cf 119 2m I m 1Y 117 tw 02 4 rn22m l 3m t 3 2g 401 and the resistance coefficient of the discharge from a plane conduit by p AH m 118 yW mlm3 In the case of a sinusoidal distribution of velocities at a discharge from a plane conduit cf 410 w I IMsin2kn2 119 iý WO b where Aw is the deviation of the velocity from the mean at a given point over the section msec k is an integer 314 the resistance coefficient of the discharge is calculated by the following formula 119 74 2 1110 2g 4 The pressur losses in a diffuser in the case of free discharge into a large volume are made up of the loss in the diffuser proper ed and the loss of dynamic pressure at the exit x AH N 70 Cd ex d 1111 IT The velocity distfribution at the discharge of a diffuser is assumed to be uniforjm N I to compensate for this assumption a corrective coefficient in the form I is lintro duced cf 118 11111 I d Cd r1aCa H 1112 2g where tcal dTifr Cexp V is the calculated resistance coefficient of a diffuser with discharge into a large volume and is determined from the corresponding graphs of diagrams 112 to 114 tfr and cxp are friction coefficient and resistance coefficient due to diffuser expansion determined fromthe data of diagrams 52 to 54 a is the tentative corrective coefficient allowing for the nonuniformity of velocity distribution at the diffuser exit The value of the correction fordiffurers of nearoptimum divergence angle lies within the limits 0 to 05 depending on the relative diffuser length jd The optimum divergence angle is the angle f6r which Cca is minimum cfdiagrams 112 to 114 The optimum diffuser length Id lies in the range 25 to 40 Df for circular and rectangular diffusers with unobstructed exits and in the range 50 to 60a 0 for aplane diffuser 402 5 If a stream encounters a baffle after its discharge from a pipe the loss will de pend on the relative distance between the baffle and the exit edge of the pipe In some cases the installation of a baffle will lead to an increase of losses and in other cases to a decrease In particular a baffle behind a cylindrical stretch or behind a straight diffuser of divergence angle a30 will always cause an increase in losses A baffle behind a curved diffuser or behind a straight diffuser of divergence angle larger than 300 can considerably decrease the total losses provided the distance from the diffuser to the baffle is correctly chosen 6 A baffle behind a diffuser creates a head forcing the stream to spread over the section This leads to a decrease of the stream separation zone and therefore to a more efficient spreading of the stream As a result both the losses inside the diffuser and the losses of dynamic pressure at the exit are reduced Simultaneously the baffle forces the stream to be deflected at an angle of 900 before the exit If the exit edge of the diffuser is not smoothly rounded this deflection willbe accompanied by a considerable contraction of the jet Figure 111a and therefore by an increase of its kinetic energy it follows that when a baffle is placed behind a diffuser of small area ratio so that the mean stream velocity at the deflection is large the gain obtained from the spreading and more complete expansion of the jet can be smaller than the additional losses caused by the jet contraction at the discharge In the case of considerable area ratio divergence angle the losses due to the stream deflection are relatively small and the influence of the baffle is greater Wex Rounding a b FIGURE 111 Flow pattern at a diffuser exit with baffle a sharp discharge edge of the diffuser brounded discharge edge of the diffuser 7 The smooth rounding of the discharge edge of the diffuser or the straight stretch reduces the jet contraction Figure 111b and leads to the formation of an annular diffuser in which additional expansion takes place and kinetic energy is transformed into pressure energy As a result the installation of a baffle behind a diffuser with rounded edges is advantageous in all cases independent of the area ratio 403 8 The optimum distance between the baffle and the discharge orifice at which the resistance coefficient of the stretch with discharge against a baffle is minimum exists for rectilinear diffusers of wide divergence angle and for straight stretches with diffuser of rounded edges When this distance is very large of the order of F06 the baffle influence is not felt and the losses are equal to a discharge without baffle When it is very small VP150 the flow velocity between the baffle and the discharge edge is increased and thelosses increase shaiolyr Fihnally Whefi withinthnerangoe1O 1ý5 025 the velocity of flow will substantially decrease and the eddy formation caused by the stream separation in the course of its deflection and expansion will also decrease h this is the optimum range of values of D 9 The following parameters are recommended for diffusers with rounded edges and baffles relative lengt 25 divergence angle 14to 160 relative radius of curvature of the discharge edge 2 06 to 07 relative baffle diameter ý 30 relative distance of the baffle from the ýiffuser 024 to 026 cf 118 The coefficient of total resistance of such a diffuser is equal to C 025 to 035 10 When an exit ditffuser is installed behind a centrifugal fan the recommendations stated under points 22 to 25 of S 52 should be taken into account The installationof a diffuser behind an induceddraft fan is especially necessary since it can reduce the exit losses by a factor of three to four cf Lokshin and Gazirbekova 1113 The relative length of a pyramidal diffuser placed behind an induceddraft fan should not be larger than L 25 to 30 at divergence angles e 8 to 120 and that of a plane diffuser not larger than d 4 to 5 at a 15 to 250 The resistance coefficients of diffusers placed behindjans are determined from the data of diagrams 1111 and 1112 11 In a free discharge of flow from a ringtype diffuser formed by a conical diffuser located behind an axial fan with a diverging back fairing the resistance of the ring shaped diffuser differs from the resistance of an equivalent conical diffuser to a much greater degree than in the case of a ringshaped diffuser installed in a pipe network cf point 27 of 52 Due to more uniform velocity distributions the loss of kinetic energy at thedischarge from an annular diffuser is much smaller than at the exit from an ordinary conical diffuser with equal discharge The annular diffuser is also characterized by a more ordered stream flow along its entire length contributing to the decrease of losses in the diffuser proper The resistance coefficient of such a difffiser 404 placed behind an axial fan can be determined by the formula AN 1113 where t is the resistance coefficient of the same diffuser at uniform distribution of the velocities in its narrow section determined from the data of Bushel 113 cf Table 113 of diagram 118 k is the corrective coefficient determined by diagram 518 12 The radialannular or axialradialannular diffusers used in axial turbines cfpoints 28 and 29 of 52 with induced draft and discharging the stream into a large volume can also be considered as discharge stretches The resistance co efficients of such diffusers are given in diagrams 119 and 1110 13 Another type of discharge is represented by exhaust vents having the same shapes and characteristics as supply vents Their selection should be based on recommenda tions given in under points 14 and 15 of 32 14 Inlet nozzles into a room also belong to the category of discharge units The main requirements of such nozzles are to ensure either a rapid dissipation of the kinetic energy or to give a concentrated jet The nature of the losses in such nozzles is the same as in stream discharge from a pipe These losses reduce to the loss of kinetic energy at the given degree of expansion or contraction of a jet The nozzles whose resistance coefficients are given in this handbook include not only the most effective types of nozzles but also some less successful ones which in view of their simplicity are widely used To this category belong such nozzles as ordinary bends and elbows 15 In certain cases the distribution of the air is carried out through air ducts with perforated surfaces Figure 112 Such a distribution ensures speedy dissipation of kinetic energy which is desirable in many installations At the same time if the ratio of the total area of the orifices to the area of the duct crosssection is too large 0 the stream distribution along the duct will not be uniform the nonuni formity increasing with the decrease of the relative length of the supply part of the duct Wor f or FIGURE 112 Air duct with perforated lateral outlet Tapered air ducts give a more uniform distribution of the stream along the perforated surface than straight ducts if the ratio of the final area to the initial area lies in the F range 0I 500 405 16 The total resistance coefficient of an inlet noztzle with perforated surface within the limits 05r 30 and Oc l0 can be calculated by the following formula cfGrimitlin 114 0r0 1114 For X 0 this formula gives values approximately twenty per cent higher than the actual values More accurate results are obtained by another formula cf Grimitlin 11 5 80 jI162F 1 15 The curves of diagram 1118 have been plotted onthe basis of the simplified formula 1114 17 Elbows and bends with large discharge volumes are frequently used as discharge nozzles The resistahce of such elbows and bends dep6nds to a great extent on the length of the discharge stretch At first the losses increase with length drop sharply and finally become constaht at some value of f Such a variation of the resistance cure is explained by the shape and magnitude of the eddy zone formed along the inner wall of the elbow after the turn 18 The eddy zone in anelbow starts from the turn gradually expands and attains its maximum width at a certain distance from this turn it then contracts until finally the stream spreads over the entire section Thus when the discharge stretch of the elbow ends at the section where the eddy zone is widest and the cross section narrdwest the stream will be dircharged into the larger volume at maximum velocity and with maximum energy loss This corresponds to the maximum of mon the graphs of dia grams 1120 to 1123 19 If the length of the stretch after the turn is reduced to zero the eddy zone will be absent the strednr will be discharged into the larger volume with a lower velocity and the resistance doefficient C will be smaller Thedecrease of C will however be very small since theF stream presses by inertia toward the upper wall and the velocity at the exit as a resulftis considerably higher than the mean velocity over the sectidn 20 If the discharge stretch is suofficiently long the stream will spread over the entire section and 1the resistance coefficient will be minimum The subsequent increase 0 will be accompanied by a certain increase of due to the increase of tWe friction losses in the straight portion The resistance codfficient for elbows with free discharge of the stream and discharge section twice as large as the inlet section is lower by 40 to 50 21 Guide vanes can be used to decrease resistance of elbows discharging into a large volume The relative reduction of resistance achieved here is even larger than 406 in elbows with lengthy discharge sections since the absolute resistance value of dis charge elbows alone is considerably larger than that of elbows with discharge stretches 22 The resistance coefficient of a straight exit stretch with a grid or orifice at the exit F 0o Figure 113 with Re 101 is generally calculated by cf 1110 1111 AH I C f 1 7 x7 I41 1116 where C is a coefficient which is determined as C from diagrams 33 to 36 v is a coefficient allowing for the influence of the platewall thickness the shape of the inlet edge of the orifice and the conditions of flow through it I is the friction coefficient of unit length of the orifice plate wall determined from diagrams 21 to 25 T Fr Fg is the crosssection coefficient of the plate 23 The general case is reduced to several particular cases a sharpedged orifices for which g 055 141 0 and expression df an xreso S1116 reduces to the following formula cf 117 1111 HI 0 707 1T 1117 p b thickwalled orifices for which 05 and c is determined from the curve cI ldhof diagram 1128 c orifice edges beveled toward the stream flow or rounded for which one takes 0 dh oC M 2 Ir2 and obtains where the coefficient C is determined in case of edges beveled toward the streamas C for a conical bell mouth with end wall as a function of the convergence angle a0 and of the relative length L bygraph a of diagram 1129 and in the case of rounded edges as C for acircular beilmouth with end wall as a function of T by graph b of the same diagram 24 The resistance coefficient of the exit through an orifice plate is calculated at Calculation by 1114 and 1118 can be made for Rea 104 407 Re 10 for sharpedged orifices by the following formula derived from expression 419 go 0707V Fi 1119 Here Lis determined from the curves tfReon graph a of diagram 410 is determined from the curves e0f Reon the same graph C 0707 is determined from the curve C0 on graph b of the same diagram p is coefficient of the discharge velocity from a sharpedged orifice and depends on Re and B e Co or efficient of filling of a sharpedged orifice at For 0 and depends on Re 0 0 Oor ror 0ol a b FIGURE 113 Stream discharge from a straight stretch through a grid or orifice a grid borifice FOr flow section The resistance coefficient is calculated at Re 10I for thickedged orifices by the following formula also derived from 419 r 5 1120 25 The resistance coefficient of louvers with fixed slats installed in the exit of a straight channel can be approximated by the following formulas a bi opt C A l08 1 fr Feg 2 1121 b b i F 7 frJ kg tk 1108511T 1122 408 and k 10 for a standard louver vertically cut inlet edges k 06 for an improved louver inlet edges cut horizontally F2 is the crosssection coefficient of the louver Fg is the friction coefficient of unit relative length depth of the louver channels de dWor b1 determined from diagrams 21 to 25 as a function of FIGURE 114 Pattern of a free jet FIGURE 115 Auxiliary functions for calculating a circular free jet FIGURE 116 Auxiliary functions for calculating a planeparal lel free jet 409 26 The energy of a free jet discharged from a system into an unlimited volume Figure 114 is lost to thesystem All the basic parameters of an incompressible free jet can be determined by the data of Abramovich 111 given in Tables 111 and 112 these tables contain formulas for calculating the corresponding parameters of the free jet for both its initial and main zones The initial zone is understood to mean the jet zone starting from the exit orifice of the channel and ending at the section where the velocity at the axis begins to differ from the initial velocity at the exit The main zone is understood to mean the entire remaining part of the jet characterized by a graiual decrease of the velocity at the axis The section separating the two zones is called the transition region The coefficient of jet turbulence a is equal to 008 for a circular jet and to 009 to 012 for a planeparallel jet a 410 TABLE 111 Characteristics of a circular free jet at a distance S from its initial section No Characteristics Formulas for the initial jet zone Formulas for the main jet zone 1 2 Dimensionless diameter of the outer boundary of the jet Dimensionless area of the jet section Dimensionless diameter of the constant velocity core Dimensionless diameter of the constant mass core Dimensionless distance of the end of the initial zone from the exit section of the discharge channel Tangent of the halfangle of jet divergence Tangent of the halfangle of contraction of the constant velocity core Dimensionless velocity at the jet axis Dimensionless arithmetic mean velocity of jet Dh R h aS o K34jF I JaS2 F O 34 R I Dc Rc aS D R dS S 067 tg 34a at a 008 a 151 tgat I W at a 08 as 0 7 W e10 m aS IaS 2 a 1aS076 a 1322 Q av whr t pm 1 whn pFw 6aaS aS 2 e 0 e 2 aS Q a S 2 Dh Rh as t0 34 K I F j ý aS 12 Da Ra fa In order to determine one calculates first 052 0 29 from the given value of des the value of y8 is then found from the curve By in Figure 115 tg a an34Wý at a 008a 15 w 096 029 a 0 2 coast Wav 048 const 22 0 29 059 e s029 10 1 Dimensionless meansquare jet velocity 12 12 Dimensionless fluiddischarge across the given section Dimensionless residue of kinetic energy of the jet in the given section I 411 Table 11 lcontinhed No Characteristics Formulas for the initial jet zone Formulas for the mjin jet zone as 1 4 0 2 13 Dimensionless residue of kinetic energy of the e I 1 061 ea a B constantmass jet core in the given section W0 In order to determine Buonc calculates first B from the given value of aýSRO point 4 of thc tilble With B known one determins 1 from Figure 115 and then the value of B2corresponding to this in the same figure 14 Resistance coefficient of the free jet CIe 7W A 15 Resistance coefficient of the constant mass jet core 29 TABLE 112 Characteristics of a planeparallel free jet at a distance S from its initial section No Characteristics Formulas for the initial jet zone Formulas for the main jet zone 1 Dimensionless halfwidth of the jet 1 2 4 1 r 24 I 24 OSi1 F1 s F1 a 2 Dimensionless area of the jgt section Fo i e24 I Oc aS 3 Dimensionless halfwidth of the constant 6 I096 velocity core o Dimensionless halfwidth of the constant ds 2 41 mass core 0 0 In order to determine pa one calculates first V jiS 041 from the given ýalue of d fthe value of Y is thenfound from the curve A in Figure 116 so i 03 5 Dimensionless distance of the end of the ar initial zone from the exit section of the Fi discharge channel lit 412 Table 112 continued No Characteristics Formulas for the initial jet zone Formulas for the main jet zone 6 7 Tangent of the halfangle ofjet divergence Tangent of the halfangle of contraction of the constantvelocity core tg a 24a at a ý 009 to 01 2 a 12 to 161 tg as 096a at a 009 to 012 a u 5 to 650 We 10 We 8 Dimensionless velocity at the jet axis 9 Dimensionless arithmeticmean velocity the jet 1a vQ w I043 aS I 024 10 Dimensionless meansquare jet velocity WavmX W3 wm 1043 Q aS I 0 4 3 ý 11 12 13 Dimensionless fluid discharge across the given section Dimensionless residue of kinetic energy of the jet in the given section Dimensionless residue of kinetic energy of the constantmass jet core in the given section tg a 2401 009 0 12 a 12 to 160 OM 12 c S 0 41 av Wm q I2 4 0 094 e v j041 l73A I 0 41 In order to determine A one calculates first A from the given aeSl With known one determines a from Figure 116 and then the value of A2 corresponding to this in the same figure CIe 1o Ien e 0 e 1021 2 aS 8o ea aS ea I 0275T 0 AH 2g Am S e TW 14 1 Resistance coefficient of the free jet 15 Resistance coefficient of the constant mass jet core 413 113 LIST OF THE DIAGRAMS OF RESISTANCE COEFFICIENTS OF SECTION XI Diagram description Sturcc diagram1 Note Free discharge from a conduit at different velocity d istribut ions Free discharge froli a circular rectilinear diffuser Free discharge from a rectangular square diffuser Free discharge from rectilinear plane diffuser Discharge from a rectilinear diffuser against a baffle at ldfDh 10 Discharge from a straight stretch with rounded edges against a baffle Discharge from a diffuser with rounded edges and optimum characteristics against a baffle Free discharge from an annular diffuser Free discharge from an annularradial diffuser W 0688 Free discharge from an axialradialannular diffuser B 206 d 0688 a 8 Ca0 05 Free discharge from a plane asymmetric diffuser behind a centrifugal induceddraft fan Free discharge from a pyramidal diffuser behind a centrifugal induceddraft fan Side discharge from the last orifice of a circular pipe Straight rectangular exhaust vents lateral openings with and without fixed louvers Rectangular exhaust vents with elbows lateral openings with and without fixed louvers Straight circular exhaust ients Rel9 Duct caps Airduct with perforated lateral outlet Baturintype outlet Discharge from a 90 bend Discharge from a squaresection albi 10 sharp 90W elbow with contracted or ex panded discharge section Discharge from a rectangularsection aob Q 125 sharp 90W elbow with contracted or ex panded discharge section Discharge from a rectanguilar section alb 40 sharp 90 elbow with cofitracted or expanded discharge section Discharge from a smooth 02 90 elbow with contracted or expanded discharge section Discharge from a smooth 40 elbow with discharge section contracted or expanded by a factor of two Idelchik 119 Idelchik 118 Khanzhonkov 1118 Nosova 1114 Idelchik 118 Bushel 113 Dovzhik and Ginevskii 116 The same Lokshin and Gazirbekova 1113 The same Nosova and Tarasov 1115 The same Khanzhonkov 1119 Baturin and Shepelev 112 Grimitlin 114 115 Baturin and Shepelev 112 Khanzhinkov and Talicv 1121 According to the data of 1116 The same Yudin 1122 The same 111 112 113 114 115 116 117 118 119 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 Calculating formulas Approximate calculations The same Experimental data The same f A The authors experimental data Experimental data The same 1124 1125 I 414 A Continued Diagram description Source Nodof Note diagram Nt Discharge from a smooth 90 elbow with discharge section Yudin 1112 1126 Experimental data expanded by a factor of two balbo 20 and with five thin guide vanes Discharge froma straight conduit through a grid or Idelchik 1110 1111 1127 Calculating formula partially orifice 0 Idh 015 1112 experimental data Discharge from a straight conduit through a thick The same 1128 The same walled orifice or grid Discharge from a rectilinear conduit through an 1129 Approximate calculating orifice or grid with orifice edges beveled or rounded formulas toward the stream flow Discharge from a straight channel through a fixed 1130 According to the authors ap louver proximate formula taking into account the experiments of Bevier 1123 and Cobb 1124 Discharge stretches under different conditions 1131 Tentatively Circular free jet Abramovich 111 1132 Planeparallel free jet The same 1133 415 114 DIAGRAMS OF RESISTANCE COEFFICIENTS Section XI Free discharge from a conduit at different velocity distributions Diagram 111 