CRANE, FLOW OF FLUIDS> Through Valves, Fittings and Pipe Technical Paper No. 410 By the Engineering Department ©2010 — Crane Co. All rights reserved. This publication is fully protected by copyright and nothing that appears in it may be reproduced, either wholly or in part, without permission. CRANE Co. specifically excludes warranties, express or implied as to the accuracy of the data and other information set forth in this publication and does not assume lability for any losses or damage resulting from the Use of the materials or other application of the data discussed in this publication or in the referenced website, including, but not limited to the calculators on www.flowotfluids.com, CRANE Co. 400 First Stamford Place ‘Stamford, Connecticut 06902 Tel: 4-203-363-7300 www.craneco.com Technical Paper No. 410 PRINTED IN USA. Reprinted 10/10 ISBN 1-40052-712.0 FH-CR-TB-EN-L13-00-1010RANI 13 16. 16. Bibliography Hardee, FT: (2008). Piping System Fundamentat The Complete Guide ta Gaining 2 Clear Petre of Your Piping Systm. Lacey, WA: Engineered Sofware Inc. “Moody, LF. (194, Novorber),Friton Factor for Pipe low. ‘ansactons ofthe American Society of Mechanical Englnast, 66, 674678 ‘Verma, 4 P. "Moody Chart An ActiveX Component o Calulate Frictonal Factor fr Fluid Faw in Ppeines” Stanford Geothermal Wlorkshop, Stanoré Unversity, Januery 26-30, 2008 National Fie Protection Associtin (2008). NFPA 15 Standard for Water Spray xed Systems fr Fre Precton. Quincy, MA: Naonal Fite Protection Associaton, (Colebrook, C.F. & White, CM. (1087). The Reduction of Carying Capaety of Pipes wth Age st. Cal Eng. Londen, (10). Lamont, PA, (1981). Commmen Pipe Flow Compared wih the Theory cof Roughness, Joual American Waar Works Associavon, 595), 278, Waloc , Sharp, W.& Shield, F (1986, Precicting ilernal Roughness in Water Mains. Miscelanacus Peper El-09-2, US Army Engineer Waterways Exparimert Stator: Vicksburg, MS ‘Bhave, .& Gupta, R. (2007), Analysis of Water Distribution ‘Networks! Alpha Selene inlrnatinal Lt, Hodge, 8 K.ana Koon, K. (1985). Comprossiio Fuks Dynamics Wah Personal Computer Appcatons. Englewood Os, NJ: Prentice Ha (Gtoon, DLW. nd Perry RH. (2008). Pers Chemical Engineer Hanabook & Editon. New York: MeGraw-il. “Steady Flom in Gas Pipoines" lst of Gas Technology Report No. 10, American Gas Associaton, New York, 1965. Coelho, PM. and Pinho, ©. 2007). Considerations About Equations for Stoady State Faw in Natural Gas Pipelines. Journal of ne Brazilan Society of Mechanical Sisnces & Engineering, 2910), 202-278. Lyone, Wc, and Plea, Gs (2005) Standard Hancbook of Potrleum and Natural Gas Engineering 2 Edtion. Burton, MA Oxford, UK: Gull Poessional Pubishing Mohipour, . Golehan, Hand Muay A. (2008) Pipaline Design & Construction: A Practical Approach 2 Eaton, New Vor: ASME Press Shapiro, A H, (1953) Tho Oynarnies and Thermodynamics of Compressible Fis Flow. Jahn Wiey & Sons. (Corp and Ruble RO. (1822). Loss of Head in Vales and Pipes of One-Hatf to Tele Inones Diameter. University of Wisconsin Exporimanta Staion Butt, 91). Pigot, FLLS, (1950). Pressure Losses in Tubing, Ppo, and Ftings. Tansactons ofthe American Society of Mechanical Engineers. 72, 670.686, Idolit, 1.6, 2006). Nanabook of Hyarauls Resistance 9 Eotion Mumbai, ini: aio Putishing House. Miler, D.S. (2008). Inara Flow Systems 2~ Eton, Becton, UK: Nile Inovatons. VL (1851). Fluid Machanics 1 Elton, New York Metra ‘Standarels of Hydraulic institute 8” Eolton. 