Resistance coefficient t Al Type of velocity distribution Scheme Uniform velocity distributions 10 Exponential distribution 3V w 01a Circular or square pipe 2m Im P z 4mt2mm3 is determined from curve 1 Wmax om m 0 I0 w max b Plane pipe m3 is determined from curve 2 100 135 200 300 400 700 1 Circular pipe C 270 200 150 1 125 115106 100 2 Plane pipe S 2001 163 15 119 111211041 100 26 ZJ o o 02 a4 o 416 Type of velocity distribution Scheme Resistance coefficient z am 7002 3 iAuAt 1 s determined from the curve Ce Wf on the graph S01 i02 03 04 05 06 07 08 09 110 11001106 11311 24 11381 4 1 74 1 96 2202 50 Sinusoidal distribution of the velocities in a plane pipe As 2y I l sinUS k integer YV Wo a 440 0 r 08 Asymmetrical distribution in a plane pipe W e 0O585 3 6 7 164 sIn 02 195 Parabolic distribution a Circular or square pipe S Sgi 20 RPo b Plane pipe max 155 417 Section XI Free discharge from a circular rectilinear diffuser I aSection 2 I Diagram 112 Values of gcal d 6o N 12 4 16 1 8 120 12 14 16 IM M 10 090 079 071 062 055 050 041 O13 0X3 039 040 15 084 070 060 051 045 040 034 031 03b 040 042 20 081 065 052 043 037 033 029 0 d 035 040 044 25 078 060 045 036 030 027 026 028 033 041 044 30 074 053 040 031 027 024 023 027 035 044 048 40 066 044 032 026 022 021 022 027 036 045 051 50 052 035 028 023 020 019 022 029 038 048 053 60 041 028 021 018 017 018 024 032 042 051 056 100 040 020 015 014 016 018 026 035 045 055 060 A V a caI approximately 2g where ccal is determined from graph a a is determined tentatively from graph b When a screen is mounted in the exit sum it n 29 where C is determined by the basic formulas Cs is determined as C from the data of diagram 86 Id 10 20 40 60 100 W o 1o0 o oo I 0I 418 Free discharge from a rectangular square diffuser Section XI Diagram 113 Q noperimeter Values of Ccal id 10 10 089 079 064 059 056 052 052 055 15 10 084 074 053 047 045 043 045 050 20 10 080 063 045 040 039 038 043 050 25 10 076 057 039 035 034 035 042 052 30 10 071 052 034 031 031 034 042 083 40 10 065 043 028 026 027 033 042 053 50 10 059 037 023 023 026 033 043 055 60 10 054 032 022 022 025 032 043 056 10 10 041 017 018 020 025 034 045 057 S O I C ca very approximately where Ccal is determined from graph a a is determined tentatively from graph h d1DC 1 20 140 160 1100 1 5104 0o30o1 0201 o0 b 419 b width constant along the diffuser AH 4 Tor 1 ocal approximately 2g where Cca1 is determined from grapl a a is determined tentatively from graph b Values of Ccai d U O 10 100 Og95 089 084 079 075 070 064 058 055 052 051 050 051 15 100 0 93 086 078 071 066 061 053 049 046 045 045 046 048 20 100 090 080 072 065 059 054 047 042 041 041 042 045 0oal 25 100 088 076 066 0b9 053 048 042 038 038 039 042 046 0i51 30 100 086 072 062 054 048 043 037 036 036 038 042 0 47 054 40 100 083 066 055 046 041 037 033 032 034 038 042 049 058 60 100 0ý76 0b6 045 037 032 030 028 030 034 040 047 056 065 100 100 067 043 033 027 025 024 025 030 037 045 053 063 073 S10 20 4 to G 111 045 040 030 00 00 LJ 04 4 7 I I2 a b 41 420 4F n Values of C 11 as perimeter e F P1Fe 11010 1 01 1020510301040FTD0D11 IosIo Io 0 joo 0Iow oI 0 10 137 120 111 100 15 159 150 106 072 061 059 058 058 30 237 123 079 066 064 066 066 067 067 45 334 150 085 073 075 079 081 082 082 082 60 465 098 076 080 090 096 100 101 102 102 90 907 150 072 074 0S 089 0941096 098 100 100 AH is determined from the curves t Baffle EOJ ND 005 07 1 015 020 026 030 0o36 040 t0 00 1oo A I I o I oI I I I I 1o 1 50II rD 02 I J 230 1 090 I 052 1 051 1062 107510821085108610851 085 rID 03 1 1160 1075 I 047 I 048 1055 I0o66107310781081 10821 082 riD 05 CI 250 1 130 063 044 I 041 1049 10581065107110761087 1 078 11 1 AM hO iW dcicro ined from the curves f 2g correspond in g to d ifferent 10 V a 4 az V 3 04 05 05 4 421 Section XI Discharge from a diffuser with rounded edges and optimum characteristics against a baffle Diagram 11 7 hIDeo010 015J020 O25l030I033I040 0 ED 0 6D 0 C 078 046 036 032 032 033I033 034 034 035 II D25 a a 14 DR Do D07 3A 08 Dof 10w6 is determined from the curve Free discharge from an annular diffuser Section XI Diagram 118 2g where C is taken from Table 113 kj is taken from diagram 518 TABLE 113 id00 0Ii 0 170 0 125 12 67 87 i6 82 0 9 3 6 3 C 047 043 035 034 029 Ir 422 Free discharge from an annularradial diffuser d 0688 DSection XI Diagram 119 AH 7 2 is dctermined from the curves 4 0 Values of b I Dd d n2 hD D 7 d 7 Q Q Q discharge m3sec u peripheral velocity at maximum radius insec 1 1 18 j1 22 126 130 1 4 38 42 a Diffuser behind an operating compressor 05 15 1076 107610761 17 0651069 071 072 07 19 058 064 067 071 072 22 049 065 061 066 071 b Diffuser behind nonoperative compressor 14 082 072 069 070 07 1 7 16 076 064 061 061 063 064 18 070 057 054 053 055 0571058 20 051 046 045 046 048j050 a b 423 Free discharge from an axialradialannular diffuser Section XI 206 00688 2 8 05 Diagram 1110 noH 431 2 is determined from the curves Cn a 7100 Valuesof C 12 061 054 052 049 049 049 2 056 045 043 042 043 044 045 047 4 052 039 034 0 0351038 040 046 b 1 Dd n 2 D 2h D Do Q aow d a Q discharge m 3sec L aa peripheral velocity at maximum radius msec IV 11 2 26 1 Z Section XI Free discharge from a plane asymmetric diffuser behind a centrifugal induceddraft fanDiga 1111 Digrm 11 1 F5 L 20 J25 30 35 40 AH V is determined 0 2g C I 051 1 034 1025 I 021 1018 017 from the curves Ctn corresponding to different a 054 036 1 027 I 024 11022 I 020 I055 1038 I031 1 027 1 0251 024 C I 059 I 043 J 037 1035 11033 033 30 2 063 050 1 046 1 044 11043 1042 O 350 C I 065 I 056 I 053 I 052 jiO51 I 050 ZX4 is 22 Z6 30 34 3g 442 ci 4 424 all Free discharge from a pyramidal diffuser behind a centri Section XI fugal induceddraft fan Diagram 1112 1 tis determined from the curves Ccafn corresponding to different e TuI 4P F where n F 15 20 25 30 35 L 054 o042 1037 1034 1032 1031 C 15 C 1 067 1 058 I 053 I 051 I 050 i 051 075 1067 1 065 I064 1064 1065 AfB 250 080 1074 1072 1 070 070 1072 a 300 z J i jq I085 078 1076 1 075 1075 076 Side discharge from the last orifice of a circular Section XI pipe Diagram 1113 102 03 041051 06 07 0s 09 10t 12j 141 1aI 1 One orifice C 1 657 1 3001 164 1001730 1550 1 4481 367 1316 1244 I I o 2 Two orifices C 167713301 172 116 845 1 680 I586 500 438 347 290 1 252 225 2 single orifice 1 Single orifice on each side is determined from the curves where t or F z 0u ta o u z I 425 Straight rectangular exhaust vents lateral openings with and Section XI without fixed louvers Diagram 1114 h nbh Y0 5 f F A Layout of the openings Resistance coefficient an C 0 0o E z without louvers 1 b without louvers GW 16 a 460 I 14 00 One Two Thrqe Di D D 036 036 036 036 024 012 15 15 155 500 350 220 530 156 220 Four The si rne 15 720 5 0J 260 196 I U 1 05 350 100 290 Vp 426 Section XI Rectangular exhaust with elbows lateral openings with and without fixed louvers Diagram 1115 h nbh 427 wDDO Section XI Straight circular exhaust vents Re104 Diagram 1116 No I Vent characteristic Resistance coefficient SAN I With plane baffle Values of 010 1020 1025 1030 1 035 1 04 1 O100e 340 260 210 170 140 120 110100 2 350200150 1201110 3 400 230 190 160 140 1 30 115I110 100 1 00 4 290 230 190 170 150 1301o20110100 5 2 60 120 100 080 070 065 060060 060 060 2 With split canopy 3 With hood 2J3 a 16 I 2 i 05 4 With split hood a Oz o4 t0 it 5 With diffuser and hood 428 Dut ap Section XI Duct caps Diagram 1117 Resistance coefficient Type of cap View With three diffusers 4 10 Hemisphere with orifices 10 For P 0564 Hemisphere with orifices C 10 For o 39 A 4 Hemisphere with slots r20 For 14 Cylinder With perforated surface 45 090 F or 47 Bend Do 04 0 I 152 141 429 Air duct with perforated lateral outlet T Section XI SDiagram 111 8 4Fd Dh 9 perimeter Ior ro SV F1 H18 L 015 S 05730and0fIH C8 RIO 051 06108 110o1 15 20 25 1 30 10 10 861 641 422 321 221 186 169 161 20 877 557 438 337 237 202 185 177 30 887 667 448 347 247 212 195 187 t O N e i i 1 10 Z 0 1 4 f 40 894 674 455 354 2541219 202 194 Baturn tpe otletSection XI Baturntye outet Diagram 11119 AK is determined from the cures C T9o 4i 641 271 171161 2 Plane vanes I I 1151121121 14118124135 X9 4 430 Section XI Discharge from a 900 bend Diagram 1120 Values of Cm 0I105 110I1I5I120 130 140 1 0 1S0 1220 00 295 313 323 300 272 240 224 210 205 200 02 215 215 208 184 170 160 156 152 149 148 05 180 154 143 16 132 126 122 119 119 119 10 146 119 111 109 109 109 109 109 109 109 20 119 110 106 104 104 104 104 104 104 104 At where Cn is determined from the curve Cm S for differentj A is determined from diagrams 21 to 25 431 Ia Section XI Discharge from a squaresection 10 sharp 90 elbow SectionXI with contracted or expanded discharge section Diagram 1121 2g where Cm is determined from the cur wcs I b for different X is determined from diagrams 21 to25 Cm iib0 0 05 0 1 5 1 20 40 60 80 150 9 bdbo 05 m I 901 10 I761 67 165 1621 62 16 1 59 bdb 10 t C o m 129 30 29 I28 126 1 221 2l 221 22 bb 14 z C rn 20 J 22 I 22 21 19 1 17 1 1 1 15 1 15 bb 20 Discharge fronw a rectangularsectionh 025 sharp elbow Section XI with contracted or expanded discharge section Diagram 1122 A H lb 2t where Cm is determined from the curves Cym f for different b X is determined from diagrams 21 to 2 5 il i o 0 6 1 15r 20 40 60o 80 150 i blb 05 C 5 I2 66 1 1601 91 58 I58 bjbK 0I 105 Cm 27 32 31331329 123 121120120 tI btlbo 1 4 Cm n118 21122 221 21 1 18116 114 1 14 bJbo 20 4Cm j13 115 1 16 115 115 114 13 11 11 432 Discharge from a rectangularsection Q 40 sharp 900 elbow with contracted or expanded discharge section Section XI Diagram 1123 t f mj LIby whereCmis determined from the curves Cm for different A is determined from diagrams 21 to 25 I 0o 105 10o1 151 20 1 40 o I0 Iso m 9 85 76171 681 62 59 57 56 2 10 Cm 1321 33j35 I 34 1301 21 211 2A 20 3 ý 1 b Cm 120 22 23 122 120 117 116 16 15 b 4 4 1 1 12 I Discharge from a smooth 602 90 elbow with contracted or expanded discharge section Diagram 1124 ra r 56 bjbe 05 10 20 52 0 7 9 28 9 V4 o8 z is Z0 433 Section XI Discharge from a smooth 90 elbow with discharge section contracted or expanded by a factor of two Diagram 1125 Ibo 01 02 03 04 105 06 08 10 1 blba 05 k C 15201492 4641444 14J01424 4214 18 2 brb 20 C 1 1 401 1301 1231 I171111110610951087 Viq a AM is determined from the curvesC 2g 0 tO Di 10 Discharge froma smooth 90 elbow with discharge section Section XI expanded by a factor of two 2 and with five thin guide vanes Diagram 1126 rlb0 02 05 10 00 70 7274 7274 154 99 90 059 049 044 C is determined fromn the curve CtL 20 072 C 478 902 1r0 t 434 4f dh d IOrT perimeter or orr Grid a Re o d 0 t A 0707 2 o is determined from the curve C I I b Re HY A0R 2g where C is determined from the curvesC tRe h on 5 graph a of diagram 410 R5 is determined from the curve TIRe on the same graph a of diagram 410 1 0707 VI I is determined from the curve area ofone orifice For total crosssection area of r fflon graph b of diagram 410 the grid openings v is determined from 13 b I1 05 010 015 O0 025 03D 036 040 045 j 060 5 60 065 070 07 OW l 09 10 1i 140 0122 167 416130 1 l59001740 620 48013901330127012221 180 10 710 705 5O ZoneA 2L I I I P9 04 05 of OP 05 8 A W 20 Zone A I l TbkLlll 0 07 02 e 04 0AS 05 07 491 es is 435 Section XI Discharge from a straight conduit through a thick walled orifice or grid Diagram 1128 or 4o 17 dhu for perimeter to area of one orifice For total crosssection area of the grid openings W fe r or a Re or dh 10 V I where v is determined from the curve cimt 0 o 1 05 t Vit Ais determined from diagrams 21 to 25 b Re 10 approximately 4e K where 4 andiare determined from diagram 410 C is determined as under a v is determined from 13 b 0 1 02 04 06 08 10 12 16 20 24 135 122 110 084 042 024 016 007 002 0 12 I I I I I I I f dh a OA 08 12 15 20 2 x 436 t Discharge from a rectilinear conduit through an orifice or grid Section XI with orifice edges beveled or rounded toward the stream flow Diagram 1129 Resistance coefficient c Shape of the orifice edges Scheme Beveled wor dh 3 or rRe 10 where is determined from the curve q fo dh 001 002 003 004 006 008 012 016 Woor for or Fr 046 042 038 035 029 023 016 013 Wor or 03 0d O 09 008 812 0o1 Wor dh 0 Rounded Re o h b10 we Fo Wfr l Iil W where C is determined from the curve 0 001 002 003 004 005 006 008 012 016 020 Wooo or Uor or v 050 044 037 031 026 022 019 015 00 006 003 Voro 03 0 00W 000 012 016 02 437 Section XI Discharge from a straight channel through a fixed louver Diagram 1130 No 1 Inlet edges of the slats cut vertically w2i w2 wo77 a 10i o whereL a I II AH t bop C2Lg 1 05k F9 f jX Y Quo F9 WI b1 P 2 m hW C 2 Inlet edges of the slats cut horizontally where k 10 for No1 k 06 for No 2 bf A is determined from diagrams 21 to 25 or t Fg louvergrid front For free cross section of the louver At F o To and l om054 b1 bJ0 pt 7g M F at Re s 10 the values of C are deter mined from the curve C v is taken from 13b A 8 01 02 03 04 1 05 1 08 07 08 09 10 C 247 I550 238II03I700 460 300 206 143I 100 438 4 A I Sction XI Discharge stretches under different conditions Diagram 1131 Resistance coefficient AN Conditions of discharge V iew f I o or or From a straight conduit with screen at I the exit where C is determined as C for a screen by diagram 86 approximately From a gutter with screen 11 approximately oForr T 08 8I Scree Through a stamped standard louver at C3 35 approximately F or t F a 08 with completely 00wo opened adjustable slats LO Wo Through stamped or cast grids cf diagram 322 p 111 C is determined from the curve Clfi of diagram 1127 approximately Saloo hly con verging nozzle 105 439 Circular free jet Section XI Diagram 1132 1 Initial zone S 8 to iOR a a101s 061 so 12 Main zone S8BtoI0R q 222 t029 1R 0 1 S 0 1o 15 M 1 2T H 1 3 q 100 152 238 324 412 500 586 762 937 100 070 061 040 031 026 022 017 014 e5 100 064 048 024 016 010 007 004 001 100 100 100 064 051 042 036 027 022 we I 100 557 138 257 4150 6080 8390 14100 21300 7 059 laS R 029 178B2 eaS 029 for B2 cf Table 111 096 WO as029 3 For the entire jet F I 34 1R1 q dimensionless discharge across the section of a jet e dimensionless kineticenergy residue in the section of a jet e8 dimensionless kineticeneigy residue of the constantmass jet core in ihe section dimensionless area of the jet section The values of q e and Tare r i n S determined from the graph as functions of IR 440 Planeparallel free jet Section XI Diagrain 1133 ag009 0 is 2 2 30 4j so q 100 119 139 160 179 196 211 240 266 e 100 091 081 071 063 058 054 047 042 a 100 088 075 060 049 042 036 029 023 f 100 100 100 090 081 074 068 060 056 Wo F j 100 208 316 424 532 640 748 964 118 AM C Tt I e 2i 1 InitialI zone S 10 to 12Aý WS a I 043 8 aS e 0275 80 2 Main zone S 10 tol28g S 12 v T041 094 e S J1 al 041 173A t 041 V 0 for A 3 cf Table 112 U 12 404 3 For the entire jet aS T124 S 80 q dimensionless discharge across the section of a jet e dimensionless kineticenergy residue iii thlc section of a jet e dimensionless kineticenergy residue of the constantmass jet core in the section F dimensionless area of the jet section The values of q e andF ar We s S determined from the graph as functions of 4 441 Section Twelve STREAM FLOW THROUGH VARIOUS TYPES OF EQUIPMENT Resistance coefficients 121 LIST OF SYMBOLS F area of the inlet section or the narrowest section of a radiator m 2 F crosssection area of a filtering cloth radiator or total cross section of the dustseparator element mi2 Fc crosssection area of the working chamber of a unit m 2 n area ratio D diameter of the inlet orifice m w mean stream velocity at the inlet or in the narrowest section of a radiator m isec W mean stream velocity before the filtering cloth filtration rate before the radiator in the free section of the dust separator msec AH pressure lss resistance of the apparatus device kgm resistance coefficient A4 momentum coefficient for imA et orifi v N kineticenergy coefficientfor the inlet orifice 122 EXPLANATIONS AND RECOMMENDATIONS a Gas or air scrubbers 1 Gas or air scrubbers can be divided into groups according to the princilple used for separating suspended particles The following types are treated here inertial louvertype dust separators ordinary and batterytype dust separators porous and cloth filters and electrostatic filters 2 In inertial louvertype dust separators the entering gas stream is split by the louver slats into find jets which turn sharply about these slats Figure 121 As a result centrifugal forces separate the dust particles from the stream The impact of thle dust particles on the slats and their reflection helps this separation To the dust separator TA s h e n r i c h e d g a s e s t Path followed by the S gases and the dust particles Gas inlet Cleaned gases 4 To the smoke exhaust FIGURE 121 The working of a louvertype dust separator 442 The degree to which the gas is cleaned is a function of stream velocity upon reaching the louver slats dustparticle size and specific gravity viscosity and specific gravity of the gases curvature of the trajectory of the jet passing through the louver and dust separator design 3 Cyclones are based on the utilization of inertia forces during the helical motion of the stream in the dust extractor starting at the tangential inlet and ending at the dust discharge orifice in the body bottom Figure 122 During the stream motion along the descending outer spiral a part of the stream is directed with decreasing velocity toward the exhaust pipe while the particles suspended in it are thrown toward the body wall and continue to move with the remaining part of the stream toward the dust discharge orifice Gas Gas a Droppingout dust particles b FIGURE 122 Pattern of stream motion in the body of a cyclone FIGURE 123 Extractor elements of a bat terytype dust separator awith screw blade bwith rosette A certain part of the stream moving along the outer spiral passes through the dust discharge orifice into a bunker carrying the suspended particles with it In the bunker the stream gradually loses its velocity and as a result the particles suspended in it settle out The clean stream reenters the dust separator body through the same discharge orifice but along the ascending inner spiral The stream flows along this spiral until it 443 enters the exhaust pipe and then continues along the pipe Here it is rejoined by the part of the stream which was separated from it during its descending motion 4 The degree to which the stream is cleaned in cyclones is a function of the design and dimensions of the unit stream velocity physical properties and size of the dust particles physical properties of the moving medium dust concentration etc In general cyclones operate efficiently when the dust particles are larger ýthan 5 microns 5 The capacity or output of a cyclone is in reverse ratio to its hydraulic re sistance Theoretically the resistance coefficient of a cyclone can be assessed by the method of Klyachko 1218 or Minskii 1225 The values of resistance coefficients of different types of cyclones given in this handbook have been determined experimentally Since the performance of a given type of cyclone is best characterized by the stream velocity in its body and it is more convenient in calculations to use the inlet velocity two values of the resistance coefficient are given for each cyclone correspond ing to the mean velocity at the inlet and to the mean velocity over the free cross section of the body f 6 Since the output of a cyclone increases with an increase of its diameter while the increase of diameter reduces the degree of cleaning in the case of large streams it is more expedientto use agroup of cyclones of smaller diameter or a batterytype dust separator instead of a single cyclone of large diameter The difference between a batterytype dust separator and a group of cyclones lies in the considerably smaller dimensions of the separator elements of the former and in the different design The extractor elements of a batterytype separator have special guide wheels a screw blade or a rosettewith blades set at angles of 25 to 300 toward the separator axis Figure 123 which ensure a rotary motion in the extractor elements 7 Wetscrubbing apparatus are used to increase the amount of removal of suspended particles Here the gas stream is wetted by a liquid sprayed through nozzles or by a water film on the scrubber surface The values of the resistance coefficients of different types of wetscrubbing apparatus are given in diagrams 126 to 128 8 A highperformance type of wet scrubber is the Venturi scrubber consisting of two main parts a tube sprayer 1 which represents a Venturi tube and a drop catcher 2 Figure 124 This unit is characterized by a high velocity at the throat 60 to 150 misec The liquid introduced in the tube sprayer in the form of jets or drops is split as a result of the high stream velocity at the throat into fine particles with large total surface area large number of particles per unit volume In addition the high velocityileads to an increase of the stream turbulence These factors increase the probability of c6llision betweenq the liquid and solid particles in the polluted gas It follows that the cleaning process in this unit can be considered essentially a coagulation process The coagulated particles are subsequentlycaught by the second part of the Venturi scrubber the drop catcher 9 The resistance coefficient of the tube sprayer is determined on the basis of the data of Teverovskii Zaitsev and Murashkevich 129 1226 1234 1235 by the following formula 444 tkc 121 444 where is the resistance coefficient of the tube sprayer without liquid wetting it 2g can be determined approximately as the sum of the resistance coefficients of the straight stretch the nozzle and the diffuser by the data given in Sections 11 III and V C is the resistance coefficient of a tube sprayer allowing for the influence of wetting by a liquid values of this coefficient are given in diagram 126 wg mean velocity of the gas in the tubesprayer throat msec g y are the specific gravity of the gas at the tube throat and of the wetting liquid kgmr mis the specific discharge of the wetting liquid 1mr3 of the gas The hydraulic resistance of the drop catcher is determined from the data of this section as a function of its design inlet 101 f FIGURE 124 Venturi scrubber 10 The dry cleaning of gas or air from fine dustis frequently achieved by means of cloth filters The resistance of a filtering cloth increases with time during the passage of dirty gas through it This increase in resistance is due to the settling of dust particles at the pore inlets these coalesce and form a secondary porous partition which aids the dust separation The resistance of the resulting filtering medium made of the cloth and dust increases with the increase of the dustlayer thickness 11 The resistance of the contaminated filtering cloth can be considered Zaitsev 128 as made up of two parts AH resistance caused by the unremovable dust and AH resistance of the dust layer removed during the periodical cleanings of the cloth It is therefore recommended Gordon and Aladzhalov 127 that the total re sistance of a contaminated filtering cloth be calculated by the following formula AH ABpqw kgrm2 122 where A is the experimental coefficient depending on the kind of dust the cloth type and the degree of contamination B is the experimental coefficient depending on the dry weight 445 I iI Gas b FIGURE 125 Electrostatic filters a vertical bhorizontal a wy ý and permeability of the dust layer ii is the dynamic viscosity of the gas kgsecm 2 p is the degree of contamination of the gas kgmr2 w is the filtration rate m 3 m 2sec 12 A different formula is sometimes used for the resistance of a contaminated cloth Rekk 1230 AH A AO Q 123 where A and A are proportionality coefficients depending on the kind of dust the type of clotih and the degree of contamination Q 1 is the specific loading of the cloth per F hour m3 m 2 hr Qh is the volume of gas filtered per hour nAhr F is the filteringcloth area m2 The values of AHi for different types of cloth are given in Tables 129 to 1215 13 The pressure losses in bag filters are mainly in the cloth sleeves so that the resistance of such filters can be calculated on the basis of data for resistance of different types of cloth The characteristics and resistance of two specific types of bag filters DIZ and MFU are given in diagrams 1213 and 1214 14 An efficient means of trapping the dust is also achieved by means of porous media such as layers of loose or lump materials sand gravel slag Raschig rings etc and also by sets of metallic gauze screens specially prepared porous materials filters from threadlike fibers and threads paper filters etc The fluid resistance of some of these filters can be determined from the data for checkerworks and screens cf Section VIII 15 The pressure losses in industrial electrostatic filters of almost all types Figure 125 are mainly made up of 1 the loss at the inlet to the working chamber 2 the loss at the exit from the working chamber and 3 the loss at the passage through the interelectrode space For a plate electrostatic filter this is the passage between the settling plates and in the case of a pipe electrostatic filter this is along the settling pipes The total resistance coefficient of an electrostatic filter can be considered equal to ARCi ch 124 where i is the resistance coefficient of the inlet stretch of the unit calculated relative to the velocity w at the inlet Cdi is the resistance coefficient of the discharge stretch calculated relative to this same velocity w tch is the resistance coefficient of the working chamber of the unit with the settling elements likewise calculated in relation to the velocity w 16 In almost all industrial apparatus the gas expands suddenly upon entering the working chamber Figure 12 5 a and b and therefore the resistance coefficient of the inlet can be determined in the absence of gasdistributing devices by formula 43 Afin 2 1 4 125 2g The case of a stream inlet through a diffuser horizontal electrostatic filters can also be considered as a case of inlet with sudden expansion with the diffuser angle generally larger than 60 to 90W 447 where n 1 is the area ratio of the unit ratio of the workingchamber area to the F area of the inlet orifice N0 dF is the kineticenergy coefficient characterizing F the velocity distribution at the inlet The values of this coefficient and of the mbmentum coefficient MFS3mdF can be very tentatively determined from Tables 121to 128 PO corresponding to different cases of stream inlet TABLE 121 TABLE 122 Elbow 450 o Elbow W 0 b Z X K 0i2 325 50 12 30 6j t 112 108 M 02 Mo 180 150 10 102 N 136 125 106 N 350 280 130 106 TABLE123 TABLE 124 ElbowS90o L0ot0 Elbow a 90 with expansion bt b P FO be 60 o b 0 o o o6 15 30 o Mt 140 125 112 106 102 1 70 1 40 125 110 102 448 TABLE 125 Bend 90 g05 TABLE 126 2 6 TABLE 127 a60 e 10 n r 30 40 60 10 30 40 60 to Mý 115 120 140 125 120 130 901 40 N 145 160 220 175 160 190 370 220 a 15 a 300 rr M 150 185 230 180 200 250 310 255 N 250 340 4005307201570 a450 a an 60P Mz 250 2901390 450 270 330 450 590o N 600 6901970 115 580 800151 157 a900 a 1800 MO 280 3751520 700 400 510 730 900 N 690 9001135 190 100 130 200 250 TABLE 126 Circular or rectangular diffuser with expansion in two planes I tt I a 60 a 100 n Too 30 40 60 10 30 40 60 10 M 110 115 135 115 112 120 160 130 N 130 145 205 145 136 160 28D 190 a15 30 M 1 40 150 170 140 180 2501220 180 S2202501310 220 340540 460340 8 450 60 Mz 20012601230 200 210 2901370 350 No 4001580 490 400 430170019001850 a900 a 1800 225 320 480 660 300 450 700 800 N 510 780 135 170 700 5 490 220 TABLE 127 Planediffuser W4 I 449 The resistance coefficient of the discharge can be determined on the basis of 33 C d is I 7dis 1 2 6 25 where C is a coefficient which is determined as C for the inlet stretch from diagrams 31 to 33 35 and 36 Fdis is the area of the narrowest section of the discharge stretch m 2 The resistance coefficient of tje chamber can be determined by the formula A 7R Ch Cdi Cf 127 where 5 1 F is the resistance coefficient of the discharge into the inter electrode space Cds I F is the resistance coefficient of the discharge from the interelectrode space Cfr I e is the friction coefficient of the interelectrode space Fe is the total area of the gap between the settling plates or total crosssection 4F area of the settlingpipes mi2 1e is the length of the settling plates or pipes m De is the hydraulic diameter of the gap between the settling plates or diameter of settling pipe m lie perimeter of the gap between the settling plates or of the section of the settling pipe m 17 Many units including electrostatic filters use gas distributing grids for uniform distribution of a stream after its entrance into the working chamber The entire stretch from the en d sectionof the inlet branch pipe including the grid can be con sidered as a unit There are three ways of introducing a stream into the working chamber 1 central impingement of a stream on the grid Figure 126a 2 peripheral impingement of a stream on the grid Figure 126b 3 side impingement of a stream on the grid Figure 126c f f ch I i ch tc C S L ch1 a b c FIGURE 126 Different methods of stream introduction a central impingement of the stream bperipheral impingement of the stream side impingement of the stream qt 450 Either a single grid or a system of grids in series are used depending on the area ratio chcf 1215 and 1216 F41 18 The resistance coefficient of the inlet stretch of the unit at central im pingement of a stream on the grid is calculated by the following formula proposed by the author 0 AH bNO07 F p P 128 c Hg tintýb oPoR o where Cobe 0 5 tobe ýobe is the resistance coefficient of the bend through which the stream is discharged against the grid it is determined as from the corresponding diagrams of Section VI Cp is the resistance coefficient of the grid determined as from diagrams 81 to 87 Hp is the distance from the exit opening of the intake bend to the grid m Do is the diameter of the discharge section of the intake bend m lip The last term on the righthand side of 12 8 is to be takeninto account for D12 only The resistance coefficient of the inlet stretch of the unit at peripheral stream impingement on the grid is calculated by the following formula tin C b N 0 7 pF0 129 d where D is the relative distance from the exit of the intake bend to the apparatus bottom or to a baffle if a baffle has been installed behind the bend The last term of the righthand side of 129 is tobe taken into account for Ldl2only The resistance coefficient of the inlet stretch of a unit at side impingement of the stream on a grid is calculated by the formula 1210 where Dh is the diameter or large side of the chamber section m Hp The last term on the righthand side of 1210 is to be taken into account for AO 01 only In the case of a series of grids the resistance coefficient of the inlet stretch is determined by the same formulas 128 to 1210 but with Cp replaced by the sum of the The term grid is used here in a very general sense it can mean not only a plane grid perforated sheet but also other types of uniformly distributed resistances various checkerworks or layers of loose or lump material Raschig rings etc These formulas differ from the formulas in 1215 certain refinements having been introduced as a result of the authors subsequent experiments 451 resistance coefficients of all the grids of the system C p ClCp Ctý 1211 where n number of grids b Heat exchangers 19 The total pressure losses in honeycomb radiators used for cooling air are made up of the loss at the inlet to the radiator tube the frictional loss in the tubes and the loss at sudden expansion at the discharge from the tubes into the common channel The resistance coefficient of a honeycomb radiator is determined by the following formula Maryamov 1223 IAH Z3IOF zF 2F101 TinWq mdh FJ 0hiFo 29 3 h 2 CshA 1212 where Csh F 2 1213 sh 7Ft T 1214 TexTnis the ratio of the difference between the temperatures OK of the outfiowing Tin and incoming streams to the temperature of the incoming stream inK absolute w is the velocity in the pipe before the radiator front msec F0 is the total flow area of the radiator m 2 F is the crosssection area of the radiator front mi2 1o is the length of the radiator4tube radiator depth m dh is the hydraulic diameteyr of the nnt o radiator tube m fIt is the perimeter of the radiatortube section m I is the friction coefficient of unit radiator depth The friction coefficient I of honeycomb radiators with circular or hexagonal tubes is determined by the following formula Maryamov 1223 a for 35Re 275 O0375Re 1215 b for 275 Re500 021414 1216 where 4 a is the relative roughness of the radiator tubes dh 452 20 The total pressure losses in ribbedtube and tubeandplate radiators are made up of friction loss and losses at contraction or expansion of the stream during its passage from one row of tubes to another The resistance coefficient of such radiators is determined by the following formula Maryamov 1224 where 15i F 1218 is a coefficient allowing for the losses at contraction and expansion of the stream during its passage between the radiator tubes 1L 1ý11214 F is the area of the narrowest radiator section between the tubes m 2 FO is the area of the section between the plates in the zone between the rows m 2 b is the mean gap between the fins or plates m h is the gap between adjacent tubes of the radiator m z is the number of rows of tubes I is the friction coefficient of unit radiator depth for the remaining symbols cf point 19 The friction coefficient X for ribbedtube radiators can be calculated approximately by the following formula Maryamov I077 1219 which is correct for 3OOORe 6inah 25000 The friction coefficient I for tubeandplate radiators can be calculated by the following formulas Maryamov 1224 a for 4 10 e 1 indh 104 098 1220 b for Re O 021 1221 453 21 The resistance of heaters is similar to the resistance of radiators It is also made up of the loss at the inlet the friction loss and the shock loss at discharge from the narrow section between the tubes and plates of the heater The main parameter used in the selection of a heater is the weight rate of flow in its cross section TmW kgm 2sec where o kgn 3 mean specific gravity of the heated air flowing through the heater This is the reason why the data on resistance of heaters given in the literature are presented in the form of a relation between AH kgm 2 and ymw kgm 2sec The same relationship is adopted in this handbook too With multipass heat exchangers the transverse stream flowing over the tubrls turns sharply through 180 on moving from one bundle into the next Figure 127a The phenomenon is similar to the one taking place in a Ushaped elbow without bundles of tubes i e an eddy zone is created at the inner wall after the second 900 turn but is reduced somewhat due to the smoothing effect of the tube bundles Oeex Tex ex ab FIGURE 127 Twopass crosscurrent heat exchanger astraight partition in the intermediate channel bpartition in the inter mediate channel bent against the direction of stream flow The reduction or elimination of this eddy zone increases the efficiency of the heat exchange To acilieve this guide vanes can be placed at the point of bending lAnother method is Elperfn 1244 to place a partition either straight or bent against the direction of stream flow at the point of bend Figure 127 c Ventilating hoods roof ventilators and exhausts 23 Ventilating hoods are used when it is required to utilize the wind energy in order to achieve greater ventilation When the wind blows on the hood a negative pres sure is created on part of its surface and this contributes to the displacement of air from the room outside The total pressure losses in the hood are made up of the loss in the duct properand the loss ofdynamric pressure at the exit The ventilating hoods of greatest interest are those of the TsAGI ChanardEtoile and Grigorovich types The resistance coefficients of these hoods are given in dia gram 1226 24 Roof ventilators or exhausts are installed on the roof of industrial buildings for A the natural elimination of polluted air The most efficient types of such ventilators are the ventilator house the LEN PSP ventilators followed by the KTIS doublelevel Giprotis and RyukinIlinskii ventilators cf Taliev 1233 454 8 The rectangular ventilator with panels the BaturinBrandt LEN PSP KTIS PSK 2 and Giprotis ventilators and the ventilator house belong to the category of practically draftproof ventilators The values of the resistance coefficients of different types of ventilators are given in diagrams 1227 and 1228 The resistance coefficient of rectangular ventilators with panels can be calculated by the following formula which follows from the data of Taliev 1233 and Frukht 1239 Af a 3 1 where w is the mean velocity in the gaps of the ventilators msec a is an empirical coefficient depending on the angle of opening of the ventilator flap a and determined from the following table TABLE 128 a 35 45 55 a 825 525 315 I is the distance from the panel to the outer edge of the flap m h total height of all the gaps on one side of the flap m 455 123 LIST OF THE DIAGRAMS OF RESISTANCE COEFFICIENTS OR RESISTANCE MAGNITUDES OF SECTION XII Diagram description 1Source Ndiagra Notes Various dust separators NIIOGAZ cyclones BTs batterytype dust separators Inertial louvertype conical KTIS separator lnertial louvertype dust separators of dif ferent types Venturi scrubber tube sprayer Scrubber with wooden packing VTI centrifugal scrubber Twine wedgeshaped shaking twostage MIOTtype filter Twine wedgeshaped shaking simple stage MIOTtype filter Boxtype filter from corrugated gauze with moist filter of Rekk design Porous boxtype filter with moist packing Filtering cloth Melstroi wool Filtering cloth serge wool mixture Filtering cloth unbleached coarse calico Filtering cloth wool flannelette Filtering cloth cotton thread Filtering cloth flax flimsy 2ply thread Filtering clothscalico moleskin and cottonthread flannelette DIZ cloth shaking filter with various types of cloth MFU suctiontype hose filter with various types of cloth Industrial electrostatic filters Inlet stretches of unitwith grid packing or other type of obstruction placed in the working chamber Honeycomb radiator With hexagonal or cir cular Ribbedtube radiator TubeandPlate radiator Platetype air heater Spiralribbed air heater Petaled fin heater Gerasev 126 Zalogin and Shukher 1212 Kouzov 1220 Standards 1242 The same KTIS 123 Kucheruk and Krasilov 1221 Shakhov 1243 Zverev 1213 Kucheruk and Krasilov 1221 Shakhov 1243 Zaitsev and Murashkevich 129 Teverovskii and Zaitsev 1235 Zalogin and Shukher 1212 The same Kucheruk 1222 The same Rekk 1230 The same Adamov Kucheruk 1222 Gordon and Aladzhalov 127 Idelchik 1216 126 Maryamov 1223 Maryamov 1224 The same Trichler and Egorov 1236 Polikarpov 1229 Trichler and Egorov 1236 The same 121 191 123 124 126 126 127 128 129 1210 1211 1212 Table No 129 1210 1211 1212 1213 1214 1215 Diagram No1213 1214 1215 1216 1217 Experimental data The same According to the authors approxi mate calculations The same Experimental data The same 1218 1219 1220 a 1221 1222 456 Diagram description Source Plain pipe air heater Taliev 1232 Air heater made from heating elements Ritshel and Greber 1231 Various heat exchangers Various ventilating hoods Khanzhonkov 1240 1241 Eliminators Taliev 1233 Various types of roof ventilators Frukht 1239 Rectangular roof ventilators with panels Uchastkin 1238 continued Notes The same Approximate calculations Experimental data The same r 457 124 DIAGRAMS OF THE RESISTANCE COEFFICIENTS Section XII Various cyclones Diagram 121 Type View Resistance coefficient Simple conical cyclone AH 00 2g Q F total crosssection area of cyclone body 42 C 595 b Conical SIOT cyclone Ordinary LIOT cyclone and shortened LIOT cyclone with untwisting spiral The same without untwisting spial 2 56 1263 av4Au7 if LV AZ54 gf74ap4 4p 2 8 293 A 4 1 1 458 Various cyclones continued Section XII Diagram 121 Type View Resistance coefficient Cyclone with dust removal Gas LIOT cyclone with water film and a specific liquid discharge of 013 to 030 litermr 3 2g AN 133 2g 3 0 11 where resistance coeffi cient of a single cyclone mb Grouped cyclones 459 NIIOGAZ cyclones Section XII Diagram 122 I I 460 Bs batryeds eaaosSection XII Bs atteytye dst sparaorsDiagram 123 Resistance coefficient rm AN Type View Gas with screw blade alternative C 85 outlet with rosette a 250 C 90 65 WQ Fm with rosette a 30 F total crosssection area of the dust separator body Inertial louvertype conical KTIS dust separator Diagram 124 HA 7 rm2 461 Section XII Inertial louvertype dust separators of different types Diagram 125 0 462 ISection XII Twine wedgeshaped shaking twostage MIOTtype filter Diagram 129 SDiagra3 129 Resistance of the entire filter at QT 500m3m hr 1 unsoiled filter layer H 6 kgmr2 2 after the feeding into the filter olf 400gmr2 dust AM 25kgm 2 The relationship AH I QT for separate stages with clean layer is given in graph a The relationshipAH I pgmr for the first stage at QT 500m3mZnhr is given in graph b The filtering layer of the first stage is binding twine OST 6707407 article 883 The filtering layer of the second stage is cable yarn No 03 GOST 90541 Asbestos dust Particle sized microns 2 I 210 025125100 Weight content 6 1005 364 1894 8736 Cleaning efficiency at Q 500mrnm hr kst 986b T Clean twine layer hr Soiled twine layer kgm2 7 aY I SV 5 o 0 0I0 2494 W grn b 465 I Section XII Twine wedgeshaped shaking singlestage MIOTtype filter Diagram 1210 Filtering layer knitting twine wound in four rows material handled asphalt road dust Particle diameter 05 510 1020 2040 40 d microns Weight content 6 900 496 219 184 106 Cleaning efficiency kst 97 lo Resistance of the whole filter at Q 864 m 3m 2hr and dust content p 1250 gm 2 1 before the shaking AH 35kgmi 2 after the shaking AH 16 to 19kgmi Boxtype filter from corrugated gauze with moist filter ofSeto I SRekk design Diagram 1214 320Z Filler corrugated gauze pitch of the corrug tion 7 mm height of the corrugation 4 mm wetted by almond oil of dust Type Small model 1951 ISmall model 1952 hst 10t pgm p gm 4 C Foundry 88 350 9 400 Cement 96 450 97 550 Cement 86 280 87 400 Coal 94 240 92 500 Coal ashes 94 450 93 700 Filter resistance with clean air within the limits 11 wlg 24 msec 1 small model 1951 hol S A 40hwl1 7 kgm 2 small model 1952 AH l6hw7kgm2 where h layer thickness m The value of AHis doubled when the limiting dust con tent given in the table is reached 466 Section XII Venturi scrubber tube sprayer Diagram 126 ygW 2 AffCg kg1112 where g010015 depending on the manufacturing inlet faccuracy to9r f Cw is determined from the graph as a function of mg and q q m i g kgkg g 7 1 specific gravity of the working gas in the throat and the sprayed liquid respectively kgmi3 m specific discharge of the sprayed liquid 1mi3 of the gas Values of Cw 9gkgkg Wg msec qkkg 50 60 70 1 a 1 90 1 00 110 I120 02f 025 061 061 061 061 061 061 061 061 47 Ox 041 063 064 065 066 066 067 068 069 062 0651066 068 070 072 074 076 076 083 0671070 075 079 083 088 092 097 104 075 082 088 094 100 103 114 122 j O 5 O 7 U N I1 mrsec to 78 a seto n AP N I e Scrubber with wooden packing DSection XII I Diagram 127 Tank Wetting intensity A 522 Distributing t i packing Am Gr as e xit C 960 LouversI Main packing Q Shield FI total crosssection area of the scrubber body packing Diffuser for gas SScrubber S bunker 463 VTI centrifugal scrubber cDiagram 128 4 AH is determined from the curve CO jDO Tat 1o0mm 0 no So o0 I WO II0 I2n0I0 131 140 Jis Discharge ofwater 022 028 033 039 045 050 056 061 070 078 at spray ing kgsec C 338 317 304 294 287 281 276 272 268 265 2 u 45o U 000 500 N0O 7000 I 2p 0 7000 mm A 464 Section XII Porous boxtype filter with moist packing Diagram 1212 2 Filter dimensions 710x510x90mm LIOT packing 13x15x8 mm china rings wetted by Viscin oil dust a mixture of coal and cement Particle size 112 11256 560 d microns Weight content 0 339 661 1o Oilwettc filling 1 Filter dimensions 500X50OX50mm LIOT packing 127x122x0 25mm metal rings wetted by turbine oil dust fineground coal after passage through the LIOT dust separator Particle size 48 48224 224112 i 112 4 microns Weight con 10 17 60 22 tent 016 Air load Oj Filter dust Cleaning Resistance m 3 m 2 hr content efficiency kgi 2 p gm 2 t 0 4320 0 0 124 4200 1200 76 185 4120 1600 79 215 4040 2000 80 244 3 Filter dimensions 500x500x50 mmMIOT packing first half of the box 9 rows of gauze woven gauzes with cells 10xlO m 2 wicker gauzes with cells OxlO0mm and 3 woven gauzes with cells 5x5 mm second half of the box 68 to 