1847 22, 23, 2 2 2 28 2 a 6, a 38 «. a“ # 42 4s, 46, Bol, KH, (1995) Pressure Losses fr Fluid Flow in 90 Degree Pipe ‘Bends. Jounal of Research ofthe National Bureau of Standard, 2 ‘renbach H. (1985). Loss of Enorgy in Miter Bands. ransactions ofthe Munich Hydraute Insitute, American Society of Mechanical Engineer, 3. ‘Skousen, PL. (2008) Valve Handbook 2 Editon. New York: MeGraw-ti LUpisk, 8, (2005). nsrumont Enginaere’ Hancboote recess (Conte! and Optimization 4° Eaton. Beca Raton, FL CRC Press. Flow Equations for Sizing Contra Valves. ANSUISAL75.0101 (IEC {60594-2-1 Mod)-2007; pages 1-2 ‘Measurement of Fluid Flow in Pipes Using Orie, Nazzle, anal Venu. ASME MFC-3-2006, CCantetugal Pump Tests. ANSVI 16-2000; Hydraulic Insite; 2000, Etec of Liquid Vscosty on Retodynamic (Cenitugal anc Veqical) Pump Periormance. ANSI! 8.6.7 2004: Hyaraulc institute; 2004, Mentor Pump Selection Toot (2008). Ret ieved July 13, 2000 rom ‘Crane Pumps and Systems Website: htptnweranepumpscom! pumpsolecorahp Flow of Fis. 2008). Revived July 13, 2008, tom Flow of Fis Vie sta: hipsiwaw wal. com’ Val, M2008). Pump Charsterlses and Apoleations 2* Editon. Boca Raton, FL Taylor & Francis Group Intematonai Association or he Properties f Water and Steam. (2009). Revised Release onthe IAPWS Formulation 18985 for he Thormodiynamic Properties of Ordinary Water Substance for General land Scisnite Use. Bouler, CO: Intemational Assocation forthe Proper of Water and Steam, "ASHAAE Handbook: Fundamentals (2005). Amorican Society of Heating, Rotigorating and AisCondtiening Engineer. Alanis, GA. Yaws CL. (2003). Yarws' Henaboak of Tamedyremc and Physical ‘Propores of Chemical Compounds. Houston, TX: Gul Publishing, ‘Not used ide, BI. and Haynes, W. Meds. Handbook of Chemistry and Pays 90° Eaton. Boca Raton, FL: CRC Pros. ‘Avalone, E.A., Baumeister, I, and Sadegh, A.M eds (2007) ‘Marks’ Standard Handbook for Mechanical Engines. 1” Edion. Now York: MeGraw-i Viswenath, D., Ghosh, T, Prasad, D., Dut, N. snd Rai, K, (2007). Viscosty of Liguc: Theory, Estat, Experimentation, and Data, Eouare, S, (1998). Mechanical Enginoers erence Hook 12° alin. Boston, MA: Buterworth Heinemann ‘Guo, 8. and AG. (2008). Naural Gas Engineering Hanabook. Houston, TX: Gulf Publishing CGraium: Property Estimation (2008). Computer sotware. Bede, Nr: Aotocular Knowledge Systems. PIPE-FLO Pression (2003).Computer sotware. Lacey, WA: Engineered Sotware, nc. [Nelcn, WL (1988) Petoleum Retinery Enginocrng. Now York, NY: MeGeau-Hil Book Co ASME Steam Tables (1967) American Society of Mechanics! Engineers. Now York, NY. 298, Fig Meters (1971). American Seciey of Mechanica Engineers, New York, NY. Part 16" Editon “Testrical Paper No. 410CRANE, Foreword In the 21st cantury, the global industrial base continues to expand. Fluid handling is stil at the heart of new, more complex processes and applications. In the 19th century, water was the only important fluld which was conveyed from ‘one point to another in pipe. Today, almost every conceivable fluid is handled in pipe during its production, processing, transportation, or utilzation. in the 1950's new fluids such as liquid metals i.e., sodium, potassium, and bismuth, as well as liquid oxygen, nitrogen, etc., were added to the list of more common fluids such as oil, water, gases, acids, and liquors that were being transported in pipe atthe time. In the ‘current decade of new technologies, heattransfer fluids for solar plants, mineral slurries, and new chemical compounds expand the envelope of materials of construction, design, Process pressures and temperature extremes as never before. Transporting fluids is not the only phase of hydraulics which warrants attention either. Hydraulic and pneumatic mechanisms are used extensively for the precise controls of modern aircraft, sea-going vessels, automotive equipment, machine tools, eaiti-moving and road-building machines, scientific laboratory equipment, and massive refineries where precise control of fluid flow is required for plant automation. So extensive are the applications of hydraulic and fluid ‘mechanics that most engineering disciplines have found it necessary to teach at least the elementary laws of fluid low, ‘To satisfy a demand for a simple and practical treatment of the subject of flow in pipe, Crane Co. in 1938, first published 2 booklet entitied Flow of Fluids and Heat