77 X2 to 5 x 01 mm copper coated rings wetted by mineral oil dust white Portland cement grade 300400 the largesize fractions 776 to 783 J0 of the weight of the cement have been removed from the air by a LIOT dust separator mean dust concentration 500 mgm3n average cleaning efficiency at QT 25003600m 3m2 hr and p 3000gm2 kst 80 Air loadQT Resistance AH kgmi 2 m 3m 2 hr Clean Dust content Dust content filter p2600 grn3 p 3600gn 3 1000 075 250 375 1500 150 425 525 2000 225 630 100 2500 375 900 147 3000 525 125 212 3500 750 165 467 stroi wool Section XII Filtering cloth Table 129 Cloth characteristics Substance Wool Weave Serge Approximate cloth thickness mm 375 Weight of 1 m2 cloth g 463 warp 59 Number of threads per 50 mm woof 44 Approximate thickness of the threads warp 083 mm woof 083 Twist of the threads per 25cm warp 43 Fwoof 35 Presence of nap Long nap on one side Exponent m 1012 Constant coefficient Ao 503 10 3 Dust content p gm 2 Value of A 0 0 305 241104 589 466 10 4 894 605104 1139 900104 p gm 2 200 400 600 800 1000 1100 1200 st 6 98 6 975 950 920 865 800 6H Ao AoQ kgm 2 is determined from graph aas a function of Q for differentp Q specific load per hour mSmZhr kst cleaning efficiency of thc cloth lo determined frnom graph b The values given for A and ksthave bc n dit minied fýr mineral dust from a sandblast machine of particle size not larger than 90 microns Sm 3 M2 hr 100 200 1300 1400 50 600 1800 11000 1 p0 AH kgmI I 1101 1521 2201 2501 3301 430 540 2 p 305 gm 2 AH kgm2 j 3301 710 110 1451186 130 1310 1 380 3 P 589 gm Al kgm 2 5501 116 1161 1224 1270 1340 1450 1 560 4 p 894 gm 2 AH kgM 2 16501 137 1200 1270 1350 1400 1550 700 5 p 1139gm2 A k m19501 200 1300 1405 1510 1620 1830 1103 S K a t p DO ZM qug Ow gM a 468 Filtering cloth serge wool mixture Table 1210 Cloth characteristics f warp Cotton Substance woof Wool Weave Serge Approximate cloth thickness mm 16 Weight of 1 m2 cloth g 300 warp 118 Number of threads per 50mm woof 8 woof 83 Approximate thickness of the threads warp 040 mm woof 046 warp 124 Twist of the threads per 25cm woof 73 Presence of nap Medium nap on one side Exponent m 111 Constant coefficient Ao 53410s Dust content p gm 2 Value of A0 0 0 117 232104 ANH A AVQ7 kgm12 I is determined from graph a as a function of Q for different p QT specific load per hour n3 nIm 2 hr kst cleaning efficiency of the cloth determined from graph b The values given for Ao and kst have been determined for mineral dust from a sandblast machine of particle size not larger than 90 microns m Tm 2 00 2 00 400 500 1600 800 1000 1 PO0 AH kgin 2001 3161 001 550 6801 8601 114 2 p 117 gm 2 Al kgm 2 1 5001100 1156 1210 P70 P20 1440 1 550 3 p 308 gm 2 An kgm 1102 1218 1335 1450 1575 700 1950 1125 4 p 367 gm 2 AH kgmi 1138 1276 1400 1540 1680 k20 1120 1148 308 610104 I i gq e n b g III 469 Filtering cloth unbleached coarse calico Section XII Table 12 11 Cloth characteristics Substance Cotton Weave Garnish Approximate cloth thickness mm 06 Weight of I m2 cloth g 171 Number of threads per 50mm wafp 128 woof 106 Approximate thickness of the threads warp 029 mm woof 028 warp 141 Twist of the threads per 25cm woof 121 Presence of nap Without nap Exponent M 117 Constant coefficient As 32410 Dust content p gm 2 Value of A0 0 0 201 184104 277 253104 AHA A Q Ckgmin is determined from graph a as a function of Q for different p Q specific load per our in 3n 2hr kst cleaning efficiendy of the cloth lo determined frjn graph b The values given for A and kst have been determined for mineral dust from a sandblast machine of particle size not larger than 90 microns QT 1 2 30 40 I0 50 0 1 1 000 msrn2 hr 100 200 300 400 800 1 P0 H kgi 1781 3001 4201 5501 650 920 118 2 p 201 gmZ AH kgm t 14201108 178 1262 1350 1450 1650 800 AN kgm1J 600 1146 AH kgml 710 1170 3 p 277 gm 2 1254 1360 1460 4 p 361 gm 2 1296 1410 1520 1600 1940 1120 1730 f0S 1140 361 330 104 300 510 05 So S51 st b I 470 Section XII Filtering cloth wool flannelette Table 1212 Cloth characteristics Substance Wool Weave Serge Approximate cloth thickness mm 156 Weight of 1 m2 cloth g 3556 Number of threads per 50mm warp 104 woof 85 Approximate thickness of the threads warp 047 mm woof 044 Twist of the threads per 25cm warp 1325 woof 1115 Presence of nap Medium nap on one side Exponent m 11 Constant coefficient As 497 10 s Dust content p gm 2 Value of A0 0 0 145 173104 313 37410 468 580104 AM A AoQm kgim is determined from graph a as a function of QT for different p QT specific load per hour m 3m 2 hr kst cleaning efficiency o the cloth 16 determined from graph b The values given for Ao andkst have been determined for mineral dust from a sandblast machine of particle size not larger than 90 microns I I 4 0 I II I mSm2 hr 100 200 300 400 500 600 800 1000 In m IuI I II I AM g 2I110 2601 3010 557501 950 2 p 145 gm 2 Al kgmi1 4001 8001120 1160 1220 1250 1345 1 440 AM kgm2 l 700 145 3 p 313 gm 2 1220 1300 1360 1440 1600 It0 4 p 468 gm 2 Al kgmm1 100 210 1320 1450 1560 1700 1 980 1130 5 p 603 gm 2 1450 1600 1750 1900 1120 1160 AH kgm1150 300 603 720 104 600 860 L r I X7l b a 471 Sch c nSection XII Filterinig cloth cotton thread Table 1213 Cloth characteristics Substance Cotton Weave Serge Approximate cloth thickness mm 107 Weight of 1 m2 cloth g 3625 Swarp 105 Number of threads per 50mm wap 0 Jwoof 180 Approximate thickness of the threads warp 024 mm woof 063 Twist of the threads per 25cm warp 240 woof 675 Presence of nap Without nap Exponent m 114 Constant coefficient A 756 10 Dust content p gmZ Value of 4 0 0 183 44810 330 810104 AH A AQn kgm 2 J is determined from graph a as function ofQ7 for differentp QT specific load per hour mhn2 hr kst cleaning efficiency of the cloth 0 determined flvn graph b The values given for A and ksthave been delerinJ fr mineral dust from a sandblast machine of particle size not larger than 90 microns m 3m 2 hr 100 200 300 400 500 600 800 1000 1 p0 Ahl kgm 1145 13151 500 1705 1910 111001 162 20d 2 p 193 gm 2 AH kgm 10 123 1375 1 525 16701 810 120 150 3 p 330 gm2 AH kgm 2 150 135 10 1750 I95 1115 1170 1 210 X II b 4 472 Filtering cloth flax flimsy 2ply thread Section XII Table 1214 4 Cloth characteristics Substance Flax Weave Approximate cloth thickness mm 10 Weight of 1 m2 cloth g 203 warp 66 Number of threads per 50mm woof 43 Approximate thickness of the threads warp 043 mm woof 055 warp 59 Twist of the threads per 25cm woof 41 Presence of nap Without nap Exponent m 146 Constant coefficient A 002910 3 Dust content p gm 2 Value of A 0 0 Mineal dust 229 0625104 413 1128104 Flour dust 123 3700 10 4 253 761010 4 362 10600104 AH Ao AQrm kgm2 is determined from graph a as a functior of Qt for different p QT n specific load per hour tn3m 2hr kst cleaning efficiency of the cloth determined from graph b The particle size of the mineral dust is not larger than 90 microns hr 100 200 300 400 500 600 1800 11000 m M2 hrI I I II I I I am A1H aHll tAH All AH tiH kgm I kgm 2 010 kgm 2 012 kgIm2 045 kgmi 050 kgm 2 1080 kgmn 0901 Mineral dust 1 p 0 101201 020 10251 035 2 P229gm2 025 1042 1 060 1081 1 105 3 p 413 gm 2 037 1056 I 080 1105 1 140 Flour dust 4 97 gmZ 110 1176 1 260 1350 1 445 5 p 123 gm 2 125 1210 1 310 1 410 1 520 6 P 253 gm 2 200 1350 1 510 1720 1 920 7 P 362 gm 2 250 1450 1 700 1960 1104 0511 070 11501 202 12001 255 16201 820 I 75ojo0 132 196 jl94 k80 I kgi 1 Flour dust tit Mineral dust 4W Z a IX5 ZVO 7 gW b gm a 473 Filtering cloths calico moleskin and cottonthread flannelette Section XII Table 1215 Clean unsoiled filtering cloths Cloth Exponent m Coefficient A AHAQ kgm 2 Calicowithout nap 147 006 10 3 2 Moleskin without nap 120 318 i V3 Qr specific load per horn m3r hr Cottonthread flannelettemediurn nap on the two sides 118 421103 Qo m 3m 2 hr 600 800 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 20000 30000 40000 1 Calico LII kgrn2 140 1801 230 520 870 126 170 12101 270 3201 39 0 450 126 229 369 2 Moleskin N kgrn 900 109 138 12 a1460 660 830 1105 1129 1145 167 195 457 759 1080 3 Cottonthread flannelette AM kgrn 109 139 170 350 1530 1 730 1930 1 1 1138 1160 1182 1 209 70 767 1110 kgmr 5000 ZOO 7000 770 4 500 W0W70 20 SWA500 WI BW M 5rn 2 hr 4 474 Section XII DIZ cloth shaking filter with various types of cloth Diagram 1213 Diagram1213 r pi Section 11 Section 11I Cloth Dust n E u W U W Tricot Sand blast 347 9919 605 melange V VBlack mole From the 835 8530 260 skin shakingout foundry screens of the Ian Kompres wool sot plant Moleskin Sand blast 1235 535 2idense 11000 9751 1130 MFU suctiontype hose filter with various types of cloth i Section XII Diagram 1214 Discharge of a a clean gas Cloth Dust clean BlWing UU U air Velveteen Flour dust 1870 99824 280 Sandblast 2130 97185 320 Chamois The same 770 99966 114 1410 99885 262 1980 99817 481 Linen for 759 99907 181 19 press filter The same 135 99707 373 1940 99 929 947 Cloth No 2 771 99020 980 1423 99733 535 Gas inlet 1810 98968 1562 Flour dust 1950 99795 270 Velveteen Sand blast 1500 620 1500 400 750 320 750 140 Discharged from the 780 9850 478 bottom of flour mills The same 870 9900 533 1240 9904 600 Cloth No 2 Zinc and lead oxide 590 9952 655 for BET 590 9912 610 filters 475 Industrial electrostatic filters I Section XII n erDiagram 1215 AH where Cinis determined as C from diagram 1216 ex g is determined as C from I diagram 3 6 as a function of a andf at 0 C05 Cha Cin Cis fr 05 1 o FV f o IL D e F X is determined from diagrams 22 to25 as a function of Re and 4 Fe Deee Fe and le are respectively the cross section area and the perimeter of the settling tubes or of the gap between the settling plates 476 Section XII Inlet stretches of unit with grid packing or other type of obstruction placed in the working chamberDiga 12 6 Resistance coefficient C AM Streaminlet conditions Scheme w Central impingement of the C Cobe N 07C F z 0013 stream on the grid FA chl g t rch I wherecbeis determined as 05 Cfor the given bend from the diagrams of Section V1 No is determined from Tables 121 to 127 C Cp is determined as C for a grid packing or other type of resistance from diagrams 81 to 86 and 816 to 821 0013 the term 71 y is only taken into account if 0 Do Peripheral impingement of the stream on the grid h F 0 05 CF om benoIa obe4 0 ch d the term 005 is only taken into account for 1 2 ldO Side impingement of the CF stream on the grid ch D N07Cp 0i2 20 c the term A 220 P is only taken into account for Hc 01 weDch ch For a system of grids installed in series instead of a single grid Cp is replaced by the sum a X tPin1p 2p A where n number of grids arranged in series 477 Honeycomb radiator with hexagonal or circular tubes Section XII Diagram 1217 4hp d h 613l perimet er 1 f A Tinwq 29 o jinl where 1 at 35Re 275 X 0375 Re0 0 is determined by graph a 2 at 275 Re 500 I 0 214 1 4 is determined by graph a F a sh is determined by graph b I FI 3 Tex Tin A T Tin h A is taken from Table 21 v is determined by 1i3 b t f cross section area of one tube b total flow area of radiator Values of Jk 30 0032 04 0039 0043 0046 0050 40 0031 0035 01o38 0042 0045 0049 60 0030 0032 0036 0040 0043 0047 80 0029 0032 0035 0039 0042 0046 100 0028 0031 0034 0038 0041 0045 150 0028 0030106034 0036 0039 0042 200 0027 00290033 o05 0038o 0041 300 0026 0028 0031 0034 0037 0039 500 0026 0028W0031 00340037 0039 0 01 02 03 04 05 06 07 08 09 10 100 810 250 160 11 1 543 625 225 40O 100 278 045 204 018 156 005 123 001 100 0 a b 478 Ribbedtube radiator Section XII Diagram 1218 q where I P ý is determined from graph a as a function of Womindh Re taken in the range 3000ReG 25000 15 O is determined from graph b a 17 Tex Tin T Tin z number of rows of tubes is taken from 13 b AAB UUQ37 SD a A AS VWl I o foot foa l0o a 240V 3o 4159 to f2 N 1li 5 141 4Ii 9 Dl 02 to DV 05 05 07 to 68 b 479 Tubeandplate radiator Section XII Diagram 1219 2hb 0 ha bO AH to IF V ig where 1 at 4 000 Re 0 000 098 f is determined from the curve Rqe Re 2 at R 10000 16v is determined from the same curve X Re Cc is determined from graph b of diagram 1218 rl7 ahl oI eTip S Tin z number of rows of tubes v is taken from 13 b 410 3 1 0 610 3 8103 0 062 0057 0054 O050 007 005 005 Tl 1 YAMU I I 2i0 310 110 I0 210 YVrt 480 I Section XII Platetype air heater Diagram 1220 0 Wo P flow area 1 For model S onerow AH 01363ymw66 kgm2 is determined from curve SI 1 tworow AH 0276 ImW one row AH 0150 YfmwO tworow AH 03267 w69 kgm2 is determined from curve Sj 2 For model 8 of 1 kgm2 is determined from curve B kgmr2 is determined from curve 3 For model M AHis determined from curveM Imis specific gravity kgmI kg 2 m sec Values ofAMl kgm 2 kmMe 0 2 4 6 8 10 12 14 16 18 20 kgin2 sec M 0 030 090 190 310 460 640 850 105 130 152 S 0 040 140 270 440 630 850 110 138 163 199 S2 0 090 290 580 950 138 188 246 310 396 459 BI 0 050 170 340 560 830 113 148 189 230 275 B 0 100 340 670 109 159 217 280 353 429 546 481 Section XII Spiralribbed air heater Diagram 1221 86q F flow area 1 KB and T twentytube Af 0345mwoo 0 tUkgm 2 is determined from curve No 1 2 Universal elements and KU heater tworow AH 00824 TmwoIkgm2 is determined from curve No 2 threerow AH 0156mwflkgm2 is determined from curve No 3 fourrow AHl 0130ymwjIkgm2 is determined from curve No 4 7m is the specific gravity kgmn K kgm 2 No0 No 3 r No2 i b 5 4 t ValuesofAH kgmr 20 kg 2 C rnse 1 0 2 r a 10 1214 i6 18 2D kgrn sec No 1 0 123 4141 934 158 238 350 444 565 704 850 No 2 0 030 109 231 394 597 838 116 143 177 217 No 3 0 053 182 373 619 919 127 167 211 260 313 No 4 0 050 194 448 750 116 166 223 290365 451 482 Petaled fin heater ScDiagram 1 Diaram1222 me Q I Fe flow area 1 Onechannel Threerow AH 0118 Tm85 kgm2 is determined from curve No 1 Sixrow AH m 0315Tmwo0 kgmr is determined from curve No 2 2 Twochannel Onerow AM 0153Tmwjl7 kgrm is determined from curve No 3 Tworow AH 0336 Iwne71 kgmi2 is determined from curve No 4 3 Threechannel onerow AH 0227Tmw71 kgmz is determined from curve No 5 lmiS the specific gravity kgmr kgmi goNo I I Y h Sh 8 V g 1112 sec Values of AH kgmr2 7mme 0 2 4 6 8 10 12 14 16 8 2 kgrmsec No 1 0 012 153 325 551 835 116 155 200 247 303 No 2 0 113 404 852 144 218 305 406 520 644 780 No 3 0 052 176 358 595 880 122 156 202 248 299 No4 0 110 360 720 118 172 233 300 385 473 561 No5 0 074 243 486 795 116 158 202 26 3201381 I 483 Section XII Plain pipe air heater Diagram 1223 Q2 Wo F Fo flow area Tworow kgr AHo 0625 mvj AN IIt kgr 2 is determined J 4 rows of tubes from curve No 1 3 rows of tubs o1 2 Threerow 2 rows of tube Ah 00877yMw kgr 2 is determined from curve No 2 a 0 1 Fourrow 00 olH0113 fmWo 8 ipo IDSolII 10001 kgmr is determined 1000 from curve No 3 0m specific gravity L I tf C kgm 3 L L k2 kg m2 e Values AH kgmr2 2e tmh kgm2 sec 0 1 2 4 6 8 10 12 14 16 18 20 2 rows No 1 0 006 022 077 160 270 400 600 780 980 117 143 3 rows No 2 0 008 031 110 220 380 570 790 104 132 163 201 4 rows No 3 0 011 040 140 290 490 730 102 134 171 1210 260 Section XII Air heater made from heating elements Diagram XII I Diagram 1224 1 Radiator installed in a vertical kgm 2 position 5 V17 AH is determined from curves a b 2 Radiator installed in inclined position L Afis determined from curve b 7 ispecific gravity kgms3 1 2 ro0 3ro a r3 rows and more a b Values AH kgm4 3 mg secsec Tmokgm 2 se 0 05 10 15 20 25 30 35 40 50 60 LOne row 0 001 003 006 011 016 022 029 037 055 076 a Two rows 0 001 003 007 012 018 025 033 043 064 090 Three rows 0 001 004 008 014 021 029 139 049 073 099 b 0 002 007 016 026 039 054 074 092 4 484 Varou hatexhages Section XII Varoushea exhaner Diagram 1225 Resistance coefficient Type Schematic view 2g Shelltube exchanger with C051i o longitudinal stream flow around the tubes where 00000d u 0080000 1 zdut L 4iW ex000000000000 ttn e 000oooooOggso for a shell of circular section and Tin ex 0 oooooooo 0 Xn exoooo0ooooo 0 a in 000008000 out dh 2 ub Z outt 00oo O for a shell of rectangular section 1100 kis determined from diagrams 21 to 25 12 Shelltube with stream flow C 05 1 I P through the tubes F1 a X is determined from diagrams 21 to 25 Twostage heat exchanger 406 f1 with transverse flow around C 10oCbd A the tube bundle 1800 turn Yin where C is determined as C for a Ushaped elbow at 0 from diagrams 621 to 624 Cidis de termined as 4 for the corresponding tube bundles from diagrams 811 and 812 With mixed flow around the wi Win Fe Ctbd At tubes aLternating sections in in where in the case of design a Cbd is determined as of transverse and longi iin C for the corresponding bundle from diagrams 811 tudinal flows and 812 taken only for half the rows of the wgex tubes in each zone of transverse flow in the tex case of design b as Cbd from the same diagrams Sexfex I but for all the rows of tubes enclosed by ýt ex the partition and for half of the tubes protruding Yex from it a b ex in tin tex Yo ACI 2 t 7 3 tin t rn 2 t tn 273 2t3 273tm Wo0m WA in Wy3tin 485 Various ventilating hoodsSeto I Diagram 12 26 Resistance coefficient Type Schematic view Iwo Circular TsAGI hood C 064 4 Square TsAGI hood C 064 Chanard Etoile hood c10 4 486 Var ious ventilating hoods continued Section XII I Diagram 1226 Resistance coefficient Type Schematic view Grigorovich hood 104 Standardized TsAGI hood without Without lid C 14 reducing piece for railroad cars With lid C 30 487 Various ventilating hoods continued DSectiona XII II Diagram1226 Resistance coefficient Type Schematic view An Standardized TsAGI roof ventilator With lid C 26 with reducing piece for railroad cars li Chesnokov roof ventilator Witho id C 106 4 488 E t Section XII Eliminators Diagram 1227 is taken from the table ýwF FQ flow area Eliminator Position IO 1 After the chamber 177 2 jAfter the chamber 940 IBefore the chamber 730 3 After the chamber 840 4 Before the chamber 340 5 After the chamber 139 Before the chanber 890 6 After the chamber 107 After the chamber 800 I lBefore the chamber 550 8 After the chamber 880 9 960 10 169 0V 489 Various types of roof ventilators I Section XII Vaiu f rDiagram 1228 LD 4 LEN PSP ventilator with two flips The same with three flaps 490 Various types of roof ventilators continued DSection XII I Diagram 122 8 Type Schematic view Twocircle 40 112 42 Giprotis 40 112 46 Ryukin Ilinskii 85 40 058 43 Ventilating house 40 112 33 Rectangular roof ventilators with panels Section XII Ill 05 10 15 20 25 AC 16 50 26 13 07 AH A mo a A Ii 2g where a is taken from Table 128 as a function of a 3 f is taken from the curve AC TABLE 128 a 35 45 55 825 525 315 491 BIBLIOGRAPHY Section One 11 Agroskin 11 GT Dmitriev and F1 Pikalov Gidravlika Hydraulics Gosenergoizdat 1954 12 Al t s h u 1 A D Istechenie iz otverstii zhidkostei s povyshennoi vyazkostyu Discharge of HighViscosity Liquids through Orifices Neftyanoe khozyaistvo No 2 1950 iI 13 Altshul AD Raschetnye zavisimostipri istecheniizhidkostei bolshoi vyazkosti Calculating Relationships for the Discharge of HighViscosity Liquids Vestnik inzhenerov i tekhnikov No 4 1951 14 Altschul AD Ob istechenii zhidkostei znachitelnoi vyazkosti priperemennom Urovnei teorii viskozimetra On the Discharge of HighViscosity Liquids at Variable Level and Theories of the Viscosimeter Zhurnal tekhniches koi fiziki Vol XXVII No 4 AN SSSR 1957 15 Velikanov MA Dinamika ruslovykh potokov Dynamics of Channel Flow Gostekhizdat 1954 16 Ide 1 c hi k IE Gidravlicheskie soprotivleniya fizikomekhanicheskie osnovy Fluid Resistances Physical and Mechanical Fundamentals Gosenergoizdat 1954 17 Makarov AN and M Ya Sherman Raschet drosselnykh ustroistv Calculation of Throttling Devices Metal lurgizdat 1953 18 Malkov MP and KF Pavlov Spravochnik po glubokomu okhlazhdeniyu Cooling Handbook Gostekhizdat 1947 19 Glinkov MA Editor Metallurgicheskie pechi Metallurgical Furnaces Metallurgizdat 1951 110 Mostkov MA Gidravlicheskii spravochnik Handbook of Hydraulics Gosstroiizdat 1954 111 Nevelson MI Tsentrobezhnye ventilyatory Centrifugal Fans Gosenergoizdat 1954 112 Normy aerodinamicheskogo rascheta kotelnykh agregatov Standards for the Aerodynamic Calculation of Boiler Units Mashgiz 1949 113 Normy rascheta tsirkulyatsii vody v parovykh kotlakh Standards for Calculating the Water Circulation in Steam Boilers TsKTI Mashgiz 1950 114 Normy teplovogo rascheta kotelnogo agregata Standards for the Thermal Calculation of a Boiler Unit VTI Gos energoizdat 1954 115 Polikovskii VI Ventilyatory vozdukhoduvki kompressory Fans Blowers Compressors Mashgiz 1938 116 Prandtl L Fundamentals of Hydro and Aerodynamics McGraw Hill 1934 Russian translation GILL 1953 117 Rikhter G Gidravlika truboprovodov Hydraulics of Pipe Lines ONTI 1936 118 Solodkin E and AS Ginevskii Turbulenmnoe techenie vyazkoi zhidkosti v nachalnykh uchastkakh ossesim metrichnykh i ploskikh kanalov Turbulent Flow of a Viscous Liquid in the Initial Stretches of Axisymmetric and Plane Channels Trudy TsAGI No701 Oborongiz 1957 119 Spravochnik khimika Handbook of Chernistry Vol 1 Goskhimizdat 1951 120 Spravochnik Hirtte Russian translationj Vol 1ONTI 1936 121 Vargaffik NB Editor Spravochnik teplotekhnicheskie svoistva veshchestv Handbook of the Thermal Properties of Materials Gosenergoizdat 1956k 122 Fabrikantý N Ya Aerodinamika Acrodynamics Gostekhizdat 1949 123 Filippov GV 0 vliyanii vkhodnogo uchastka na soprotivlenie truboprovodov On the Influence of thedInlet Stretch on the Resistance of Pipelines Doctorates thesis Kuibyshevskii industrialnyi institut 1955 124 Frenkel VZ Gidravlika Hydraulics Gosencrgoizdat 1956 125 Shill e r D Dvizhenie zhidkostei v trubakh Flow of Liquids in Pipes Tekhizdat 1936 126 Yu r e v B N Eksperinientalnaya aerodinamika Experimental Aerodynamics ONTI 1936 492 Section Two 21 Abramovich GN Prikladnaya gazovaya dinamika Applied Gas Dynamics Gostekhteorizdat 1953 22 Agroskin 1 1 GT Dmitriev and F1 Pikalov Gidravlika Hydraulics Gosenergoizdat 1954 23 Adamov GA and IE Idel chik Eksperimentalnoe issledovanie soprotivleniya fanernykh trub kruglogo i kvadratnogo sechenii pri vpolne razvivshemsya turbulentnom techenii Experimental Study of the Resistance of Plywood Pipes of Circular and Square Section at Fully Developed Turbulent Flow Trudy No 670 MAP 1948 24 Adam ov G A and IE I del c h i k Eksperimentalnoe issledovanie turbulentnogo techeniya v nachal nykh uchastkakh pryamykh trub kruglogo i kvadratnogo secheniya Experimental Study of the Turbulent Flow in Initial Stretches of Straight Pipes of Circular and Square Section Tekhnicheskie otchety No 124 MAP 1948 25 A d a m o v G A Obshchee