Transmission. A revised edition on the subject of Flow of Fluids Through Valves, Fittings, and Pipe was published in 1942 as Technical Paper 409. In 1957, a completely new edition with an all- ‘new format was introduced as Technical Paper No. 410. In TP. 410, Crane endeavored to present the latest available Information on flow of fluids, in summarized form with all auxiliary data necessary to the solution of all but the most Unusual fluid flow problems. ‘The 1976 edition presentedaconceptualchangeregardingthe values of Equivalent Length L/D and Resistance Coefficient K for valves and fitings relative to the friction factor in pipes. ‘This change had a relatively minor effect on most problems dealing with flow conditions that result in Reynolds numbers falling in the turbulent zone. However, for flow in the laminar zone, the change avoided a significant overstatement of pressure drop. Consistent with this conceptual revision, the resistance to flow through valves and filings became ‘expressed in terms of resistance coefficient K instead of ‘equivalent length L/D, and the coverage of valve and fitting types was expanded. Further important revisions included ‘updating of steam viscosity data, orifice coefficients, and nozzle coefficients. As in previous printings, nomographs ‘were included for the use of those engineers who preferred graphical methods of solving some of the more simple problems. Inthe 2009 edition of Technical Paper 410, Crane Co. hasnow included new flow contro! and measurement components to the pages of this paper. Pumps and Control Valves, critical elements of fiuid handling, are included forthe first time, as well as Flow Meters, and several adcitianal types of valves and fittings. We have added new illustrations and updated the content throughout. Many of the nomographs have been replaced with online calculators. Visit www flowoffluids.com for the latest data Originally, data on flow through valves and fittings were obtained by carefully conducted experiments in the Crane Engineering Laboratories. For this 2009 update, additionat tests were performed within Crane to increase the number of valves with defined resistance coefficients. In addition, industry research was also gathered and refined to provide the reader with the latest methods for calculating hydraulic resistance. Resistance values for fittings were correlated with existing industry research and, when appropriate, more updated methods are provided in this paper, particularly seen with the new treatment of Tees and the addition of Wyes. Since the last major update of TP-410, personal computers and Web applications have become the computational tools of choice. To meet the needs of today’s engineers we have presented a variely of proven computational methods to simplify fluid flow calculations for those interested in Geveloping custom spreadsheets or computer programs. In addition, Flow of Fluids has its own web site (www. Flowoftluids.com) with a variaty of Web based tools to simplify your most common fluid flow calculations, ‘The 2009 version of the Technical Paper 410 employs the most current references and specifications dealing with flow through vaives, fittings, pipes, pumps, control valves and flow meters. The fluid property data found in Appendix ‘A has been updated to reflect the current research on estimating fluid property data with references for the data cited throughout the paper. From 1957 until the present, there have been numerous printings of Technical Paper No. 410. Each successive printing is updated, as necessary, to reflect the latest flow information available. This continual updating, we believe, serves the best interests of the users ofthis publication, The Flow of Fluids software and updated web site provide users with electronic tools and a source for the latest information, We welcome your input for Improvement CRANE CO. (CRANE Flow of Ful -Tectoical Paper Wo. 