uravnenie dlya zakona soprotivleniya pri turbulentnom techenii i novye formuly dlya ko effitsienta soprotivleniya sherokhovatykh trub General Equation for the Law of Resistance at Turbulent Flow and New Formulas for the Friction Coefficient of Rough Pipes Vestnik inzhenerov i tekhnikov No 1 1952 26 Adam ov GA Priblizhennye raschetnye formuly dlya koeffitsientov gidrodinamicheskogo soprotivleniya Approximate Formulas for Calculating the Coefficients of Hydrodynamic Resistance Vestnik inzhenerov I tekhnikov No2 1953 27 A d a m o v G A Priblizhennyi raschet gidravlicheskogo soprotivlenlya i dvizheniya gazov i zhidkostei v truboprovodakh Approximate Calculation of the Fluid Resistance and Motion of Fluids in Pipe Conduits In Sbornik Voprosy razrabotki i ekspluatatsii gazovykh mestorozhdenii Gostopizdat 1953 29 A lt s h u 1 A D 0 zakone turbulentnogo dvizheniya zhidkosti v gladkikh trubakh On the Law of Turbulent Flow of a Liquid in Smooth Pipes DAN SSSR Vol LXXV No 5 1950 29 A It sh u 1 A D 0 raspredelenii skorostei pri turbulentnom dvizhenii v trubakh Velocity Distribution at Turbulent Flow through Pipes Gidrotekhnicheskoe stroiielstvo No1 1951 210 Al ts h u I A D Zakon soprotivleniya truboprovodov Resistance Law of Pipelines DAN SSSR Vol XXVI No 6 1951 211 Al 1 t s hu 1 A D Obobshchennaya zavisimost dlya gidraviicheskogo rascheta truboprovodov General Relationship for the Hydraulic Calculation of Pipelines Gidrotekhnicheskoe stroitelstvo No 6 1952 212 A I tshul AD Soprotivelenie truboprovodov v kvadratichnoi oblasti ResistanceofPipesin Square Conduits Sanitamaya tekhnika Collection No 4 Gosstroiizdat 1953 213 A l ts hu 1 A D 0 raspredelenii skorostei pri turbulentnom techenii zhidkosti v tekhnicheskikh trubakh Velocity Distribution at Turbulent Flow of a Liquid in Commercial Pipes Teploenergetika No 2 1956 214 A l t s hu I A D Osnovnye zakonomernosti turbulentnogo techeniya zhidkosti v tekhnicheskikh truboprovodakh Basic Laws of the Turbulent Flow of a Liquid in Commercial Pipes Sanitarnaya tekhnika Collection No 6 Gosstroiizdat 1957 215 A1tshul AD K obosnovaniyu formuly Kolbruka Substantiation of the Colebrook Formula lzvestiya AN SSSR OTN No6 1958 216 Ashe BM and GA Maksimov Otoplenie i ventilyatsiya Heating and Ventilating Vol11 Stroiizdat 1940 217 Bakhmetev BA 0 ravnomernom dvizhenii zhidkosti v kanalakh i trubakh Uniform Flow in Pipes and Channels 1931 218 G amb u r g P Yu Tablitsy i primery dlya rascheta truboprovodov otopleniya I goryachego vodosnabzheniya Tables and Examples for Calculating Heating and HotWater Piping Stroiizdat 1953 219 Gandelsman AF AA Gukhman NV Ilyukhin and LN Naurits lssledovaniya koeffitsienta soprotiv leniya pri techenii s okolozvukovoi skorostyu Studies of the Friction Coefficient at NearSonic Flow Parts I and II ZhTF VolXXIV No12 1954 220 Gi nevskii AS and EE Solodkin Aerodinamicheskie kharakteristiki nachalnogo uchastka truby koltsevogo secheniya pri turbulentnom techenii v pogranichnom sloe Aerodynamic Characteristics of the Initial Stretch of an Annular Pipe at Turbulent Flow in the Boundary Layer Promyshlennaya aerodinamika col No 12 Oborongiz 1959 221 Ze gz h d a AP Gidravlicheskie poteri na trenie v kanalakh i truboprovodakh Frictional Hydraulic Losses in Pipes and Channels Gosenergoizdat 1957 222 I d e c h i k IE Opredelenie koeffitsienta treniya stalnykh trub gazoprovoda SaratovMoskva Determination of the Friction Coefficient of the Steel Pipes of the SaratovMoscow Gas Main Tekhnicheskie otchety No 50 BNT NKAP 1945 223 zbash SV BT Eltsev and PM Sliskii Gidravlicheskie spravochnye dannye Hydraulic Reference Data ME 1954 224 Idel chik IE Gidravlicheskie soprotivleniyatfizikomekhanicheskie osnovy Fluid Resistance Physical and Mechanical Fundamentals Gosenergoizdat 1954 493 225 I zhash SV Osnovy gidravliki Fundamentals of flydraulics Stroiizdat 1952 22b Is a ev IA Novaya formula dlya opredeleniya koeffitsienta gidravlicheskogo soprotivleniya pryamoi krugloi truby New Formula for the Determination of the Coefficient of Fluid Resistance of a Straight Pipe of Circular Cross Section Neftyanoe khozyaistvo No 5 1951 227 K a r m a n von Th Some Problems of the Theory of Turbulence Russian translation in SbornikProblemy turbulent nosti edited by M A Velikanov and N G ShveikovskiiONTI 1936 228 Ki sin MI Otoplenie i ventilyatsiya Heating and Ventilating Part II Stroilzdat 1949 229 Ko n a k o v V K Novaya formula dlya koeffitsienta soprotivleniya gladkikh trub New Formula for the Friction Co efficient of Smooth Pipes DAN SSSR Vol XXV No5 1950 230 Lob a ev BN Novye formuly rascheta trub v perekhodnoi oblasti New Formulas for Pipe Calculation in the transi tional Region In Sbornik Novoe v stroitelnoi tekhnike Akademiya Arkhitektury USSR Sanitiuaya teklinika 1954 231 Lyatkher VM Analiz i vybor raschetnykh formul dlya koeffitsienta treniya v trubakh Analysis and Selection of Calculating Formulas for the Friction Coefficient in Pipes In Sbornik Statei studencheskogo nauchnogo obshchestva MEI 1954 232 Murin GA Gidravlicheskoe soprotivlenie stalnykh trub Fluid Resistance of Steel Pipes lzvestiya VTI No10 1948 233 Mu ri n GA Gidravlicheskoe soprotivlenie stalnykh nefteprovodov Hydraulic Resistance of Steel Pipelines Neft yanoe khozyaistvo No 4 1951 234 Ni k u r a d z e I Zakonomernosti turbulentnogo dvizhenniya v gladkikh trubakh Laws of Turbulent Flow in Smooth Pipes Russian translation in Sbornik Problemy turbulentnosti edited by MA Velikanov and N G ShveikoVskii ONTI 1936 235 Ovsenyan VM Vyrazhenie gidravlicheskikh poter cherez osrednennuyu skorost pri neustanovivshemsya dvizhenii zhidkosti v zhestkoi trube Expressing Hydraulic Losses through the Mean Velocity at Unsteady Flow in a Rigid Pipe Erevan Polytechnic Institute Sbornik nauchnykh trudov No 14 No 2 1952 236 P a v ovs k ii NN Gidravlicheskii spravochnik Handbook of Hydraulics ONTI 1937 237 Petukhov BS AS Sukhomel and V S Protopopov Issledovanie soprotivleniyatreniya i koeffitsienta vosstanovleniya temperatury stenki pri dvizhenii gaza v krugloi trube s vysokoi dozvukovoi skorostyu Study of the Friction and Temperature Coefficients of Restoration of the Wall with Gas Flow in a Circular Pipe at High Subsonic Velocity Teploenergetika No3 1957 238 P o z i n A A Printsipy rascheta i konstruirovaniya vsasyvayushchikh rukavov Principles of the Calculation and Design of Suction Hoses Doctorates thesis 1950 239 Pop ov V N Gidravlicheskii raschet napornykh truboprovodov gidrostantsii Hydraulic Calculation of Pressure Pipes of Hydroelectric PowerPlants Gosenergoizdat 1950 240 Prandttl L Rezultaty rabot poslednego vremeni po izucheniyu turbulentnosti Results of Recent Studies of Turbulence Russian translation in Sbornik Problemy turbulentnosti edited by M A Velikanov and NG Shveikovskii ONTI 1936 241 P r and t I L Fundamentals of Hydro and Aerodynamics McGraw Hill 1953 Russian translation GIlL 1953 242 Rikhter G Gidravlika truboprovodov Hydraulics of Pipelines ONTI 1936 243 Rysin SA Ventilyatory obshchepromyshlennogo naznacheniya GeneralPurpose Industrial Fans Stroiizdat 1951 244 Solodkin EE and AS Ginevsklii Turbulentnyi pogranichnyi sloi i soprotivlenie treniya tsilindra s uchetom vliyaniya poperechnoi krivizny poverkhnosti Turbulent Boundary Layer and Friction Resistance of a Cylinder Allowing for the Influence of the Transverse Surface Curvature Trudy MAP No 690 1956 245 S olod ki n EE andfAS Gi nevskii I Turbulentnoe techenie vyazkoi zhidkosti v nachalnykh uchastkakh osesim metrichnykh i ploskikhWkanalov Turbulent Flow of a Viscous Liquid in the Initial Stretches of Axisymmetric and Plane Channels Trudy TsAGI No701 Oborongiz 1957 246 T o I t s m a n VF and F A S h e v e I e v ý Gidravlicheskoe soprotivlenie rezinovykh rukavov Fluid Resistance of Rubber Hose In Sbornilý VNII Vodgeo Issledovanie po gidravlike truboprovodov 1952 247 F e d o r o v NF Novye issledovaniya i gidravlicheskie raschety kanalizatsionnykh setei New Studies and Hydraulic Calculations of Sewerage Systems Stroiizdat 1956 248 Filonenko GK Formula dlya koeffitsienta gidravlicheskogo soprotivleniya gladkikh trub Formula for the Coefficient of Fluid Resistance of Smooth Pipes Izvestiya VTI No 10162 1948 249 Filonenko GK Gidravlicheskoe soprotivlenie truboprovodov Hydraulic Resistance of Pipes Teploeneietika No4 1954 250 F I y a t a u RS Gidrotekhnicheskie raschcty truboprovodov Hydrotechnic Calculations of Pipes Gostoptekhizdat 1949 494 251 F renkel VZ Gidravlika Hydraulics Gosenergoizdat 1956 252 Shevelev FA Issledovanie osnovnykh gidravlicheskikh zakonomernostei turbulentnogo dvizheniya v trubakh Study of the Main Hydraulic Laws of Turbulent Flow in Pipes Inzhenernaya gidravlika VNll Vodgeo Stroiizdat 1953 253 She velev FA Gidravlicheskoe soprotivIenie metallicheskikh trub bolshikh diametrov Hydraulic Resistance of LargeDiameter Steel Pipes Gidrotekhnicheskoe stroitelstvo No1 1950 254 S he v e I e v FA Gidravlicheskii raschet asbestotsementnykh trub Hydraulic Calculation of AsbestosCement Pipes VNII Vodgeo 1954 255 Shifrinson BL Gidrodinamicheskii raschet teplovykh setei Hydrodynamic Calculation of Heating Pipes Teplo i sila No1 1935 256 Yaki mov AK Novyi zakon turbulentnogo dvizheniya vyazkoi zhidkosti A New Law of Turbulent Flow of a Viscous Liquid DAN SSSR Novaya seriya Vol4 1945 257 Blasius Das Ahnlichkeitsgesetz bei ReibungsvorgAngeh in Flussigkeiten Mitt Forschungsarbeiten VDI Heft 131 1913 258 C o I e b r oc k F Turbulent Flow in Pipes with Particular Reference to the Transition Region between the Smooth and Rough Pipes JInstCivil Engineers No4 19381939 259 Hagen GPoggendorffs Annalen Bd46 1939 260 He ring F Die Rohrreibungszahl Brennst Warme Kraft Bd4 1952 261 K i r sc h m e r 0 Der gegenwirtige Stand unserer Erkenntnisse fiber die Rohrreibung G WF Ausgabe Wasser H16 18 1953 262 M a re c h e I H Pertes de charge continues en conduite forcde de section circulaire Annales des travaux publics de Belgique No6 1955 263 Moody LF Friction Factor for Pipe Flow Trans ASME Vol 66 November 1944 264 Morris M A New Concept of Flow in Rough Conduits Proc Amer Soc Civil Engrs No390 1954 265 Mfiller W Druckverlust in Rohrleitungen Energietechnik H7 1953 266 Nikuradze J Strbmungsgesetze in rauhen Rohren VDI No 361 1933 267 Poiseuille Comptes rendus Vol 11 1840 268 Richter H Rohrhydraulik 1954 Section Three 31 d e I c h i k IE Gidravlicheskie soprotivleniya pri vkhode potoka v kanaly i protekanii cherez otverstiya Fluid Re sistance at the Inlet of a Stream in Channels and at the Flow through Orifices In Sbornik Promyshlennaya aero dinamika No2 BNT NKAP 1944 32 I d e I c hi k IE Opredelenie koeffitsientov soprotivleniya pri istechenii cherez otverstiya Determination of the Re sistance Coefficients at Dischargethrough Orifices Gidrotekhnicheskoe stroitelstvo No 5 1953 33 I d e I c h i k IE Gidravlicheskie soprotivleniya fizikomekhanicheskie osnovy Fluid Resistances Physical and Mechanical Fundamentals Gosenergoizdat 1954 34 Ide 1c hi k IE Uchet vliyaniya vyazkosti na gidravlicheskoe soprotivlenie diafragm i reshetok Allowing for the Influence of Viscosity on the Fluid Resistance of Diaphragms and Grids Teploenergetika No 9 1960 35 K a r e v V N Poteri napora pri vnezapnom suzhenii truboprovoda i vliyanie mestnykh soprotivelenii na narusheniya potoka Head Losses at Sudden Contraction of a Pipe and Influence of Local Resistances on the Stream Disturbance Neftyanoe khozyaistvo No 8 1953 36 N o s o v a MM Soprotivlenie vkhodnykh i vykhodnykh rastrubov s ekranami Influence of Inlet and Exit Bells with Baffles In Sbornik Promyshlennaya aerodinamika No 7 1956 37 Nosova MM and NF Tarasov Soprotivlenie pritochnovytyazhnykh shakht Resistance of IntakeExhaust Vents In Sbornik Promyshlennaya aerodinamika No12 Oborongiz 1959 38 Khanzhonkov VI Soprotivlenie setok Resistance of Screens In sbornik Promyshlennaya aerodinamika No2 BNT NKAP 1944 39 Khanzhonkov V1 Soprotivlenie pritochnykh i vytyazhnykh shakht Resistance of Intake and Exhaust Vents In Sbornik Promyshlennaya aerodinamika No 3 BNI MAP 1947 310 Khan zh onkov V1 Aerodinamicheskic kharakteristiki kollektorov Aerodynamic Characteristics of Headers In Sbornik Promyshlennaya aerodinamika No 4 1953 311 Khanzhonkov V1 Umenshenie aerodinamicheskogo soprotivleniya otverstii koltsevymi rebraini i ustupami Reducing the Aerodynamic Resistance of Orifices by Means of Annular Ribs and Ledges I n Sbornik Promyslhlennaya aerodinamika No 12 Ohorongiz 1959 495 312 C h epa i k in GA Opredclenie poter pri vkhode potoka v turbinnuyu kameru Determination of the Losses at the Inlet of a Stream in a Turbine Scroll Case Izvestiya vysshikh uchebnykh zavedenii Energetika No 2 1958 313 Be vier CW Resistance of Wooden Louvers to Fluid Flow Heating Piping and AirConditioning May 1955 314 Cobb PR Pressure Loss of Air Flowing through 45 Wooden Louvers Heating Piping and AirConditioning December1953 315 W e is b a c h GLehrbuch der Ingenieur und Maschinenmechanik II Aufl 1850 Section Four 41 Abramovich GN Turbulentnye svobodnye strui zhidkostei i gazov Turbulent Free Jets of Fluid3 Gosenergvtzdat 1948 42 Alt s hu 1 AD Ispolzovanie zadachi Zhukovskogo dlya opredeleniya mestnykh poter v trubakh Application of the Zhukovskii Problem to the Determination of Local Losses in Pipes Vestnik inzhenerov i tekhnikov No 6 1948 43 Al tshul AD Istechenie iz otverstii zhidkostei s povyshennoi vyazkostyu Discharge of HighViscosity Liquids through Orifices Neftyanoe khozyaistvo No2 1950 44 Alt s h u 1 AD Raschetnye zavisimosti pri istechenii zhidkostei bolshoi vyazkosti Calculating Relationships for the Discharge of HighViscosity Liquids Vestnik inzhenerov i tekhnikov No4 1951 45 Al tshu AD Ob istechenii zhidkostei znachitelnoi vyazkosti pri peremennom urovne i teorii viskozimetra On the Discharge of HighViscosity Liquids at Variable Level and Theories of the Viscosimeter Zhurnal telhniches koi fiziki VolXXVII No4 AN SSSR 1957 46 Brik PM and DA Grossman Rezultaty issledovanii gidravlicheskikh soprotivlenii drosselnykh shaib Results of Studies of the Hydraulic Resistances of Throttling Plates Naladochnye i eksperimentalnye raboty ORGRES1 NoIX Gosenergoizdat 1954 47 B r o m l e i M F Koeffitsienty raskhoda otverstii prikrytykh stvorkami Discharge Coefficients of Orifices Covered by Flaps Sovremenrnye voprosy ventilyatsii Stroiizdat 1941 48 E g o r o v S A Formula dlya poteri napora na vnezapnom rasshirenii truby pri laminarnom techenii Formula for Head Losses at Sudden Expansion of a Pipe with Laminar Flow Trudy MAI No 11 1946 49 Z h u k o vs k ii 1 E Vidoizmenenie metoda Kirchgofa dlya opredeleniya dvizheniya zhidkosti v dvukh izmereniyakh pri postoyannoi skorosti dannoi na neizvesthoi linii toka Variation of the Kirchhoff Method for the Determination of a Liquid Flow in Two Dimensions at Constant Velocity with an Unknown Streamline Collected Works Vol2 Gosizdat 1949 410 I d e 1 c hik IE Gidravlicheskie soprotivleniya pri vkhode potoka v kanaly i protekanii cherez otverstiya Fluid Re sistance at the Inlet of a Stream in Channels and at the Flow through Orifices In Sbornik Promyshlennaya aero dinamika No2 BNT NKAP 1944 411 I d e 1 c h i k IE Poteri na udar v potoke s neravnomernym raspredeleniem skorostei Shock Losses in a Stream with Nonuniform Velocity Distribution Trudy MAP No 662 1948 412 I d e 1 c h ik IE Opredelenie koeffitsientov soprotivleniya pri istechenii cherez otverstiya Determination of the Re sistance Coefficients at Discharge through Orifices Gidrotekhnicheskoe stroitelstvo No 5 1953 413 Ide 1 chik IE Gildravlicheskie soprotivleniya fizikomekhanicheskie osnovy Fluid Resistances Physical and Mechanical Fundamentals Gosenergoizdat 1954 414 I d e c h i k I E Uehet vliyaniya vyazkosti na gidravlicheskoe soprotivlenie diafragm i reshetok Allowing f6r the Influence of Viscosity on the Fluid Resistance of Diaphragms and Grids Teploenergetika No9 1960 415 K a r e v V N Poteri napora pri vnezaphom rasshirenii truboprovoda Head Losses at Sudden Expansion of a Pipe Neftyanoe khozyaisivo Nos 11 and 12 j1952 416 K a r e v VN iPoterinapora privnezapnom suzhenii truboprovoda i vliyanie mestnykh soprotivlenii na narusheniya potoka Head Losses at Sudden Contractioný of a Pipe and Influence of Local Resistances on the Stream Disturbdnces Neftyanoe khozyaisftvo No 8 1953 417 K r y I o v AV Nektory eksperimentalnye dannye ob istechenii zhidkostei cherez ostrye diafragmy Some Eýperimental Data on the Dischargeof Liquids through Sharp Diaphragms Izvestiya AN SSSR OTN No2 1948 418 Tepl ov A V Znacheniya koeffitsientov raskhoda skorosti i poter dlya vnutrennei tsilindricheskoi nasadki Values of the Coefficients of Discharge Velocity and Loss for an Internal Cylindrical Nozzle Gidrotekhnicheskoe stroitelstvo No10 1953 419 Fr c n k e V Z Gidravlika Hydraulics Gosenergoizdat 1956 496 420 K h an z honk o v VI Aerodinamicheskie kharakteristiki kolletorov Aerodynamic Characteristics of Headers in Sbornik Promyshlennaya aerodinamika No 4 1953 421 Co r ne 11 WG Losses in Flow Normal to Plane Screens Trans ASME No4 1958 422 versen HW Orifice Coefficients for Reynolds Numbers from 4 to 50000 Trans ASME Vol 78 No2 1956 423 J oh anse n F Flow through Pipe Orifice of Flow Reynolds Numbers ProcRoyal Soc A Vol 126 No 801 1930 424 Kolodzie PA and M van Winkle Discharge Coefficients through Perforated Plates AJChEJournal No 9 1959 Section Five 51 A b r a m o v i c h G N Aerodinamika mestnykh soprotivlenii Aerodynamics of Local Resistances Promyshlennya aerodinamika Trudy No 211 1935 52 BamZelikovich GM Raschet pogranichnogo sloya Calculation of the Boundary Layer Izvestiya AN SSSR OTN No12 1954 53 B a m Ze likovic h G M Vychislenie parametrov szhimaemogo gaza s neravnomernym profilem skorostei i temperatury dvizhushchegosya v kanale proizvolnoi formy pri nalichii turbulentnogo peremeshivaniya Calculating the Characteristics of Incompressable Bases with Turbulent Mixing Flowing through a Channel of Arbitrary Shape at Nonuniform Velocity Distribution Institut imeni LI Baranova Trudy No 300 1957 54 Bushel AR Snizhenie vnutrennikh poter v shakhtnoi ustanovke s osevym ventilyatorom Reduction of the Interior Losses in an Installation with Axial Fan Trudy No 673 BNT MAP 1948 55 V e d e rink o v A I Eksperimentalnye issledovaniya dvizheniya vozdukha v ploskom rasshiryayushchemsya kanale Experimental Studies of the Motion of Air in a Plane Diverging Duct Trudy TsAGI No21 1926 56 Gibson A Gidravlika i ee prilozheniya Hydraulics and Its Applications ONTI 1935 57 G i n e v s k i i AS Energeticheskie kharakteristiki dozvukovykh diffuzornykh kanalov Power Characteristics of Subsonic Diffuser Channels Izvestiya AN SSSR ONTI No3 1956 58 G i n e v s k ii AS Raschet poter v rasshiryayushchikhsya i suzhayushchikhsya kanalakh Calculation of the Losses in Converging and Diverging Channels Promyshlennaya aerodinamika No7 BNI MAP 1956 59 Ginevskii AS and EE Solodkin Vliyanie poperechnoi krivizny poverkhnosti na kharakteristiki osesimmetrich nogo turbulenmnogo pogranichnogo sloya Influence of the Transverse Curvature of the Surface on the Characteristics of an Axisymmetrical Turbulent Boundary Layer Prikladnaya matermatika i mekhanika Vol XXII No6 1958 510 G r i sh a n i n K V Ustanovivsheesya turbulentnoe dvizhenie zhidkosti v konicheskom diffuzore s malym uglom raskrytiya Steady Turbulent Flow of a Liquid in a Conical Diffuser of Low Divergence Angle Trudy Leningradskogo politekhnicheskogo instituta inzhenernogo transporta No22 1955 511 Gurzhienko GA Ob ustanovivshemsya turbulentnom techenii v konicheskikh diffuzorakh s malymi uglami rasshireniya Steay Turbulent Flow in Conical Diffusers of Low Divergence Angles Trudy TsAGI No462 1939 512 Dovzhik SA and AS Ginevskii Eksperimentalnoe issledovanie napornykh patrubkov statsionarnykh osevykh mashin Experimental Study of Pressure Connections of Stationary Axial Machines Tekhnicheskie otchety No130 BNI MAP 1955 513 E v d o m i k 0 v I F Opyty po otsasyvaniyu pogranichnogo sloya v aerodinamicheskikh trubakh bolshikh skorostei Experiments on the Suction of the Boundary Layer in HighVelocity Wind Tunnels Trudy TsAGI No 506 1940 514 Egor ov BN Opyty s diffuzorami aerodinamicheskikh trub Experiments with Diffusers of Wind Tunnels TVF No 3 1930 515 I d e 1c h i k IE Aerodinamika vsasyvayushchikh patrubkov Aerodynamics of Suction Connecting Pieces TVF Nos 56 1944 516 Idel chik IE Aerodinamika potoka i poteri napora v diffuzorakh Aerodynamics of the Stream and Head Losses in Diffusers Promyshlennaya aerodinamika Col No 3 BNT MAP 1947 517 I d e I c h i k IE Vyravnivayushchee deistvie soprotivleniya pomeshchennogo za diffuzorom Equalizing Effect of a Resistance Obstruction Placed behind a Diffuser Trudy No 662 BNT MAP 1948 518 1 d e 1c h i k IE Gidravlicheskie soprotivleniya fizikomekhanicheskie osnovy Fluid Resistances Physical and Mechanical Fundamentals Gosenergoizdat 1954 519 I d e lc h ik IE Issledovanie korotkikh diffuzorov s razdelitelnymi stenkami Study of Short Diffusers with Dividing Walls Teploenergetika No8 1958 520 Levi n AM Polozhenie tochki otryva v ploskikh diffuzorakh Position of the Separation Point in Plane Diffuers DAN SSSR VolXXXVII No5 1952 497 521 Li fs hi its AG 0 preobrazovanii skorosti gaza v davlenie v diffnzore Transformation of Gas Velocity into Pressure in a Diffuser Trudy Uralskogo politekhniclieskogo instituta inieni S M Kirova No 1 1955 522 Lokshuin 1L and AKh Gazirbekova Rabota diffuzorov ustanovlennyklh za tsentrobezhnynii ventilyatoraini Operation of Diffuers Placed Behind Centrifugal Fans Pronuyshlennaya aerodinamika col No 6 BNI MAP 1955 523 M a k a ro v 1M K raschetu koeffitsienta poter v diffuzornykhi reshetkakh pri ploskom potoke Calculation of the Coefficient of Loss in Diffuser Grids at Plane Stream Kotloturbostroenie No 1 1950 524 O vc h i a n i k ov ON Vliyanie vkhodnogo profilya skorostei na rabotu diffuzorov Influence of the Inlet Velocity Distribution on the Operation of Diffusers Trudy Leningradskogo politekhnicheskogo instituta No 176 19551 525 S a n oy a n V G Dvizhenie zhidkosti v osesimmetrichnom kanale zadannogo profilya i raschet deistvitelnykh lavlenii Motion of a Liquid in an Axisymmectrical Channel of Specified Shape and Calculation of the Actual PressuicLs Trudy Leningradskogo politekhnicheskogo instituta No 176 1955 526 Solodkin EE and AS Ginevskii Turbulentnoe techenie vyazkoi zhidkosti v nachalnykh