410CRANE] Table of Contents HAPTER “Theory of Flow in Pipe lnrocustion Physical Ropers of Fluids Viscosity Weight density Specie wlume ‘Specie gravy Vapor pressure Nature of Flow in Pipe Laminar and Turbulent Flow ‘Mean velaciy of fw Reynolds number Noncirearconcuit General Energy Equation - Bemoul's Theorem Measurement of Pressure Head Lose end Pressure Drop Through Pipe eton factor (ebro equation Expt approximations of Colebrook Hazon Willams formula fr fw of water Ect of age and uso on pipe trcton Prnopies of Compressbe Faw in Pipe Definition ofa perect ges ‘Spied of sound and mach puriber ‘Approaches to comprossibl ow probloms ‘Application ofthe Darcy equation fo compressie tds Complete isothermal equation Sinplied isothermal - gas pene equation Other commonty used equations for eompesibe ow in ong pipelines ‘Comparsen of equatons fr compressible town pipoknes ‘Modifications tothe isothermal flow equation Limiting ow of gases and vapors ‘Simple compressible fons ‘Sofware solutions to compressibio flow probleme ‘Stoam - Generai Dscussion ‘Saurated eteam Supemeated sam chapter 2 Flow of Fluids Through Valves and Fittings {rwrosueton “Types a Vahes and Fitings Used in Pipe Systems Pressure Drop Atribted to Vanes and Ftings (Grane Pow Tests [Description of apparatus usod Wiatar Row tose ‘Steam fow tect Rolaionsip of Pressure Drop te Volt of Flow sistance Costilent K, Equivalent Lengih LD, ‘ad Flow CostisentC, Hydraulic resistance (Causes of head oss vales ar tings Equivalent length Resistance concent Fesistance cosficlens for sipsines, valves and tings in ‘series ard parle! Fesisiance coeficlent for geometricaly dissimilar vaves ana iting ‘Geometrical simi ftings “Agjsting K fr pip schedule Fw eooticient C, {Use of flow cosfsiont for piping and components Flow coelicets fer ppeines, valves, ngs m eeriee and paral Laminar Flow Conditions ‘dusting th resistance cootclet fr Reynalés number Contraction and Enlargement Vahee with Reduced Seats m 4" 4 12 12 13 13 42 13 + +4 6 +5 6 6 7 uv Ww wv 18 +8 +8 +8 +8 19 8 27 26 27 27 27 27 27 28 29 28 240 20 210 20 an 22 ‘CRANE Flow o Flas Fesitance of Bends ‘Secondary How Fosttance of bende to fow Fesstance of mor bonds Hysrauic Rasietance of Teas an Wyee Converging fow Diverging ow Graphical representation of Ky, 2 Kay Discharge of Fuld through Valves Ftings, a Pipe Lge tow Compressive tow Types of aves cHapTen 3 ‘Regulating Flow with Contr Valves Inweduction ‘Components Inherent eharaceritc eve Installed characterise une Pressure velooty and energy profes CCaviaton, choked flow, anc flashing Conta Valve Sizing and Selection ‘Sizing or ncamprossi ow Sizing for compressible tow Conversion of C, 1K, CHAPTER 4 Measuring Flow with Diferential Pressure Meters Intodction Dierental Pressure low Meters Oiitce plate Limits of use Flow nozzle Limits of use Vertu meter mils of use Liquid Flow Through Orcas, Nozzles and Vertu Mtr dferental prassure(eP) Pressure los (NAPD) Discharge coeticentsC, Cries tate Flow nozzles \entr meters CCompressito Flow Through Ortices, Nozzies, ana Ventut Flow of gases and vapors Expansbiay factors Y Orie plates Flow nozsies and ventur meters Maximum fow of compressible fis in a nozzle Fw trough shor tubes CHAPTERS Pumping Flulé Through Piping Systems Ietoduetion Centitagal Pume Operation Cental Pump Sizing and Selection Pump curve NPSHa NPSHa optimization Vieeosty eoractions Pump ating rules Pump power ealetations Pump section Posie Displacement Pumps ‘Types of pumps “octal Paper No. #10 pee 22 Bae 213 ea 25 25 26 20 an a7 bao a a Bt 32 22 32 32 33 a4 34 3s 36 5a st 5A 82 53 53 63 53 53 54 a4 54 55, 56Table of Conients (CHAPTER 6 61 APPENDIX at Formulas For Flow 1 Physical Propertos of Fluids and Flow Charscteristies Invodseiion 1 of Valves, Fitings, and Pipe a Summary of Formulas 51 Inveduoton x ‘Basie conversions 62 Viscosity of Steam and Water Re Bernoults hear 62 Viecosty of Water and Liquid Petoleum Products 43 Mean velocty of ow in pipe 62 Viscosity of Various Ligue na Head loss and pressure oop foc ncompressbl fw in Viscosity of Gases and Vapors AS ‘right pipe 6:2 Viscosity of Ratigerant Vapors AG Reynolds numberof flowin pipe 6-2 Physical Properties of Water a? Lamina ftion factor 62 Spaclie Gravy - Temperature Retatonahp for Potcleum ie AB Turbulent reton factor 62 Weight Densty and Spectic Gravy of Various Ligugs ae Colebrook imate equation 62 Physical Proper of Gases a9 Serge expi equation 62 Volumes Composiion and Speclic Grauly ol Gaseous Fuele AD ‘Swarnec-Jan 2 Steam -Valies ol Ientopic Exponent. K a0 ‘Head loss ava to tron straight pipes (Darcy) 63 Reasonable Veloctes For the Faw of Water Through Pipe m0 Hazon. Wiliame forma for fow of water 3 Reasonable Veontes ft Flow of Steam Through Pipe ao Limitations ofthe Datey formula 63 Weight Density and Speci Volume of Gases and Vapors an Isothermal compressive fw equations 6-3 Sstuated Steam and Saturats Waler ane ‘Simpiied Isothermal equation fr ong pps 63 Suporneated Steam M7 \Wioymouth equation (ly tule sow) 83 Suporneated Siew and Compreseed Weer x20 Panhande A equation (parvallytuouleat fs) 3 Fw Gootieen!C For Square Ecge Oriioes and Novae Aa Panhard B equation (ly turoulet fs) 64 NetExpansion Factor, Y and Criial Presoure Fata. ae ‘AGA equation (parla turbent lon) 54 Net Expansion FacorY for Compressiie Flow ae ‘AGA equation (ly urlent flaw) 5:4 Relatve Roughness of Ppo Matorals ard Fron Factor for ‘Speed of sound and Mach nuriber 54 Compe Turbuence 26 Head loss and pressure cop trough valves and ings ‘844 Fichon Facios for Any Type of Commercial Pipa 25 Pressure drop and How o igus of ow vscaety using ow Ficion Factors for Clean Commarea Ste! Pipe 28 oetiewnt 64 Ropresontative Resistance Coetconts K for Valves and Ftings Fosletance and tow coctcions K and ©, i Factor Table Agr In ries and paratol 65 ‘Changes in sistance coetcent Krequred 10 — ‘compansat or eferetpipo ID. 65 APPENDIX 4 Fpresontativa resistance coeficients K fr various Engineering Data Ba valves and figs 65 inveducton cs Discharge of ud trough valves tings and pipe: Equivalent Volume and Weight Flow Rates of Compress Fuis 2 Darcy formate 65 Equlvalonis of Absolute Dynamic Visceaty 23 Flow trough orice, nares are venturi 55 Equivaloris of Kinomate Viscosity Ba CConto valve sizing equations 68 Kinematic and SaybotUniversat Ba Pump perormanes equations 67 Kinematic nd Saybot Fol ba Pump afiny rues 8:7 Kinemati, Saybot Universal, Saybat Foland Absolute Viscosty B.S Pump power esiouitions 5:7 Equvalonis of Degroes API, Degrees Baume, Spaciie Gravy, ‘Specie gray of iquds 6:7 Weight Density and Pounds per Gaon 86 Specie gray of gases 67 Power Required for Pumping 87 ideal gas equation 67 US Comersion Tables Bo ysrauie eas 67 Length a8 Ara 58 — Volume 8 ‘CHAPTER? ” Voter Be Examples of Flow Problems nm Mase Ba trarecuction Mass tow rate 29 Determination of Vave Resistance nL, UO,K, and Coeiient ©, 72 alumetc lw rato be (Check Vales, Reduced Por aves 73 Fovce Bo Laminar Flew in Values, Fitings and Pipe 74 Pressure and iqud head 840 Prossure Crop and Veocty In Piping Sysiems 76 Energy, workhest BH0 Pipeline Flow Probiems HO Power B10 Discharge of Fluide ftom Piping Systems 742 ensity B10 Flow Through Oritee Meters 745 Temperate equivalents Bao Aplieaion of Hysrause Radius To Flow Probleme 746 Flow of Water Trough Schedule 40 Steel Pipa ea Conta Vas Calevlaione 748 Flowt Ar Tough Schedsle 40 Stel Pipe ae Flow Mtr Galclstone 72) Pipa Data Carbon and Aloy Sst Staines Stee! B13 Pump Bampies 72 ‘Tess and Wives 724 (CRANE Fiw of Filds Technical Paper Na. 410 vCRANE] Nomenclature Unless otherwise stated, all symbols used inthis book are defined as fllows: A = cross sectional area (tt) = cross sactional area (n*) bhp = brake (chaft) horsepower (he) C= How coaticient for ortices and nozzles G, = discharge coefficient or orices and nozzles CC), = flow