uchastkakh osesim metrichnykh i ploskikh kanalov Turbulent Flow of a Viscous Liquid in the Initial Stretches of Axisymmetrical and Plane Channels Trudy TsAGI No701 Oborongiz 1957 527 S ol od k i n EE and AS G i ne vsk i i Stabilizirovannoe turbulentnoe techenie vyazkoi zhidkosti v ploskom diffuzornom kanale pri malykhuglakh raskrytiya Steady Turbulent Flow of a Viscous Liquid in a Plane Diffuser Channel of Small Divergence Angle Trudy BNI MAP No728 1958 528 S ol od ki n EE and AS Gi ne vski i Turbulentnoe techenie v nachalnom uchastke ploskogo diffuzornogo kanala Turbulent Flow in the Initial Stretch of a Plane Diffuser Channel Trudy BNI MAP No 728 1958 529 Solodkin EE and AS Ginevskii K voprosu o vliyanii nachalnoi neravnomernosti na kharakteristiki diffuzornykh kanalov The Influence of the Initial Nonuniformity on the Characteristic of Diffuser Channels Promyshlennaya aerodinamika col No 12 BNI MAP 1959 530 Z s i 11 a r d C S Issledovanie diffuzorov aerodinamicheskikh trub bolshikh skorostei Study of Diffusers of Highf Velocity Wind Tunnels Tekhnicheskie zametki TsAGI No160 1938 531 T a r g S M Osnovnye zadachi teorii laminarnykh techenii Basic Problems of Laminar Flow Theory Gostekh teorizdat 1951 532 Fed y a e vs k i i KK Kriticheskii obzor rabot po zamedlennym i uskorennym turbulentnym pogranichnym sloyam Critical Survey of the Papers on Decelerated and Accelerated Turbulent Boundary Layers Tekhnicheskie zametki TsAGI No158 1937 533 Acke ret J Grenzschichtberechnung ZVDL Vol35 1926 534 A c k e r e t J Grenzschichten in geraden und gekrdmmten Diffusoren Intern Union fir theor und angew Mechanik Symposium Freiburg ldr1957 1958 535 An dres K Versuche Giber die Umsetzung von Wassergeschwindigkeit in Druck VDI Forsdhungsarbeiten Heft 76 Berlin 1909 536 Bardil Notter Betz and Evel Wirkungsgrad von Diffusoren Jahrbuch der Deutschen Luftfahrtforschung 537 Borry H Ducts for Heating and Ventilating April 1953 538 D 6 nc h F Divergente und konvergente turbulente Strdmungen mit kleinen tffnungswinkeln VDI Forschungs arbeiten Heft 282 1929 539 E i ffe 1 G Souffleries aerodynamiques Resumi de principaux travaux executes pendant la guerrre au laborqtpire aerodynamique 19151918 540 Flieg ne r A Versuche diber das Ausstr6men von Luft durch konischdivergente Dfisen 1 Z ivilingenieur 1875 2 Schweiz Bauztg 31 1898 541 Frey K Verminderung der Str6mungsverluste in Kanglen durch Leitflchen 7 Forschung No3 1934 542 G a I I e KR and RC Bind er TwoDimensional Flow through a Diffuser with an Exit Length J Applied Mechanics Vol20 No3 1953 K 543 Gibson A Onthe Flow of Water throughbPipes and Passages Having Converging or Diverging Boundaries Proc Royal Soc Vol83 NoA563 1910 544 G i bson A Onthe Resistance to Flow of Water through Pipes or Passages Having Diverging BoundariesTrans Royal Soc I Vol48 Part 1 No 5 1911 545 H o c h s c h i 1 d H Versuche 6iber Str6niungsvorgange in erweiterten und verengten Kanilen VDI Forschungsarbeiten Heft 114 Berlin 1912 546 Ho f m a n n A Die Energieumsetzung in saugrohrhnlich erweiterten Dasen Mitteilungen Heft 4 1931 547 Johnston JH TheEffect of Inlet Conditions on the Flow in Annular Diffusers CP No 178 Memorandum NoM 167 No1 January 1953 498 548 Johg AD and GL Green Tests of HighSpeed Flow in Diffusers of Rectangular Cross Section Reports and Memoranda No2201 July 1944 549 Kmoniek VK Unterschallstr6mungen in Kegeldiffusoren Acta Technica No5 1959 550 Kr6ner K Versuche 6iber Str6mungen in stark erwelterten Kanfilen VDI Forschungsarbeiten Heft 222 Berlin 1920 551 Little BH and SW Wilbur Performance and Boundary Layer Data from 12 and 23 Conical Diffusers of Area Ratio 20 at Mach Numbers up to Choking and Reynolds Numbers up to 75106 Report NACA No 1201 1954 552 M a r g o u lis W Recherches experimentales et thordtiques effectuies de 19301933 sur la mtcanique des fluides et la transmission de la chaleur dans les fluides en mouvement La technique aironautique No 139 1934 553 M i 1 li at ZP Etude exprimentale de l6coulement turbulent dans un conduit divergent par lair La houille blanche 11 NoB 1956 554 Nau m an n Efficiency of Diffusers on High Subsonic Speeds Reports and Transaction No 11 A June 1946 555 N i k u r a d z e I Untersuchungen iber dieStromungen des Wassers in konvergenten und divergenten Kanalen VDI Forschungsarbeiten Heft 289 1929 556 Patterson G Modern Diffuser Design Aircraft Eng 1938 557 Peters H Energieumsetzung in Querschnittserweiterung bei verschiedenen Zulaufbedingungen IngenieurArchiv No 1 1931 558 Polzin J Str6mungsuntersuchungen an einem ebenen Diffuser IngenieurArchiv Heft 5 1940 559 P r and t 1 L Neuere Ergebnisse der Turbulenzforschung VDI Bd 77 No 5 1933 560 Robertson JM and J W Holl Effect of Adverse Pressure Gradients on Turbulent Boundary Layers in Axisym metric Conduits J App1 Mech VI Vol24 No2 1954 561 Stratford BS Turbulent Diffuser Flow ARC CP No307 1956 562 Szablewski W Turbulente StrdmungenindivergentenKang len IngenieurArchiv BdXXII Heft4 1954 563 Turuja J and K Suzuki Experiments on the Efficiency of Conical Diffusers The Initial State of Separation of Flow TransJapan Soc MechEngrs 23 No 125 1957 564 Squire HB Experiments onConicalDiffusers Reports and Memoranda No2751 November 1950 565 W i nte r H Stfrmungsverhiltnisse in einem Diffusor mit vorgeschaltetem Krdmmer Maschinenbau und WArme wirtschaft Heft 2 1953 Section Six 61 Abramovich GN Aerodinamika mestnykh soprotivlenii Aerodynamics of Local Resistances Sbornik po promyshlennoi aerodinamike Trudy No211 1935 62 A r ono v I Z Teploobmen i gidravlicheskoe soprorivlenie v izognutykh trubakh Heat Exchange and Hydraulic Resistance in Bent Pipes Doctorates thesis Kievskii politekhnicheskii institut 1950 63 Baulin KK and IE Idelchik Eksperimentalnoe issledovanie techeniya vozdukha v kolenakh Experimental Study of Air Flow in Elbows Tekhnicheskie zametki No 23 1934 64 Grabovsk ii A M Issledovanie vzaimnogo vliyaniya mestnykh soprotivIenii Study of the Interaction of Local Resistances Nauchnye zapiski Odesskogo politekhnicheskogo instituta No3 1955 65 Tu P engChi iu Issledovaniya vliyaniya stepeni sherokhovatosti vnutrennikh poverkhnostei ventilyatsionnykh otvodov na ikh koeffitsienty mestnykh soprotivlenii The Influence of Roughness of the Inner Surfaces of Ventilation Bends on Their Coefficients of Local Resistances Authors summary of thesis for Cand of Engineering Sciences Inzhenernosroitelnyi institut Leningrad 1939 66 I d e I c h i k IE Napravlyayushchie lopatki v kolenakh aerodinamicheskikh trub Guide Vanes in WindTunnel Elbows Tekhzametki TsAGI No133 1936 67 I del c hi k IE Gidravlicheskie soprotivleniya fizikomekhanicheskie osnovy Fluid Resistances Physical and Mechanical Fundamentals Gosenergoizdat 1954 68 Ide lchik IE K voprosu o vliyanii chisla Re i sherokhovatosti na soprotivienie izognutykh kanalov The Influence of the Reynolds Number and the Roughness on the Resistance of Bent Channels Promyshlennaya aerodinamika colNo4 BNI MAP 1953 69 Kamershtein AG and VN Karev Issledovaniegidravlicheskogo soprotivleniya gnutykh svarnykh kruto zagnutykh i skladchatykh kolen kompensatorov Study of the Hydraulic Resistance of Bent Welded Steeply Bent and Corrugated Elbows of Expansion Devices Vniistroineft i MUGS 1956 499 610 K ly achk o L S Utochnenie metoda teoreticheskogo opredeleniya koeffitsientov soprotivleniya otvodov razlichnogo profilya Refining the Method of Theoretical Determination of the Resistance Coefficient of Bends of Different Profiles Trudy nauchnoi sessii LIOT No1 1955 611 Nekrasov BB Gidravlika Hydraulics VVA 1954 612 Promyshlennaya aerodinamika Industrial Aerodynamics Collection No 6 13NI MAP 1f956 613 Rikhter G Gidravlika truboprovodov Hydraulics of Pipelines ONTI 1936 614 Richter LA Tyagodutevye ustroistva promyshlennykh parovykh kotlov i puti snizheniya raskhoda clektrocicgii na sobstvennye nuzhdy Fans anra Blowers for Industrial Steam Boilers with Means of Reducing Theii ElectricEnergy Consumption Trudy nauchnotekhnicheskoi sessii po ekspluatatsii promyshlennykh kotelnykh ustanovok Gosenergo izdat 1953 615 Richter LA Issledovanie na modelyakh elementov gazovozdukhoprovodov teplovykh elektrostantsii Model Study of the Elements of Gas and Air Conduits for Thermal Power Plants Teploenergetika No 1 1957 616 Richter LA Voprosy proektirovaniya gazovozdukhoprovodov teplovykh elektrostantsii Problems of the Design of Gas and AirConduits for Thermal Power Plants Gosenergoizdat 1959 617 Tatarchuk GT Soprotivlenie pryamougolnykh otvodov Resistance of Rectangular BendsVoprosy otopleniya i ventilyatsii Trudy TsNIIPS Gosstroiizdat 1951 618 K h a n z h o n k o v V1 and V1 T a I i e v Umenshenie soprotivleniya kvadratnykh otvodov napralyayushchimi lopatkami Reducing the Resistance of Square Bends by Means of Guide Vanes Tekhnicheskie otdhety No 110 BNT MAP 1947 619 Elperin IT Povorot gazov v trubnom puchke Curve Flow of Gases through a Tube Bundle Izvestiya AN BSSR No 3 1950 620 Yu din E Ya Kolena s tonkimi napravlyayushchimilopatkamiElbows with Thin Guide Vanes Promyshlennaya aerodinamika col No 7 BNT MAP 1956 621 Fly at a u RS Gidravlicheskie raschety truboprovodov Hydrotechnical Calculation of Pipes Gostoptekhizdat 1949 622 Adler M Strbmung in gekriimmten R6hren Z angew Math Mech Bd14 1934 623 B a m b a c h Pl6tzliche Umlenkung Stoss von Wasser in geschlossenen unter Druck durchstr6mten Kanalen VDI Heft 327 1930 624 C o n n HG H G C oi1 b o r n e and WG B r o w n Pressure Losses in 4inch Diameter Galvanized Metal Duct and Fittings Heating Piping and AirConditioning No 1 1953 625 De Graene EPHeating Piping and AirConditioning No10 1955 626 Franke PG Perdite di carico nelle curve circolari Lenergia Elettrica No 9 1954 627 Frey K Verminderung des Str6mungsverlustes in Kanilen durch Leitflichen Forschung auf dem Gebiete des In genieurwesens Bd 5 No3 1934 628 F r i t z s c h e und H R ic h t e r Beitrag zur Kenntnis des Str6mungswiderstandes gekrummter rauher Rohrleitungen Forschung auf dem Gebiete des Ingenieurwesens Bd 4 No 6 1933 629 Haase D Allgemeine Wirmetechnik Nos 1112 1953 630 Heating and Ventilating January February 1953 631 Hilding Beij K Pressure Losses for Fluid Flow in 90 Pipe Bends JResearch of National Bureau of Standards Vol21 No1 1938 632 H o f m ann A Der Verlust in 90 Rohrkrfimmern mit gleichbleibendem Kreisquerschnitt Mitteilungen des Hy draulischen Instituts der Technischen Hochschule M3nchen Heft 3 1929 633 Garbrecht G Uber die Linienfiihrung von Gerinnen Wasserwirtschaft No 6 1956 634 K i r s c h b a c h Der Eneigieverlust in Kniest6icken Mitteilungen des Hydraulischen Instituts der Technischen Hoch schule Mtinchen Heft 3 1929 635 K r o be r Schaufelgitter zur Umlenkung von FlussStr6mungen mit geringem Energieverlust lngenieurArchiv Heft V 1932 636 Nippe rt H Uber den Str6mungsverlust in gekrfimmten Kanilen Forschungsarbeiten auf dem Gebiete des Ingenieur wesens VDI Heft 320 1929 637 Richter H Der Druckabfall in gekraimmten glatten Rohrleitungen Forschungsarbeiten auf dem Gebiete des In genieurwesens VDI Heft 338 1930 638 Richter H Rohrhydraulik 1954 639 S c h u h a r t Der Verlust in Kniestiicken bei glatter und rauher Wandung Mitteilungen des Hydraulischen Inst der Technischen Hochschule Minchen Heft 3 1929 640 Spalding Versuche Uiber den Str6mungsverlust in gekriimmten Leitungen VDI No6 1933 500 6 41 V u s k o vi c G Der Str6mungswiderstand von Formstticken fur Gasrohrleitungen Fittings Mittellungen des Hydrauli schen Instituts der Technischen Hochschule Mkinchen Heft 9 1939 642 Was i lew sk i J Verluste in glatten Rohrkriimmern mit kreisrundem Querschnitt bei weniger als 90 Ablenkung Mitteilungen des Hydraulischen Instituts der Technischen Hochscbule Milnchen Heft 5 1932 643 Weisbach J Lehrbuch der Ingenieur und Maschinenmechanik IIAufl 1850 Experimentalhydraulik 1855 644 W h it e CM Streamline Flow through Curved Pipes ProcRoySoc Lon A Vol 123 1929 Section Seven 71 A v e r y a no v A G Koeffitsienty mesrnykh soprotivlenil v troinikakh vytyazhnykh vozdukhovodov Coefficients of Local Resistance in YBranches of Exhaust Air Ducts Otoplenie i ventilyatsiya No2 1939 72 Z us man o v ic h V M SoprotivIenie troinikov stochnykh gazovodoprovodnykh trub Resistance of YBranches ot Sewer Pipes Voprosy otopleniya i ventilyatsii Gosstroiizdat 73 K a m e ne v P N Dinamika potokov promyshlennoi ventilyatsii Flow Dynamics in Industrial Ventilation Systems Gosstroiizdat 1938 74 Ko no k o tin V V Mesmnye soprotivleniya bokovykh otverstii gladkikh vozdukhovodov pryamougolnogo secheniya Local Resistances of Lateral Orifices of Smooth Rectangular Air Conduits LISI 1957 75 L e v i n S R Analiticheskoe opredelenie velichiny poter napora v trolnikakh vytyazhnykh ventilyatsionnykh setei Analytic Determination of the Magnitude of Head Losses in YBranches of Ventilating Exhaust Systems Otoplenie i ventilyatsiya No7 1935 76 L e v i n S R SoprotivIenie troinikov vytyazhnykh vozdukhovodov Resistance of YBranches of Exhaust Air Conduits Novosibirsk 1939Otoplenie i ventilyatsiya Nos 1011 1940 77 L e v i n S R Delenie potokov v truboprovodakh Stream Division in Pipes Trudy LTI im S M Kirova No23 1948 78 Levin SR Smeshenie potokov v krestoobraznykh soedineniyakh truboprovodov Stream Mixing in CrossShaped Pipe Joints Trudy LTI im SM Kirova No 5 1954 79 Levin SR Novyi metod teoreticheskogo opredeleniya gidravlicheskikh soprotivlenii pri smeshenii potokov v truboprovodakh New Methods for the Theoretical Determination of Fluid Resistances at Stream Mixing in Pipes Trudy LTI imSM Kirova No 6 1955 710 Le vin SR Soudarenie potokov neszhimaemoi zhldkosti v truboprovodakh Collision of IncompressibleLiquid Streams in Pipes Trudy LTI imSM Kirova No 8 1958 711 M a k s i m ov GA Raschet ventilyatsionnykh vozdukhovodov Calculation of Ventilation Air Conduits Gosstroiizdat 1952 Ventilyatsiya i otoplenie Part II Gosstroiizdat 1955 712 Pludemakhe r AS and GM Itkin Mestnye soprotivleniya troinikov vozdukhovodov pri nagnetanii Local Re sistances of YBranches of Forced Draft Air Conduits Otoplenie i ventilyatsiya No 9 1934 713 Plude makhe r AS Mestnye soprotivleniya v krestovinakh vodovodov pri rozlive Local Resistances in Water Pipeline Crosses at Discharge Otoplenie i ventilyatsiya No4 1937 714 P o l e t o v N V K gidravlicheskim raschetam soprotivlenil truboprovodov Hydraulic Calculation of Pipe Resistances Vodosnabzhenie I sanitarnaya tekhnika No4 1957 715 P r u z n e r AS Soprotivlenie troinikov pri rabote na nagnetanii Resistance of Forced Draft YBranches Sovremen nye voprosy ventilyatsii Stroiizdat 1941 716 T a I i e v VN and GT T a t a r c h u k Soprotivlenie pryamougolnykh troinikov Resistance of Rectangular YBranches Voprosy otopleniya i ventilyatsii Gosstroiizdat 1951 717 Taliev VN Raschet mestnykh soprotivlenii troinikov Calculation of the Local Resistances of YBranches Gosstroiizdat 1952 718 Ta lie v V N Aerodinamika ventilyatsii Aerodynamics of Ventilation Gosstroiizdat 1954 719 Tatarchuk GT Mestnye soprotivleniya chugunnykh krestovln Local Resistances of Iron Crosses of Pipes Voprosy otoplenlya i ventilyatsii No 3 Gosstroiizdat 1936 720 F r a n k e P Die zusitzlichen Verluste bei der Vereinigung von zwei Wasserstromen in einem gemeinsamen Steigschacht VDIZeitschrift Bd97 No24 August 1955 721 Gil man SF Pressure Losses of Divided Flow Fittings Heating Piping and AirConditioning April 1955 722 K i n n e E Der Verlust in 60 Rohrverzweigungen Mitteilungen des Hydraulischen Instituts der Technischen Hoch schule Mdinchen Heft 4 1931 723 Konzo S SF Gilman JW Holl and RJ Martin Investigation of the Pressure Losses of Takeoffs for Ex tended PlenumType AirConditioning Duct Systems University of Illinois Bulletin Bulletin Series No415 1953 501 724 McNown JS Mechanics of Manifold Flow ProcAmer Soc Civil Engrs No258 1953 725 Mi ll e r LG CH Pest erf ie I d and RJ W a a I kes Resistance of Rectangular Divided Flow Fittings Heating Piping and AirConditioning No 1 1956 726 P e te r m a n n F Der Verlust in schiefwinkligen Rohrverzweigungen Mitteilungen des Hydraulischen Instituts der Technischen Hochschule M6nchen Heft 3 1929 727 Vazsonyi A Pressure Loss in Elbows and Duct Branches TransASME Vol66 1944 728 Voge 1 C Untersuchungen fiber den Verlust in rechtwinkllgen Rohrverzweigungen Mitteilungen des Hydrauljchen Instituts der Technischen Hochschule Minchen Heft 1 1926 Heft 2 1928 Section Eight 81 Abramovich h GN Turbulenmye svobodnye strui zhidkostei I gazov Turbulent Free Jets of Fluids Gosenergoizdat 1948 82 Abramovich GN Prikladnaya gazovaya dinamika Applied Gas Dynamics Gostekhteorizdat 1953 83 Antufev VM and LS Kazachenko Teploperedacha iLsoprotivlenie konvektivnykh poverkhnostei nagreva Heat Transfer and Resistance of Convective Heating Surfaces Gosenergoizdat 1938 84 Antufev VM and GS Beletskii Teploperedacha i aerodinamicheskoe soprotivlenie trubchatykh poverkhnostei v poperechnom potoke Heat Transfer and Aerodynamic Resistance of Tubular Surfaces in a Transverse Stream Mashgiz 1948 85 Bezrukin IP Aerodinamicheskie svoistva zeren Aerodynamic Properties of Grains In Sbornik Separirovanie sypuchikh tel Trudy Moskovskogo doma uchenykh 1937 86 B e r e z k i n AR Issledovanie poteri napora v reshetkakh vodozabomykh sooruzhenii Study of Head Losses in the Water Intake Screens Trudy gidravlicheskoi laboratorii VODGEO No1 Gosstroiizdat 1941 87 Bernshtein RS VV Pomerantsev and S L Shagalova K voprosu o mekhanike soprotivleniya i teplopere dachi v trubnykh puchkakh Mechanics of Resistance and Heat Transfer in Tube Bundles Voprosy aerodinamiki i teploperedachi v kotelnotopochnykh protsessakh Collection of papers edited by Knorre Gosenergoizdat 1958 88 Bernshtein RS VV Pomerantsev and SL Shagalova Obobshchennyi metod rascheta aerodinamiches kogo soprotivleniya zagruzhennykh sechenii Generalized Method of Calculating the Aerodynamic Resistance of Loaded Sections Voprosy aerodinamikiI teploperedachi v kotelnotopochnykh protsessakh Collection of papers edited by Knorre Gosenergoizdat 1958 89 Denisenko GF Filtry iz porfstogo metalla PorousMetal Filters Byulleten Kislorod No6 1952 810 Dilman VV EPDarovskikh ME Aerov and LS AkselroO 0 gidravlicheskom soprotivlenii reshetchatykh i dyrchatykh tarelok On the Hydraulic Resistance of Grids and Perforated Plates Khimicheskaya promyshlennost No3 1956 811 Dul nev VB Opredelenieipoter napora v reshetkakh Determination of the Head Losses in Grids Gidro tekhnichoskoe stroitelstvo No9 1956 812 Zhavoronkov v NM Gidravlicheskie osnovy skrubbernogoprotsessa i teploperedacha v skrubberakh Hydraulic Foundations of the Scrubber Process and Head Transfer in Scrubbers Sovetskaya nauka 1944 813 Zhavoronkov NM Gidroi aerodinamika nasadok skrubbernykh i rektifikatsionnykh koloni Gidravlicheskoe soprotivlenie sukhikh neuporyadochennykh nasadok Hydro and Aerodynamics of Packings for Scrubber and Rectification Columns Fluid Resistance of Dry Random Arranged Packing Works Khimicheskaya promyshlennost No9 1948 814 Zhavoronkov NM ME Aerov and NI Umnik Gidro i aerodinamika nasadok skrubbernykh i rektifikatsion nykh koloni Gidravlicheskoe soprotivIenie 6roshaenmykh neuporyadochennykh nasadok Hydro and Aerodynamics of Packing for Scrubber and Rectification Columns Hydraulic Resistance of Wet Randum Arranged Packings Khimi cheskaya promyshlennost No 10 1948 815 ZhavoronkoviNM ME Aerov SN Babýov and NM Umnik Gidro iaerodinamika nasadok skrubber nykh i rektifikatsionnylkh koloni Kriticheskie yavleniya v oroshaemykh neuporyadochennykh nasadkakh Hydro and Aerodynamics of Packings for Scrubber and Rectification Columns Critical Phenomena in Wet Random Arranged Packings Khimiche kayapromyshlennost No3 1949 816 Z a I o g i n NG Ob aerodinamicheskom soprotivlenii shakhmatnogo puchka trub Aerodynamic Resistance of a CheckerboardType Tube Bundle Izvestiya VTI No5 1951 817 Idel chik IE Gidravlicheskoe soprotivlenie pri vkhode potoka v kanaly i protekanie cherez otverstiya Hydraulic Resistance at Stream Entrance in Channels and Flow through Orifices Promyshlennaya aerodinamika col Nq2 BNT NKAP 1944 502 818 1 de l chik IE Vyravnivayushchee deistvie soprotivleniya pomeshchennogo za diffuzorom Equalizing Effect of a Resistance Placed Behind a Diffuser Trudy No 662 BNT MAP 1948 819 I de 1 ch ik IE Opredelenie koeffitsientov soprotivleniya pri istechenii cherez otverstiya Determination of the Re sistance Coefficients at Discharge through Orifices Gidrotekhnicheskoe stroitelstvo No 5 1953 820 I de 1 c hik IE Gidravlicheskie soprotivleniya fizikomekhanicheskie osnovy Fluid Resistances Physical and Mechanical Fundamentals Gosenergoizdat 1954 821 I de V c hik IE Prinuditelnaya razdacha potoka v gazoochistnykh teploobmennykh i drugikh apparatakh Forced Stream Distribution in Scrubbing HeatExchange and Other Apparatus Collection of papers of NIIOGAZ No 1 Goskhimizdat 1957 822 Idel chik IE Uchet vliyaniya vyazkosti na gidravlicheskoe soprotivlenie diafragm i reshetok Allowing for the d Influence of Viscosity on the 9ydraulic Resistance of Diaphragms and Grids Teploenergetika No 9 1960 823 I s h k i n NP and MG K a g a n e r Gidravlicheskoe soprotivlenie poristykh sred Hydraulic Resistance of Porous Media Kislorod No 3 1952 824 K a z a k e v i c h F P Vliyanie ugla ataki gazovogo potoka na aerodinamicheskoe soprotivlenie puchkov trub Influence of the Angle of Approach of a Gas Stream on the Aerodynamic Resistance of a Tube Bundle Izvestiya VTI No 8 1952 825 K a s a 1 a i n e n NN Teploperedacha I soprotivlenie vozdukhopodogrevatelya s poperechnoomyvaemym puchkom trub Heat Transfer and Resistance of an Air Heater with Transverse Flow Around the Tube Bundle Teploenergetika No 7 1955 826 K a f a r o v VV Soprotivlenie v nasadochnykh kolonnakh pri zakhlebyvanii i pri optimalnykh skorostyakh potoka Resistance in Packed Columns at Clogging and at Optimum Stream Velocities Khimicheskaya promyshlennost No 6 1948 827 K o m a r o v s k i i AA MS V e r t e s h ev and VV S t r e lt s o v Gidravlicheskoe soprotivlenie sloya chastits proizvolnoi formy IHydraulic Resistance of a Layer of Particles of Arbitrary Shape Trudy Novocherkasskogo politekhnicheskogo 2nstituta imeni Ordzhonikidze Vol4155 1956 828 K o n o b e e v BI VA M a I y u s o v and NM Z h a v o r o n k o v Gidravlicheskoe soprotivlenie i tolshchina plenki pri obrashchennom techenii zhidkosti pod deistviem gaza v vertikalnykh trubakh Hydraulic Resistance and Film Thickness