coeticient fr valves or piping components "= speed of sound in a tad 5) = sheet heat at constant pressure (Btu “R) ef = specific heat at constant volume (Btu/o °R) B= imornal ameter (t) D,. = equivalont nydraulic dametor(t) "= intemal diameter (in) oq = Nominal pipe or valve size (in) "= efficiency factor (uniless) hp = electica! horsepower (rp) F, = liquid citcal pressure ratio factor (nitiess) FL = spetilc heat ratio factor (unless) F = liquid pressure recovery factor (unless) FF, = combined piping geometry and liquid pressure recovery factor (urtless) = piping goometry factor (unless) £" = Darey friction factor (unless) f= ‘ction factor in zone of complete turbulence (anitiess) J = gravitational accoloration = 32.174 is? H = total nead or id energy, in fet of fua (t) = slalle pressure head at a point, in fet of fui () 1 = specitic enthalpy of saturated qui (Btu) hh, = specific latent nest of evaporation (Stull) hy = speoitic enthalpy of saturated vapor (Stub) hi = loss of static pressure head due to id flow (1) hy = static pressure head, in inches of water (in H,0) KC = resistance costficient (unless) K, = Bemoul coeticint (unites) = flow coettcient or fow factor (unites) "= ratio of spect heat al constant preesure (c, to specific eat at constant volume (c,) L_ = length of pie (1) LD = equivalent iengtn ofa resistance to flow, in pipe diameters LL, = length of pipe, in miles (m) Mi = Mach number (aniiess) M,_= relative molecular mass NPSHa = Net Positive Suction Head available (ft) NAPD = Non-Recoverable Pressure Orop (psi¢) Thumber of moles of a gas ‘gauge prossur, in bvin® (psig) absolute pressure, i i (psie) absolute pressure at standard condition uid critical pressure (psia) © absolute tank surface pressure (osia) absolute fluc vapor pressure (psia) lbsolute prassure at the vana contracta(psla) ‘gauge pressure, inf (psta) absolute pressure, in ot (peta) fate of flow (gpm) rate af low at lowing consstions, in 1 (cts) rate of low at standard conditions (14.7 psia and 60°F) (Ws, sets) rate o low a lowing conditions, in millons of cubic feet pet day (MMcta) rate o low at standard condtions (14.7 psia and 60°F), in millons af cubic feet per day (MMseld) tate of flow at lowing conditions, in hr (of) ‘ate of ow at standara conditions (14.7 psia and 60°F}, intr (eofh) rate of ow at owing conditions, in min (of) rate of ow at stendara conditions (147 psia and 60°F), in min (stn) indvidual gas constant = Ft, (ft -(b/b, “R) Universal gas constant = 1545.95 ft Imo! °F FReyrolds number (unites) hydraulic radius () ertieal pressure rato for compress fow pectic gravity of kquids at spectied temperature relative to water at standard temperature (60°F) and pressure (147 psiaiunitiess) spectic graily ofa gas relative ta ai = the rato ofthe molecular weight of the gas to that of air anitess) vi ‘CRANE Flow of Fas Technic! Paper No. 410CRANE, Nomenclature Unless otherwise stated, all symbols used in this book are defined as follows: T= absohte tomperature in degrees Rankine (A) ‘T,_= absolute temperature a standard condition = 520°R 1° = temperature, in degrees Fahrenhat CF) 1, = Saluraton lomperalure at a given pressure (F) V_= mean vlocty of fon, nin (pm) Y= spectre volume of ie io) VY, = volume ct) v' mean veloc of ow. ns tos) ¥, = sone (rertea) velocty of Row ofa pas (vs) We = fateot tow (tm w= tate of ow vs) ve, = eight) x pressure drop ratio untoss) X= ical pressure cop rato factor wthoutftings (unless) Xp = crlical pressure oop rato tater wth tings (unites) Y" = natexpansion taco for compressible flaw trough oices, nozzles, vet, contol valves oppo (unas) Z = potent! nead or elevation above reference eve (i 2, = Compressbity factor (unites) 2, = elevation at pump suction () 2 = elevation at lankesurtace() Grock Lottors Alpha a = angle (degrees) Bota = ratio ofsmalli large ameter i ofices and nozzles, and contractions ar enlargements pipes eit = iferenial between two points Epstion = absolute roughness or effective height of pipe wal regularities) Ela ‘motor efficiency (unitloss) ump otfisianay (unitiees) \atiable speed crve (vsd) efciency (unless) absolute (dynamic) viscosiy, in centipoise (cP) absolute viscosity in pound mass pe: foat second (bev -s) or poundal seconds per equare foot (el - st) absolute viscosity in lugs per foot second (sug/t-<) orn pound force seconde per sau foo lb s/t} kinomatc viscosity, in centistokes (eS!) kinematic viscosity (ts) Potential energy term to accaunt for elevation changes in isthermal compressible flow equations ‘weight density o uid (ot) mass density of tud (fer?) ‘weight densky of air at standard conelions (14,7 psia and 60°F) angle of convergence or civergence In enlargements or contractions in pipes Subscripts for Diameter (defines smatier ciameter (@) defines larger dameter ‘Subscripts for Fuld Property (1) defines iniet (upstream) condition (2) defines outlet (downstream) condition ‘Subscript for Average Value (avg) defines average condition Qs stl « ont calla aviai at menor com (CRANE Fiow of Pics - Technical Paper No. 470 vii[crane] CRANE | This page intentionally left blank. vill (CRANE Fw of Flugs- Technical Paper No. 410Chapter 1 Theory of Flow in Pipe The most commonly employed method of transporting fluid from one point to another is to force the fluid to flow through @ Piping system. Pipe of circular cross section is most frequently Used because that shape offers not only greater structural strength, but also greater cross sectional area per unit of wall surface than any other shape. Unless otherwise stated, the Word “pipe” in this book will always refer to 2 closed conduit of circular cross section and constant internal diameter. Only a few special problems in fluid mechanics (laminar flow in pipe, for example) can be entirely solved by rational mathematical means; all other problems require methods of solution which rest, at least in part, on experimentally determined coefficients. Many empirical formulas have ‘been proposed for the problem of flow in pipe, but these are often extremely limited and can be applied only when the conditions of the problem closely approach the conditions of the experiments from which the formulas were derived, Because of the great variety of fluids being handled in modem, industrial processes, a single equation which can be used {or the flow of any fluid in pipe otfers obvious advantages. ‘Such an equation is the Darcy* formula. The Darcy formula ‘can be derived rationally by means of dimensional analysis; however, one variable in the formula (the friction factor) must be determined experimentally. This formula has @ wide application in the field of fluid mechanics and is used extensively throughout this paper. “The Darcy formula is also known as the Weisbach formula or the Darey-Weisbach formula; also, as the Fanning formula, ‘sometimes modified so that the friction factor is one-fourth the Darcy friction factor. (CRANE Flew of Fluide Tecnica! Paper No. 410 1-1CRANE, Physical Properties of Fluids ‘The solution of any flow problem requires a knowledge of the physical properties of the fluid being handled. Accurate values for the properties affecting the flow of fluids (namely, viscosity and weight density) have been established by ‘many authorities forall commonly used fluids and many of these data are presented in the various tables and charts in Appendix A Viscosity: Viscosity expresses the readiness with which a fluid flows when it is acted upon by an external force. The Coefficient of absolute viscosity of, simply, the absolute viscosity of a fluid, is a measure of Ils resistance to internal deformation or shear. Molasses is a highly viscous fluid; water is comparatively much less viscous; and the viscosity of gases is quite small compared to that of water. Although most fluids are predictable in their viscosity, in some, the viscosity