at Reverse Liquid Flow Under the Action of a Gas in Vertical Pipes Khimicheskaya promyshlennost No 3 1957 829 K o 11 e t o v L D Gidrodinamika porovykh sred Hydrodynamics of Porous Media Khimicheskaya promyshlennost No 2 1959 830 K u z n e t s o v NV and A Z S h c h e r b a k o v Eksperimentalnoe opredelenie teploperedachi i aerodinamicheskikh soprotjvlenii chugunnogo rebristogo vozdukhopodogrevatelya Experimental Determination of Heat Transfer and Aero dynamic Resistances of a CastIron Ribbed Air Heater Izvestiya VTI No2 1951 831 Ku znetsov NV AZ Shcherbakov and E Ya T itova Novye raschetnye formuly dlya aerodinamicheskogo soprotivleniya poperechno obtekaemykh puchkov trub New Calculating Formulas for the Aerodynamic Resistance of Transverse Flow Around Tube Bundles Teploenergetika No9 1954 832 Kuznetsov NV and SI Turilin Vliyanie temperaturnykh uslovii na teplootdachu i soprotivlenie trubchatykh poverkhnostei v poperechnom potoke Influence of the Temperature Conditions on Heat Transfer and Resistance of Tubular Surfaces in a Transverse Stream Izvestiya VTI No11 1952 833 K u z o v n i k o v a EA Gidravlicheskoe soprotivlenie puchkov trub s peremennym shagom po vysote Hydraulic Re sistance of Tube Bundles Varying over Height Pitch Sbornik nauchnykh trudov AN BSSR 44 VI 1954 834 Lev ES Filtratsiya gaza cherez sloi sypuchego tela sostoyanie voprosa Gas Filtration through a Layer of Loose Material State of the Problem Voprosy aerodinamiki i teploperedachi v kotelnotopochnykh protsessakh Collection of articles edited by Knorre Gosenergoizdat 1958 835 Leibenzon LS Dvizhenie prirodnykh zhidkostei i gazov v poristoi srede Flow of Natural Fluids in a Porous Medium Gostekhizdat 1947 836 Linchevsk ii V P Editor Metallurgicheskie pechi Metallurgical Furnaces Metallurgizdat 1948 837 Lyapin MF Teploperedacha I aerodinamicheskoe soprotivlenie gladkotrubnykh puchkov pri bolshikh chislakh Re gazovogo potoka Heat Transfer and Aerodynamic Resistance of Bundles of Smooth Pipes at High Reynolds Numbers of the Gas Stream Teploenergetika No 9 1956 838 Minskii EM 0 turbulentnoi filtratsii v poristykh sredakh Turbulent Filtration in Porous Media DAN SSSR Vol 78 No 3 1951 f 839 Mints DM and SA Shubert Gidravlika zernistykh materialov Hydraulics of Granular Materials Izdatel stvo Ministerstva kommunalnogo khozyaistva RSFSR 1955 840 Mikheev MA Osnovy teploperedachi Fundamentals of Heat Transfer Gosenergoizdat 1949 841 Moch an IS Mestnye soprotivleniya pri dvizhenii odnofaznogo i dvukhfaznogo potokov Local Resistances at the Flow of Single and TwoPhase Streams BTI TsKTI 1959 503 842 M u 11 o k a n d o v F N Gidravlicheskoe soprotivlenie sloya sfericheskikh chastits pri izotermicheskom i neizotermiches kom vozdushnom potoke Fluid Resistance of a Layer of Spherical Particles at Isothermal and Nonisothermal Air Streams ZhTF VolXVIII No8 1948 843 P a n c h e n k o A V1 Vernilyatsionnye ustanovki melnits i elevatorov Ventilating Installations of Grinding Mills and Elevators Zagotizdat 1954 844 P I a n o v s k ii AN and V V K a f a r o v Optimalnye skorosti potokov v nasadochnykh kolonnakh Optimum Stream Velocities in Packed Columns Khimicheskaya promyshlennost No4 1946 845 R a m z i n L K Gazovoe soprotivlenie sypuchikh materialov Gas Resistance of Loose Materials Izvestiya VTI No720 1926 846 Salikov AP YaL Polynovskii and KI Belyakov Issledovanieteploperedachi i soprotivleniy0 v prodo1nykh puchkakh gladkikh trub Study of Heat Transfer and Resistance in Longitudinal Bundles of Smooth Tubes Teploenergetika No8 1954 847 T e be n k o v B P Rekuperatory dlya promyshlennykh pechei Heat Recuperators for Industrial Furnaces Metal lurgizdat 1955 848 T i m o fee v VN and E S K a r a s i n a Teploobmen v puchkakh trub chugunnogo rebristogo ekonomaizera Heat Exchange in Bundles of Tubes of a CastIron Ribbed WasteGas Heater Izvestiya VTI No 5 1952 849 T u 1 in S N Teploperedacha i soprotivlenie v puchkakh trubok s provolochnym orebreniem Heat Transfer and Re sistance in Bundles of Tubes with Wire Ribbing Teploenergetika No 3 1958 850 Us y u kin I P and LS Ak s e 1 rod Osnovy gidravlicheskogo rascheta setchatykh rektifikatsionnykh koloni Fundamentals of the Hydraulic Calculation of ScreenPacking Rectification Columns Kislorod No 1 1949 851 U c h a s t k i n P V Issledovanie effektivnosti i gidrodinamicheskogo soprotivleniya eliminatorov Study of the Efficiency and Hydrodynamic Resistance of Roof Ventilators Otoplenie i ventilyatsiya No 6 1940 852 F e d e r o v I M lkoeffitsienty ispareniyaj teplootdachi i soprotivleniya pri sushke zernistykh materialov s produvkoi vozdukha cherez sIbi Coefficients of Evaporation Heat Transfer and Resistance when Granular Materials Are Dried by Blowing Air througo a Layer In Sbornik Sovremennye problemy sushilnoi tekhniki Gosenergoizdat 1941 853 F u k s SN Sopr6tivlenie trubnogo puchka pri kondensatsil v nem para Resistance of a Bundle of Tubes at Con densation Stream ifi It Teploenergetika No 4 1954 854 Kh an zhonkov V 1 Soprotivlenie setok Resistance of Screens Promyshlennaya aerodinamika col No2 BNT NKAP 1944 855 Ch avt orae v AI 0 poteryakh napora v reshetke Head Losses in a Grid Gidrotekhnicheskoe stroitelstvo No 5 1958 856 C h u d n o v sk ii AF Teploobmen v dispersnykh sredakh Heat Exchange in Dispersed Media Gostekhteoretizdat 1954 857 S h e p e le v 1A Osnovy rascheta vozdushnykh zaves pritochnykh strui i poristykh filtrov Fundamentals of the Calculation of Air Locks Influx Streams and Porous Filters Stroiizdat 1950 858 S h c h e rb a k o v A E and N I Z h i r n o v Teploperedacha i aerodinamicheskoe soprotivlenie chugunnogo rebristo zubchatogo vozdukhopodogrevatelya Heat Transfer and Aerodynamic Resistance of a CastIron RadiatorType Air Heater Teploýnergetika No 8 1954 859 Cornell WG Losses in Flow Normal to Plane Screens Trans ASME No4 1958 860 Fla c h sb a r t 0 Widerstand von Seidengazefiltern Runddraht und Blechstreifensieben mit quadratischenMaschen Ergebnis der aerodynamischen Versuchsanstalt zu Gbttingen IV Lieferung 1932 861 K i r s c h m e r 0 Untersuchungen fiber den Gefallsverlust an Rechen Mitteilunge des Hydraulischen Instituts der Technischen Hochlchule Miinchen Heft 1 1926 862 S p a n d 1 e r I Untersuchungen 6iber den Verlust an Rechen bei schriger Zustrrmung Mitteilungen des Hydraulischen Instituts der Techfiischen Hochschule Miinchen Heft 2 1928 863 W a 11 is RP ardd CM W hit e Resistance to Flow through Wests of Tubes Engineering Vol 146 Nos 3802 3804 3806 1938 t I Section Nine 91 Abramovich GN Turbulentnye svobodnyestruizhidkostei i gazov Turbulent Free Jets of Fluids Gosenergoizdat 1948 J 92 Ar onov IZ CTeploobiben i gidravlicheskoe soprotivlenie v izognutykh trubakh Heat Exchange and Fluid Resistance in Bent Pipes Doctorates thesis Kiev Polytechnic Institute 1950 504 93 Aronovich VA Vybor razmera reguliruyushchikh klapanov Selecting the Size of Control Valves Khimicheskaya promyshlennost No4 1950 94 Aronovich VV and MS Slobodkin Armatura reguliruyushchaya i zapornaya Control and Shutoff Valves Mashgiz 1953 95 Ba u Ii n KK Ispytanie labirintnykh uplotnenii Testing Labyrinth Seals In Sbornik Statei po kompressornym mashinam VIGM No10 1940 96 G ur e v i c h D F Osnovy rascheta truboprovodnol armatury Fundamentals of Calculation of Pipe Fittings Mashgiz 1956 97 Dub B I Armatura vysokogo davleniya dlya truboprovodov HighPressure Pipe Fittings Gosenergoizdat 1954 98 i d e I c h i k I E Gidravlicheskoe soprotivIenie pri vkhode potoka v kanaly i protekanie cherez otverstiya Hydraulic Resistance at Stream Entrance in Channels and Flow through Orifices Promyshlennaya aerodinamika col No2 BNT NKAP 1944 99 I d e I c h i k IE K rascheru soprotivieniya labirintnykh uplotnenii Calculating the Resistance of Pipe Seals Kotloturbostroenie No 3 1953 910 I d e 1 c h i k IE Gidravlicheskie soprotivleniya fizikomekhanicheskie osnovy Fluid Resistances Physical and Mechanical Fundamentals Gosenergoizdat 1954 911 K u z n e t s o v LA and BV R u d o m i n o Konstruirovanie i raschet truboprovodov teplosilovykh ustanovok Design and Calculation of Pipes of ThermalPower Installations Mashgiz 1949 912 M u ri n G A Gidravlicheskoe soprotivlenie pryamotochnykh ventilei Hydraulic Resistance of DirectFlow Valves Otoplenie I ventilyatsiya No5 1941 913 O s i p o v s k i i N F Ekspluatatsiya barabannykh kotlov vysokogo davleniya Operation of HighPressure Drum Boilers Gosenergoizdat 1953 914 R o 11 e N L Koeffltsienty soprotivleniya i raskhoda koltsevogo zatvora Resistance and Discharge Coefficients of a RingSeal Gate Valve Gidrotekhnicheskoe stroitelstvo No4 1953 915 Che by she v a KV K voprosu o raschete labirintnogo uplotneniya Calculating a Labyrinth Seal Tekhnicheskie zametki TsAGI No142 1937 916 Fr e n k e 1 V Z Gidravlika Hydraulics Gosenergoizdat 1956 917 E r likh AM Paroprovody ikh armatura i prochie detail Steam Conduits Their Fittings and other Parts ONTI 1937 918 B a c h C Versuche diber Ventilbelastung und Ventilwiderstand 1884 919 H o tt i n g e r M Bericht fiber die an Rohrverschraubungen Rohrschweissungen und Ventilen durchgef aihrten Unter suchungen Gesundheltsingenieur No45 1928 920 Guilleaume M Die Wirmeausnutzung neuerer Dampfkraftwerke und ihre Ueberwachung VDIZeitschrift No17 1915 u Feuerungstechnik 19131914 921 Pfleiderer G and A Closterhalfen Versuche iber den Stromungswiderstand von Heissdampfventilen ver schiedener Bauart Die WVrme No43 1930 und Archiv fur Wirmewirtschaft No1 1931 922 W eisbach J Lehrbuch der technischen Mechanik 1875 Section Ten 101 Ide 1 ch ik IE Poteri na udar v potoke s neravnomernym raspredeleniem skorostei Shock Losses in a Stream with Nonuniform Velocity Distribution Trudy MAP No 662 1948 102 K r a s n o p e r o v EV Eksperimentalnaya aerodinamika Experimental Aerodynamics ONTI 1935 103 K u zn et sov B Ya Lobovoe soprotivlenie trosov provolok tenderov i aviatsionnykh lent Drag of Ropes Wires Ties and StaysTrudy TsAGI No 97 1931 104 Kuznetsov B Ya Aerodinamicheskie issledovaniya tsilindrov Aerodynamic Studies of Cylinders Trudy TsAGI No 98 1931 105 Skochinskii AA AI Ksenofontova AA Kharev and IE Idelchik Aerodinamicheskoe soprotivlenie shakhtnykh stvolov i sposoby ego snizheniya Fluid Resistance of Mineshafts and Methods of Reducing It Ugletekhizdat 1953 106 Khanzhonkov VI Aerodinamicheskoe soprotivlenie trubchatykh ferm Aerodynamic Resistance of Tubular Girders Tekhnicheskie otchety No 131 BNI MAP 1955 107 K h a r e v A A Mestnye soprotivleniya shakhtnykh ventilyatsionnykh setei Local Resistances of MineVentilating Systems Ugletekhizdat 1954 505 108 Chesalov AV Koeffitsienty vrednykh soprotivIenii samoletov Coefficients of Aircraft Resistance Trudy TsAGI No42 1929 109 Y u r e v B N and M P L e s ni 1k ova Aerodinamicheskie issledovaniya Aerodynamic Studies Trudy TsAGI No33 1928 1010 Yur e v BN Eksprlmentalnaya aerodinamika Experimental Aerodynamics ONTI 1932 1011 Eiffel Resistance de lair et laviation Paris 1910 1012 Ergebnisse der aerodynamiIschen Versuchsanstalt zu G6ttingen Lieferung U 1923 Lieferung 111 1927 1013 Frachsbart 0 Neue Unteesuchunge fiber den Luftwiderstand von Kugeln Phys Z 1927 1014 Jacobs Sphere DragTests in the Variable Density Wind Tunnel Nat Advisory Commission for Aeronautics 1929 1015 Hutte Handbuch Russian translationONTI 1936 Section Eleven 111 Abram ov i c h G N Turbulentmye svobodnye strui Zhidkostel i gazov Turbulent Free Jets of Fluids Gosenergoizdat 1948 112 Baturin VV andiA Shepelev Aerodinamicheskie kharakteristiki pritochnykh nasadkov Aerodynamic Characteristics of Intike Nozzles Sovremennye voprosy ventilyatsti Stroiizdat 1941 113 B u s h e I A R Snihhenie vnutrennikh poter v shakhtnoi ustanovke s osevym ventilyatorom Reduction of the Interior Losses in an Installation with Axial Fan Trudy No 673 BNT MAP 1948 114 G r i m i t I n M I Gidravlicheskli raschet pritochnykh perforirovannykh truboprovodov na zadannuyu stepen raVnomer nosti razdachi Hydraulic Calculation of Intake Perforated Pipes for a Specified Degree of Uniformity of Stream Distribu tion Promyshlendaya energetika Trudy LIOT 1958 115 G r imtoiIt 11 n M I NVremennye rukovodyashchie ukazaniya po gidravlicheskomu raschetu primenefniyu i izgotovleniyu pritochnykh perforirovannykh vozdukhovodov Provisional Instructions for Hydraulic Calculation Application iand Manufacture of Perforated Intake Air Conducts Nauchnotekhnicheskaya informatsiya po voprosam okhrany truda UIOT No19 1959 116 Do v z hi k S A anbi A S Gin e vs k ii Eksperimentainoe issledovanie napornykh patrubkov statsionamykh1osevykh mashin Experimental Study of Pressure Connections of Stationary Axial Machines Tekhnicheskie otchety No 130 BNI MAP 1955 117 Idel c h 1ik IE didravlicheskie soprotivleniya pri vkhode potoka v kanaly I protekanii cherez otverstiya Fluid Re sistance at the Inlet of a Stream in Channels and at the Flow through Orifices In Sbornik Promyshlennaya aero dinamika No2 BNiT NKAP 1944 118 I d e l c h i k IE Aerodinarnika potoka i poteri napora v diffuzorakh Aerodynamics of the Stream and Head Losses in Diffusers Promyshlefinaya aerodinamika col No 3 BNT MAP 1947 119 I d e I c h i k I E Poteri na Udar v potoke s neravnomernym raspredeleniem skorostei Shock Losses in a Stream with Nonuniform Velocity Distribution Trudy MAP No 662 1948 1110 Id el ch ik IE Opredelenie kocffitsientov soprotivleniya pri istechenii cherez otverstiya Determination 6f the Re sistance Coefficients at Discharge through Orifices Gidrotekhnicheskoe stroitelstvo No 5 1953 1111 I d e I c h i k IE Gidravlicheskie soprotivleniyafizikomekhanicheskie osnovy Fluid Resistances Physicil and Mechanical Fundamhntals Gosenergoizdat 1954 1112 Ide lch ik IE Uchet vliyaniya vyazkosti na gidravlicheskoe soprOtivlenie diafragm i reshetok Allowingifor the Influence of Viscosity on the Hydraulic Resistance of Diaphragms and Grids Teploenergetika No 9 1960 1113 L ok shin I L andA Kh Ga z i r be k o va Rabota diffuzorov ustanovlennykh za tsentrobezhnymfi ventilydtorami Operation of Diffusers PlacBehind Centrifugal Fans Promyshlennaya aerodinamika col No 6 BNI MAP 1956 1114 Nosova MM Sbprotivlenie vkhodnykh i vykhhdnykh rastrubov s ekranom Influence of Inlet and Exit Bells with Baffles In Sbomik Promyshlennayaaerodinaimika No 7 1956 1115 Nosova MM arfd NF Tarasov Soprotivlenie pritochnovytyazhnykhshakht Resistance of IntakeExhaust Vents in Sbornlk Promyshlennaya aerodinamika No12 Oborongiz 1959 1116 Promyshlennaya aer6dlnamlka Industrial Aerodynamics Collection No 6 BN1 MAP 1956 1117 Khanzhonkov VN Soprotivlenie setok Resistance of Screens Promyshlennaya aerodinamika col No 2 BNT NKAP 1944 1118 Khanzhonkov VN Uluchshenie effektivnosti diffuzorov s boishimi uglami raskrytiya pripomoshchi ploskikh ekranov Improvingthe Effidiency of Diffusers with Large Divergence Angles byMeans of Plane Baffles Promyshlen naya aerodinamlka colNo3 BNT MAP 1947 506 1119 K h a n z h o n k o v V1 Soprotivlenie pritochnykh i vytyazhnykh shakht Resistance of Intake and Exhaust Vents In Sbornik Promyshlennaya aerodinamika No 3 BNI MAP 1947 1120 K han z honk o v VL Umenshenie aerodinamicheskogo soptotivleniya otverstii koltsevyimi rebranii i ustupamni Reducing the Aerodynamic Resistance of Orifices by Means of Annular Ribs and Ledges In Sbornik Promyshlen naya aerodinamika No 12 Oboronglz 1959 1121 Khanzhonkov VI and V1 Talev Umenshenie soprotlvleniya kvadratnykh otvodov napravlyayushchimi lopatkami Reducing the Resistance of Square Bends by Means of Guide Vanes Tekhnicheskie otchety No 110 BNT MAP 1947 1122 Yudin EYa Kolena s tonkimi napravlyayushchimi lopatkami Elbows with Thin Guide VanesPromyshlennaya aerodinamika col No7 BNT MAP 1956 1123 Bevier CW Resistance of Wooden Louvers to Fluid Flows Heating Piping and AirConditioning May 1955 1124 Cobb PR Pressure Loss of Air Flowing through 45 Wooden Louvers Heating Piping and AirConditioning December 1953 1125 Hofmann A Die Energieumsetzung in saugrohrihnlichen erweiterten DiisenMitteilungen Heft 4 1931 Section Twelve 121 A bra am o vi c h G N Turbulentnye svobodnye strui zhidkostei i gazov Turbulent Free Jets of Fluids Gosenergoiz dat 1948 122 Atlas Inertsionnye pyleuloviteli Inertial Dust Separators Series OV122 Lenpromstroiproekt 1947 123 Atlas KTIS Series V327 1943 124 Batareinye tsiklony rukovodyashchie ukazaniya po proektirovaniyu izgotovleniyu montazhu i ekspluatatsii Battery Powered Dust Separators InstructionsRelative to Their Design Manufacture Installation and RunningGoskhimizdat 1956 125 Gazoochistnoe oborudivanie GasScrubbing Equipment Catalog of the Fazoochistka Trust Goskhimizdat 1958 126 Geras ev AM Pyleuloviteli SIOT SIOTDust Separators Profizdat 1954 127 Gordon GM and 1A Aladzhalov Gazoochistka rukavnymi filtrami v tsvetnoi metallurgil Gas Cleaning by BagType Filters in Nonferrous Metallurgy Metallurgizdat 1956 128 Zaitsev MM Raschet rukavnogo filtra Calculation of a BagType Filter Trudy Nlltsement No3 1950 129 Zaitsev MM and FI Murashkevich Vremennye rukovodyashchie ukazaniya po raschetu trubyraspylitelya dlya opymnopromyshlennykh ustanovok Provisional Instructions for Calculation of TubeSprayers for Pilot Plants Report of NIIOGAZ 1954 1210 Z a it s e v MM Normali giprogazoochistki na batareinye tsiklony i tsiklony NIIGAZ Standards for Gas Cleaning by Battery Powered Dust Separators and NIIGA Z Dust Separators Trudy konferentsii po voprosam zoloulavlivaniya shlakoulavlivaniya shlakozoloispolzovaniya Gosenergoizdat 1955 1211 Za itsev M M Ochistka gazov v tsiklonakh i gruppovykh tsiklonakh Gas Cleaning in Dust Separators and Group Dust Separators Sbornik materialov po pyleulavlivaniyu v tsvetnoi metallurgii Metallurgizdat 1957 1212 Zalogin NG and SM Shukher Ochistka dymovykh gazov Cleaning of Exhaust and Waste Gases Gos energoizdat 1954 1213 Zv e r e v N1 Malogabaritnyi zhalyuziinyi zoloulovitel SmallSize LouverType Dust Collector Izvestiya VTI No3 1946 1214 Zv e rev NI Proektnaya normal zhalyuziinogo zoloulovitelya VTI Design Standard for the VTI LouverType Collector 1948 1215 Idel chik IE Prinuditelnaya razdacha potoka s pomoshchyu reshetok v gazoochistnykh teploobmennykh i drugikh apparatov Forced Stream Distribution by Means of Grids in Gas Cleaning Heat Exchange and other Instruments Trudy NIIOGAZ col No 1 Goskhimizdat 1957 1216 Idel chik IE Vyravnivayushche deistvie sistemy posledovatelno ustanovlennykh reshetok The Equalizing Effect of a System of Grids Arranged in a Series Teploenergetika No 5 1956 1217 Kirpichev VF andAA Tsarkov Sravnitelnye ispytaniya razlichnykh tsiklonov na stende Comparative Tests of Different Dust Separators on a Test bend Teploenergetika No 10 1957 1218 Klyachko LS Metodteoreticheskogoopredeleniyapropusknoi sposobnosti apparatov s vrashchayushchimsya osesimmetrichnym techeniem zhidkosti Theoretical Determination of the Discharge Capacity of Apparatus with Rotating Axisymmetrical Flow of the Liquid Teoriya i praktika obespylivayushchei ventilyatsii LIOT Leningrad Profizdat 1952 507 1219 Kouzov PA Ochistka vozdukha ot pyli Dust Removal from Air LIOT 1938 1220 K o u z o v PA Tsiklony LIOT s vodyanoi plenkoi LIOT Dust Separatibn with the Aid of Water Film Vsesbyuznyi nauchnoissledovatelskii institut okhrany truda v Leningrade 1953 1221 Kucheruk VV ahd G1 Krasilov Novye sposoby ochlstki vozdukha ot pyli New Methods for Removing Dust from the Air Mashgiz 1950 1222 K u c h e r u k V V Ochistka or pyli ventilyatsionnykh i promyshlennykh vybrosov Dust Removal from Ventilating and Industrial Exhaust Air Siroiizdat 1955 1223 M a r y a m o v N B Eksperimentalnoe issledovanie i raschet aviatsionnykh radiatorov Experimental Study arai Calculation of Aviation Radiators Trudy TsAGI No367 1938 1224 Mar yamov NB Raschet trubchatoplastinchaiykh i trubchatorebristykh radiatorov Calculation of Tube and Plate and Fin andTube Radiators Trudy LII No 18 1946 1225 Minskii EM and MP Korchazkhin K raschetu propusknoi sposobnostitsiklonnykh separatorov CalCulation of the Discharge Capacity of Dust Separators Gazovaya promyshlennost No11 1956 1226 M u r a s h k e v i c h F I Effektivnost pyleulavlivaniya turbulentnym promyvatelem Efficiency of Dust Collection by a Turbulent Washer Inzhenernofizicheskii zhurnal AN BSSR Vol 11 No 11 1959 1227 Normy aerodinamicheskogo raicheta kotelnykh agregatov Standards of the Aerodynamic Calculation of Boiler Units Mashgiz 1948 1228 Ochistka vozdukha otupyli inertsionnye pyleotdeliteli IP20 rabochie chertezhi Cleaning the Air of Dust Inertial IP20 Dust Separators Working Drawings TsBSP Strolizdat 1948 1229 P o 1 i k a r p o v V F Ispytanie plastinchatykh kaloriferov Testing Baffle Feed Air Heaters TsNILOV Prormstroi proekt 1936 1230 Re k k EE Sravnitelnaya otsenka tkanel primenyayushchikhsya dlya ochistki vozdukha ot pyli v ventilyatsionnykh filtrakh Comparative Evaluation of the Fabrics Used for Cleaning the Air from Dust in Ventilation Filters Otoplenie i ventilyatsiya No 1 1933 No 4 1934 1231 Ritshel G and Gý Grebe r Rukovodstvo po otopleniyu i ventilyatsii Manual of Heating and Ventilating Vols I and llGosstrioiizdat 1932 1232 Ta li e v V N Rashet gladkotrubchatykh kaloriferov Calculating SmoothTube Air Heaters Otoplenie i ventilyatsiya No 6 1940 1233 T a I i ev V N Aerodinamicheskie kharakteristiki novykh konstruktsii aeratsionnykh fonarei Aerodynamic Character istics of New Designsfor Roof Ventilators Gosstroiizdat 1955 1234 T e v e r o v s k ii E N Opyt ekspluatatsii i promyshlennykh ispytanii razlichnykh zoloulovitelei i rekomendatsil po lkh vyboru ExperienceAccumulated in Operating and in Testing Various Ash and Slag Collectors and Recommenraations for Their Selection Trudy konferentsii po voprosam zoloulavlivaniya shlakoulavlivaniyai shlakozoloispoilzovaniya Gosenergoizdat 1955 1235 Teverovskii EN and MM Z a i t s e v Pyleulavlivayushchii absorbtsionnyi i teploobmennyi apparat TP s vysokoskorostnym potbkom gaza Collecting Absorbing and Heat Exchanging Apparatus Type TP with HighSpeed Gas Stream Trudy NIIOGAZ No1 Goskhimizdat 1957 1236 Trichler r AL andd LD Ego rov Metallicheskie kalorifery dlya nagreva vozdukha Steel Air Heaters Stroiizdat 1940 1237 Uzhov VN Santarnaya okhrana atmosfernogo vozdukha AirPollution Control Medgiz 1955 1238 Uchastkin PV Issledovanie effektivnosti i gidravlicheskogo soprotivleniya eliminatorov Study of the Efficiency and the Fluid Resistance of Roof Ventilators Otoplenie i ventilyatsiya No 6 1940 1239 