depends upon the previous working of the fluid. Printer’s ink, wood pulp slurries, and catsup are ‘examples of fluids possessing such thixotropic properties of viscosity Considerable confusion exists concerning the units used to express viscosity: therefore, proper units must be employed whenever substituting values of viscosity into formulas. In the metric system, the unit of absolute viscosity is the polse which is equal to 100 centipoise. The poise has the dimensions of dyne seconds per square centimeter or of grams per centimeter second. It is believed that less confusion concerning units will prevail if the centipoise is used exclusively as the unit of viscosity. For this reason, and ‘since most handbooks and tables follow the same procedure, all viscosity data in this paper are expressed in centipoise, ‘The English units commonly employed are “slugs per foot second” oF "pound fore seconds per square foot; however, “pound mass per foot second" or “poundal seconds por square foot may also be encounteree. The viscosity of water ata tomperature of 68°F s (0.01 poise = 1 eentipcise* = } 0.01 gram por cm second 0.01 ayne Second per sq cm 1p, = (0.000 672 pound mass per foot second "= (0.000 672 poundal second per square foot 1, =)0000 0209 sug per fot second “©. .000 0209 pound force second per square ft “Actually the viscosity of water at 68°F is 1.005 centipoise. 1-2 ‘CRANE Flow of Fids Technical Paper No. 10 Kinematic viscosity is the ratio of the absolute viscosity to the mass density. In the metric system, the unit of kinematic viscosity is the stoke, The stoke has dimensions of square centimeters per second and is equivalent to 100 centistokes. Equation 1-1 b_(centipoise) “ © (eontistokes) = grams per cubism) ""S., By definition, the specific gravity, Sin the foregoing formulais based upon water at a temperature of 4°C (39.2°F), whereas specific gravity used throughout this paper is based upon water at 60°F. In the English system, kinematic viscosity has dimensions of square feet per second. Factors for conversion between metric and English system Units of absolute and kinematic viscosity are given on page B-3 of Appendix B. The measurement of the absolute viscosity of fluids (especially gases and vapors) requires elaborate equipment and considerable experimental skil. On the other hand, a rather simple instrument can be used for measuring the kinematic viscosity of oils and other viscous liquids. The instrument adopted as a standard is the Saybolt Universal Viscometer. in measuring kinematic viscosity with this instrument, the time required for a small volume of liquid to flow through an orifice is determined; consequently, the “Sayboit viscosity” of the liquid is given in seconds. For very viscous liquids, the Saybolt Furol instrument is used. Other viscometers, somewhat similar to the Saybolt but not Used to any extent, is the Engler, the Redwood Admiralty, and the Redwood. The relationship between Saybolt viscosity ‘and kinematic viscosity is shown on page B-4; equivalents. ‘of kinematic, Saybolt Universal, Saybolt Furol, and absolute viscosity can be obtained from the chart on page B-5, The viscosities of some of the most common fluids are given on pages A to A. It willbe noted that, witha rise in temperature, the viscosity of liquids decreases, whereas the viscosity of gases increases. The effect of pressure on the viscosity of liquids and ideal gases is so small that itis of io practical interest in most flow problems. Conversely, the viscosity of saturated, or only slightly superheated, vapors is appreciably altered by pressure changes, as indicated ‘on page A2 showing the viscosity of steam. Unfortunately, the data on vapors are incomplete and, in some cases, contradictory. Therefore, itis expedient when dealing with vapors other than steam to neglect the effect ot prossure because of the lack of adequate data (Chapter 1 Theory of Flow in Pipe