Fruk ht IA Gidravllcheskoe soprotivlenie fonarei snabzhennykh vetrootboinymi shchitkami Fluid Resistance of Roof Ventilators Equipped withWind Shields Stroitelnaya promyshlennost No1 1958 1240 K han z honk ov V I Ventilyatsionnye deflekto6ry Ventilation Hoods Stroiizdat 1947 1241 K h a n zh on k ov V1 Aerodinamicheskie kharakteristiki unifitsirovannogo deflektora TsAGI dlya vagonov Aero dynamic Characterisfics of the Unified TsAGI Ventilation for Railroad Cars Promyshlennaya aerodinamika col No 10 Oborongiz 1958 1242 Tsiklony NIOGýAZ iukovodyashchie ukazaniya poproektirovaniyu izgotovleniyu montazhu i ekspluatatsii NIIOGAZ Dust Separators Instkuctions forTheir Design Manufacture Mounting and Operation Goskhimizdat 1956 1243 Shakhov TF Sravniteln6e izucheniý razlichnykh konstruktsii reshetok zhalyuziinykh inertsionnykh pyleulovitelei Comparative Study of Different Designs of Louvers for LouverType Inertial Dust Collectors NIIOGAZ reýort 1949 1244 El per in IT P6vorot gazov v trubnom puchke Gas Flow through the Bends of Tube Bundles Izvestiy i AN BSSR No 3 1950 508 I 1ý SUBJECT INDEX Bar grating with an angle of approach a 0 O 330 and d 05 331 Bell cf Bellmouth conical 86 87 95 96 98 Bellmouth conical converging orifice cf Inlets various into a conduit with a screen at the inlet 109 Bellmouth conical with end wall 96 without end wall 95 converging cf Inlet with smooth contraction 96 set in a large wall 146 smooth made by an arc of a circle with flat end wall and with screen cf Bell mouth smooth 94 without screen and without end wall 82 with end wall 93 Bend 90V corrugated at 5 25 227 discharge from 431 standard threaded castiron 30 211 standard threaded castiron 450 211 standard threaded castiron 90 211 RO at 136167 211 twin bentbypass 213 twin bent Sshaped gooseneck shape 213 Ushaped twin bent bends at different 8 and Y 05 213 a Bends sharp at 0 5AS 15and 08 1800 206 207 Ro smooth atRh 15 and 06180 208 209 standard threaded castiron 211 212 turn bent at different 6 and R0 Rh05 212 213 Sshaped with turn in two planes 213 very smooth s 15 inconduits coils at arbitrary angle of bend 68 50RewDhV 21O 211 Bundle of ribbed tubes air heater with circular or square ribs 335 Bundles of tubes of different cross section shapes 1 checkerboard bundle of ribbed tubes 2 parallel bundle of oval tubes 3 checkerboard bundle of oval tubes 4 checkerboard bundle of drop shaped tubes 5 checkerboard bundle of Elesko type tubes 6 tubes with wire ribbing 336 337 Checkerwork regenerator furnaces 1 simple Siemens checkerwork 2 Siemens checkerwork 3 checkerwork of Stalproekt design 4 fencetype checkerwork of V E GruneGrzhimailo system 349 Circular free jet 440 Cloth DIZ shaking filter of various types of cloth 475 filtering coarse calico unbleached 470 cotton thread 472 flax flimsy 2ply thread 473 sergewool mixture 469 wool Velstroi 468 various types MFU suctiontype hose filter 475 Cloths filtering calico moleskin and cottonthread flannelette 474 Conduit friction coefficient at laminar flow Re2000 66 with nonuniform wall roughness commerical pipes friction coefficient Re2000 70 71 with rough walls friction co efficient flow conditions according to square law of resistance 72 509 Conduit with smooth walls friction coefficient Re2000 67 with uniform wall roughness friction coefficient Re2000 68 69 Conical converging bellmouth cf Inlet with smooth contraction 96 Contraction smooth cfBellmouth a rectilinear b converging 96 sudden at the inlet cf Inlet with sudden contraction Re104 99 inlet section in the end wall Re v 104 cf Inlet with sudden ontrac tion 98 moved forward relative jo the end wall Re10 4cf Inlet with sudden contraction 98 Converging beilmouth orifice along the arc of a circle cf Inlets various to a conduit with a screen at the inlet 109 T of type Fs Fb Fý Fs FAcs of improved shape a 90 274 standard threaded from malleableiron a 90 275 Ybranch of type FsFbF a15 267 a 30W 268 a 45 269 a 60 270 271 circular wiith smooth side bend 20 a 12151 branch 276 straight passage 277 rectangular smooth m O W branch 278 main passage 279 FsFbF FsFc a 30 brknch 260 a 45 branch 262 60 branch 264 045 main passage 2063 a 60 main passage 265 of improved shape a 45 272 60 273 Ybranches of type Ps Fb 4ý FstFc asymmetrical with smooth bends e Zv a 90 a side branch edge De slightly rounded U x01 b smooth side branch no 20 288 Corrugated elbows from galvanized R sheet for 07 a elbow 45 b elbow 2 6 2x45 c elbow 6 90V d gooseneck 2 2x45 e gooseneck 2 6 2x90 239 Cross of type Fib Fjb Fs Fc 6 90 1 Junction of streams converging cross 2 Diversion of a stream diverging cross 299 300 Curve 90 with concentric guide vanes 240 Cyclones NIIOGAZ 1 TsN15 2 TsN15u 3 TsN24 4 TsN11 460 various a simple conical b conical SIOT c ordinary LIOT and shortened LIOT with untwisting spiral d same without untwisting spiral e with dust removal 0 LIOT with water film and a specific liquid discharge g grouped cyclones 458 459 Cylinder elliptical smooth placed in a pipe threedimensional flow 392 single smooth placed in a pipe planepalrallel flow 388 Cylinders placed in pairs in a pipe plane parallel flow 395 Diaphragm with edges beveled or rounded at the passage of a stream from one conduit to another 138 orifice sharp edged 0OOI5 in a straight conduit 139 510 C Diffuser annular free discharge from 422 with converging fairing 187 with diverging fairing 187 axialradialannular free discharge 424 in a line 188 conical in a line 167 168 dp curved ýjConst of circular or pyramidal sections in a line 175 curved plane in a line 175 discharge from with rounded edges and optimum character istics against a baffle 422 multistage of optimum divergence angle behind a centrifugal fan in a duct forced draft 186 plane asymmetrical at a 0 behind a centrifugal fan in a duct forced draft 183 asymmetrical behind a centrifugal induceddraft fan free discharge 424 in a line 171 172 plane symmetrical behind a centrifugal fan in a duct forced draft 183 pyramidal behind a centri fugal fan in a duct forced draft 185 behind centrifugal induced draft fan free discharge 425 radialannular in a line 188 pyramidal in aline 169 170 rectilinear discharge against Id a baffle atr 1 0 421 short with dividing walls 182 with guiding devices or with resistance at the exit 182 stepped circular optimum divergence angle a opt 176 177 plane optimum divergence angle 180 181 pyramidal optimum divergence angle a opt 178 179 transitional from circle to rect angle or from rectangle to circle in a line 174 with baffles 182 Diffusers annular with deflecting baffles in a duct 187 of arbitrary shape at u 812 located at discharges of branches or other fitting at similar velocity profiles 174 located at the discharge of long stretches with nonuniform but symmetric velocity profile 166 with resistance at the exit screen perforated plate 182 Discharge from a straight conduit through grid or orifice 01dh015 435 from a straight conduit through fixed louvre 1 Inlet edges of the slots cut vertically 2 Inlet edges of the slots cut horizontally 438 thickedged orifice or grid 436 stretch with rounded edges against a baffle 421 side from the last orifice of a circular pipe 425 stretches under different conditions 1 From a straight conduit with screen at the exit 2 from a gutter with screen 3 through a stamped standard louvre with completely open adjustable slots 4 through cramped or cast grids 5 Smoothly converging nozzle 439 Diverging T of type FsFbFc FsFc a 90 standard threaded from malleable iron 285 Y of type a 900 branch 280 Fs Fb Fc Q 090 281 rectangular smooth Fs 01 a 90 branch 286 10 a 9or main passage 287 and FsFbFc a 0 900 straight passage 282 stFc of improved shape 283 284 Double flaps top and bottom hinged 149 Y oftype FsFbfc FsF a 15 291 292 0 30 293 294 45 295 296 511 Double flaps top and bottom hinged a 60 29q 298 Dust separator inertial louvre type conicalKTIS 461 separators batteryp6Wered HTs 1 with screw blade 2 with rosette a 25 3 with rosette c 30 461 Dynamic viscosity 4 6911 12 Elbow composite made from two 90 elbows lying in different planes 229 x ashaped 180 with con tracted exit section 231 with enlarged exit section with equal inlet and exit F bs areas IO 230 Elbow sharp rectangular section with contracted or exparhded discharge section 432 with contracted orex panded discharge section 433 square section with con tracted or expinded discharge section 432 smooth with contracted or expanded discharge section 433 Ushaped 180 with contracted exit section b 5234 with equal inlet and exit IF bs area 10I235 P b0 with widened exit section F 149236 237 with rounded corners and converging or diverging exit section F 1 217 218 at 0 05 riDhos and 0b180 219 220 Zshaped madefrom two 30 elbows 227 RewDDh 104 228 45 three 225elements 223 60 W 30 elements 223 90 five 225 elements 224 90 made from five elements 225 at different Iwith profiled bo guide vanes 241 withthin guide vanes qpl 90 242 with rounded inner corner and sharp outer corner 221 Elbow 90W rectangular section with thin guide vanes ip 95 under different conditions 1 sharp inner corner nornail number of vanes 2 same as 1 but 50W 3 same as 1 but most advantageous reduced number ofvanes 4 same as 1 but inner corner cut off 5 el bow with expansion normal number of vanes 6 same as 5 but reduced minimum number of vanes 243 with cutoff corners 222 smooth 02 rectangular at 05 with thin guide vanes qy 103 244 10 with thin guide vanes 9 107 244 atFI 20 with thin guide vanes 245 with discharge section ex panded by a factor of two M2O0 and with five thin guide vanes 434 with discharge section con tracted or expanded by a factor of two 434 three 45 elements 226 at welded with welding jointsat Re i10 226 Elbows made from separate elements at different 6 223 squareh Oat 061180 215 Elbows square 0 rectan gular section with converging or diverging exit section 214 90 circular with profiled guide vanes a smooth turn with a 512 normal number of vanes b the same with reduced num ber of vanes c cutoff corners and normal number of vanes d the same with renuced number of vanes e cutoff corners with reduced number of vanes 246 Electrostatic filters industrial 476 Eliminators 489 Ellipsoid placed in a pipe three dimensional flow 394 Entrance straight into a conduit mounted flush in the wall at an arbitrary angle 93 of constant cross section with various mountings 92 100 made by the arc of a circle without screen and without end wall cf Bellmouth smooth 93 to a conduit through a perforated plate with rounded orifice edges 108 through a fixed louver a inlet edges of the fins cut vertically b inlet edges of thefins cut horizontally 110 to a straight channel through a fixed louver 110 conduit through a perforated plate with orifice edges be veled or rounded 108 with thickedged orifices 001 5 107 with sharpedged orifices h 00015 Entrances to a conduit with a screen at the inlet 109 Exhaust flap single top hinged 147 Exhaust vents bent rectangular lateral opening with and without louvers 427 straight circular 1 with plane baffle 2 with split canopy 3 with hood 4 with split hood 5 with diffuser and hood 428 rectangular lateral openings with and without fixed louvers 426 Expansion joints various 1 Stuffing box 2 Bellows 3 Lyreshaped smooth 4 Lyreshaped with grooves 5 Lyreshaped with corrugated tube 6 Irshaped 374 sudden after a long straight stretch diffuser etc with exponential velocity distribution Circular or rectangular cross section 129 long plane and straight stretches plane diffusers etc with exponential velocity distribution 130 stretches with parabolic velocity distribution 133 behind plane diffusers with a10 elbow etc with asymmetric velocity distribution 133 of a plane channel behind orifice plates baffles in elbows etc with sinusoidal velocity distribution 131 with uniform distribution of the velocities 128 Filter boxtype from corrugated gauze with moist filter of Rekk design 466 porous with moist packing 467 twine wedgeshaped shaping single stage of MIDTtype 466 Filters cloth 468475 Fixed louvers at the inlet to a straight channel a inlet edges of the fins cut vertically b inlet edges of the fins cut horizon tally cf Entrance to a straight channel through a fixed louver 110 at side orifice in an intake shaft of rectangular section cf Straight intake shafts of rectan gular section with fixed louvers 104 in a straight intake shaft cf Straight intake shafts with fixed louvers 103 Flap 366 exhaust single top hinged 147 intake single top hinged 147 single center hinged 148 double both top hinged 148 Free discharge from an annular radial diffuser 423 from a circular rectilinear 513 diffuser 418 from a conduit at different velocity distribUtions 1 uniform 2 exponential 3 sinusoidal 4axisymmerical 5 parabolic 416 417 from a plane difftiser 420 from a rectangular diffuser 419 Friction coefficient with nonuniform wall roughness commercial pipes 70 71 of conduit with rough walls at square resistance law 72 with uniform wall roughness 68 69 ofa pipe at laminar flow Re2000 cf Conduit at laminar flow 66 from rubberized material cf Pipe from rubberized material 78 with smooth walls cf Conduit with smooth walls 59 of a plywood pipe cf Pipe plywood 79 of a steel ct castiron water pipecf Pipe water 74 of a welded pipe L cf Pipe welded with joints 73 Gate valve a cylindrical pipe b rectangular pipe 359 with symmletric contraction 360 Globe and gate valves a Globe valve Reyrtype b Forged globe valve c Wedgetype gate valve d Steamgate valve with lever gate e Gate valve with mushroom head and sliding tube 365 valve direct flow 364 standard ýith dividing walls a dividingýaalls at an angle of 450 b vertical dividing walls 363 Ypattern Kosva 1 with 30 Jo contraction of the seat 2 with full seat section I NS 363 Grid flat perf rated plate with sharpedged orifice 0 0015 at the inletof a conduit cf Entrance tq a straight conduit through a perforated plate with sharpedged orifices 106 or orifice thickwalled through with discharge from a straight conduit 436 with rounded or beveled edges through which discharge passes from a rectilinear conduit to ward the stream flow 437 plane perforated sheet or strip with sharpedged orifices 0 0 0015 Large Reynolds numbers Re wh1 321 with sharpedged orifices L 0015 Small Dhdh 5 Reynolds numbers Rel10 322 V thick perforated plate or laths 324 325 with orifice edges beveled facing the flow or made from angle iron 323 with orifices with beveled edges cf Entrance to a straight con duit through a perforated plate with orifice edges beveled or rounded 108 with rounded orifice edges 326 at the inlet of a conduit cf Entrance to a straight con duit through a perforated plate with orifice edges beveled or rounded 108 Grids stamped or cast at the inlet to a straight channel cf Entrance to a straight channel through a fixed louver 110 with orifice edges cut or rounded and screens at high stream i velocities large Mach numbers 329 with sharp inlet in the orifice of a wall of arbitrary thickness at high stream velocities large Mach numbers 328 Header with transition stretches 302 Heat exchangers various 1 Shelltube with longi tudinal stream flow around a the tubes 2 Shelltube with stream flow through the tubes 3 Twostage flow exchanger with transverse flow 514 around the tube bundle 180 turn 4 With mixed flow around the tubes alternating sections of transverse and longitudinal flows 485 Heater air made from heating elements 484 plain pipe 484 platetype 481 spiralribbed 482 fin petaled 483 Indraft shaft straight circular with diffuser and hood 105 with flat screen 105 with hood and section 105 with hood at sharp inlet edge 105 with section 105 square with hood at thickened inlet edge 105 shafts straight circular section 105 air duct with perforated lateral outlet 430 conical with end wall cf Belimouth conical 96 side to a circular straight pipe through the first orifice 102 straight in a conduit clamped between three walls 101 mounted between two walls 101 Inlet straight in a conduit mounted on a wall 101 with reinforced inlet edge 109 with sharp inlet edge through a screen 109 with end wall on one side of the conduit 100 on two adjacent sides of the conduit 100 three sides of conduit 100 two opposite sides of the conduit 100 with orifices on the one side of the conduit 102 on the two sides of the conduit 102 stretches of unit with grid packing or other type of obstruction placed in the working chamber 1 Cen tral impingement of the stream on the grid 2 Peripheral im pingement of the stream on the grid 3 Side impingement of the stream on the grid 477 with smooth contraction a rectilinear converging bell mouth b converging bell mouth Bellmouth 96 with sudden contraction or sudden contraction only inlet cross section in the end wall Re I 0 99 section in the end wall b 0 Re 10 a rounded inlet edge b inlet edge cut beveled c blunt inlet edge 98 moved forward relative to the end wall Th0 a rounded inlet edge b sharp or thick inlet edge c beveled inlet edge 98 Inlets various with screen 97 Kinematic viscosity 4 6 7 8 1012 Labyrinth seal combtype 373 with increased gap 372 Labyrinths various a short 180W elbow complex b hood with threesided inlet exit c hood with straight stretch at the inlet or exit 377 378 Louver dust separators 461 462 fixed at inlet to a straight channel a inlet edges of the fins cut vertically b inlet edges of the fins cut horizon tally cf Entrance to a straight channel through a fixed louver 110 at side orifice in an intake shaft cf Straight intake shafts side orifice with fixed louvers 103 104 stamped with adjustable slots in a large wall F08 complete opening of the louver 149 515 Orifice platecf Entrance toa straight conduit through a perforated plate with sharp edged orifices 106 sharpedged 6I0O 15 at the passage of a stream from one size conduit to another Res W 10 I 136 V in a large wall 143 in a straight conduit 139 thickwalled k at the passage of the stream from one size conduit unto another 137 S in a large wall 114 in a straight conduit 140 with edges beveled facing the stream flow a 4060t ina straight pipe 141 or rounded at the passage of a stream from one conduit to another cf Diaphragm 138 cut along the stream in a large wall 144 with rounded edges in a large wall 144 in a straight pipe 142 Orifices with various edges in a large wall 144 Packing bonded p9rous medium not granulated 345 ceramic Raschig rings edtGt2 dry or wetted 1 rings in vertical columns 2 rings in staggered 346 of wooden laths dry or wetted l chords placed in parallel 2chords placed crosswise 347 348 loose layer ofspheiical granular bodies or porous cemented layer from granular matejial constant diameter 343 344 material deposited at random loose layers from bodies of irregular shapeeat given dhdry and wetted 339342 Parallel bundle of circular tubes 332 333 Passage complex from one volume to another througha 90 elbow 1 with cutoff inlet exit stretch without vanes 3 the same but with vanes 3 with inlet exit stretchof length loas without vanes 4 the same but with vanes 375 through an oblong elbow 1 with baffle 2 without 376 through different labyrinth seals 377 through a side opening of a header pipe of constant section 303 304 Perforated plate at high Mach numbers 145 Pipe from tarpaulintype rubberized material friction coefficient 78 plywood birch with longitudinal grain friction coefficient at turbulent flow 79 reinforced by various stay rods and braces across the section 397 water of steel or cast iron allowing for the increase of resistance with use friction coefficient 74 welded with joints friction coefficient 73 Planeparallel free jet 441 Plates circular placed in pairs in a pipe threedimensional flow 395 Radiator honeycomb with hexa gonal or circular tubes 478 ribbedtube 479 tube and plate 480 Recuperators air heaters 1 ribbed castiron air heaters 2 ribbed toothed air heaters 338 Reinforced rubber hose friction coefficient 75 vsteel rubber hose friction coefficient 77 Ringseal gate free 371 in a chamber 371 Rolled section arranged in a row in in a pipe planeparallel flow 3 9 6 i Roof ventilation openings rectangular with panels 491 various types 1 Baturin Brandt with grid 2 same with pI A1 516 flaps 3 LD4 5 LEN PSP with 2 flaps same with 3 flaps 6 KTIS 7 MIOT 2 MIOT 2a 8 PSK1 9 PSK2 summer conditions PSK2 winter con ditions 10 twocircle 11 Giprotis 12 Ryukinllynskii 13 Ventilating house 490 491 Roughness 61 62 65 Screens a circular metal wire b silk threads 327 Scrubber with wooden packing 463 Shapes different placed in a pipe Three dimensional flow 1 convex hemisphere 2 con cave hemisphere 3 smooth cylinder axis parallel to direc tion of flow 4 smooth cylinder axis perpendicular to direction of flow 5 cone 6 square beam 393 Single rolled sections placed in a pipe planeparallel flow 390 Specific gravity 3 4 Sphere placed in a pipe three dimensional flow 391 Stay rods and braces single placed in a pipeplaneparallel flow 1 circular cylinder with fairing 2 streamlined rod 3 plate with rounded edges 4 wedgeshaped plate 5 square beam 389 Steelreinforced hose friction coefficient 75 Stopcock a rectangular pipe b cylindrical pipe 362 Straight intake shafts of rectangular section side orifice with fixed louvers and without them 103 Stream deformation in a straight conduit with the entry of a free jet into it ejection 134 Symmetric tee a 900 289 Tee of type Fb Fst Fe Fs Fe a 90 266 Thickened grid perforated plate or laths 324 Throat of a windtunnel 150 Transition cf Diffuser transi tional 174 Truss square placed in a pipe planeparallel flow 399 triangular placed in a pipe planeparallel flow 398 Type of cap 1with three diffusers 2 hemisphere with orifices For 06 S 0 56 3 hemisphere PC For with orifices 39 PC For 4 hemisphere with slots 14 5 cylinder with per For forated surface 47 429 Valve ball on spherical seat 370 butterfly 1 cylindrical pipe 2 rectangular pipe 361 check 368 conical on conical seat 370 on flat seat 370 control double seat 367 disk with bottom guide 369 disk without bottom guide 368 Valve suction with screen 368 Ventilating hoods various 1 circular TsAGI 2 square TsAGI 3 ChanardEtoile 4 Grigoro vich 5 standardized TsAGI without reducing piece for rail road cars 6 standardized TsAGI roof ventilator with reducing piece for railroad cars 7 Chesnokov roof ventilator 486488 Venturi scrubber tubesprayer 463 VTI centrifugal scrubber 464 Y of type Fc2Fs 301 517