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Flow Equations forSizing Control ValvesReaffirmed 18 October 1995ISA75.011985(R1995)Formerly ISAS75.011985(R1995)STANDARDISA The Instrumentation,Systems,andAutomation Society TMCopyright?1985 by the Instrument Society of America.All rights reserved.Printed in the UnitedStates of America.No part of this publication may be reproduced,stored in a retrieval system,ortransmitted in any form or by any means(electronic,mechanical,photocopying,recording,orotherwise),without the prior written permission of the publisher.ISA67 Alexander DriveP.O.Box 12277Research Triangle Park,North Carolina 27709ISA-75.01-1985(R1995),Flow Equations for Sizing Control ValvesISBN 0-87664-899-5ISA-S75.01-1985(R 1995)3 PrefaceThis preface,as well as all footnotes and annexes,is included for informational purposes and is not part of ISA-75.01-1985(R1995).This standard has been prepared as part of the service of the ISA,the international society for measurement and control,toward a goal of uniformity in the field of instrumentation.To be of real value,this document should not be static,but should be subject to periodic review.Toward this end,the Society welcomes all comments and criticisms,and asks that they be addressed to the Secretary,Standards and Practices Board,ISA,67 Alexander Drive,P.O.Box 12277,Research Triangle Park,NC 27709,Telephone(919)990-9227;Fax(919)549-8288;E-mail:standardsisa.org.The ISA Standards and Practices Department is aware of the growing need for attention to the metric system of units in general,and the International System of Units(SI)in particular,in the preparation of instrumentation standards,recommended practices,and technical reports.The Department is further aware of the benefits to USA users of ISA standards of incorporating suitable references to the SI(and the metric system)in their business and professional dealings with other countries.Toward this end,this Department will endeavor to introduce SI-acceptable metric units in all new and revised standards to the greatest extent possible.The Metric Practice Guide,which has been published by the Institute of Electrical and Electronics Engineers as ANSI/IEEE Std 268-1992,and future revisions,will be the reference guide for definitions,symbols,abbreviations,and conversion factors.It is the policy of ISA to encourage and welcome the participation of all concerned individuals and interests in the development of ISA standards,recommended practices,and technical reports.Participation in the ISA standards-making process by an individual in no way constitutes endorsement by the employer of that individual,of ISA,or of any of the standards,recommended practices,and technical reports that ISA develops.The following people served as original members of ISA Subcommittee SP75.05:NAMECOMPANYL.Driskell,ChairmanConsultantJ.ArantE.I.du Pont de Nemours and Company,Inc.H.BaumannH.D.Baumann Associates,Ltd.*C.Beard G.BordenBechtel Power CorporationL.GriffithConsultantF.HarthunFisher Controls International,Inc.R.JonesUpjohn CompanyA.McCauleyChagrin Valley Controls,Inc.J.OzolOmaha Public Power CompanyR.QuanceWalsh Inc.W.RahmeyerColorado State University*Deceased4ISA-S75.01-1985(R 1995)K.SchoonoverCon-TekJ.SimonsenValtek,Inc.H.SonderreggerITT Grinnell CorporationF.VolpeMasoneilan Division,McGraw-Edison CompanyW.WeidmanGilbert Commonwealth,Inc.L.ZinckUnion Carbide CorporationThe following people served as members of ISA Subcommittee SP75.01,who reaffirmed ISA-S75.01 in 1995:NAMECOMPANYH.BogerMasoneilan/DresserW.WeidmanConsultantH.BaumannH.D.Baumann Inc.G.Borden,Jr.ConsultantB.BossermanBoyle Engineering CorporationS.BoyleNeles-Jamesbury,Inc.R.BrodinFisher Controls International,Inc.L.DriskellConsultantA.DvorakFisher Controls International,Inc.J.GeorgeRichards IndustriesA.GlennValtekL.GriffithRetiredH.HoffmannSamson AGP.MariamFlowSoft,Inc.A.McCauley,Jr.Chagrin Valley Controls,Inc.J.OzolCommonwealth EdisonW.RahmeyerUtah State UniversityJ.ReidCashco,Inc.M.RivelandFisher Controls International,Inc.K.SchoonoverCon-TekD.Van StaverenBechtelF.VolpeMasoneilanThe following people served as original members of ISA Subcommittee SP75:NAMECOMPANYL.Driskell,ChairmanConsultantR.Terhune,Vice-ChairmanConsultantK.Schoonover,SecretaryCon-TekJ.ArantE.I.du Pont de Nemours and Company,Inc.H.BackingerJohn F.Kraus&CompanyG.BarbMuesco,Inc.H.BaumannH.D.Baumann Associates,Ltd.ISA-S75.01-1985(R 1995)5*C.Beard N.BelaefConsultantG.BordenBechtel Power Corporation*R.BrodinFisher Controls International,Inc.E.BrownDravo Engineers,Inc.E.CooneyAir Products&Chemicals,Inc.W.DewartRockwell InternationalJ.EmeryHoneywell,Inc.H.FullerWorcester Controls CorporationL.GriffithConsultantA.HanssenFluid Controls Institute,Inc.F.HarthunFisher Controls International,Inc.H.IllingKieley&Mueller,Inc.R.JonesUpjohn CompanyM.KayeM.W.Kellogg CompanyR.LouviereCreole EngineeringO.Lovett,Jr.ISIS CorporationA.McCauleyChagrin Valley Controls,Inc.T.MolloyPacific Gas&ElectricJ.MullerLeslie CompanyH.NickersonResistoflex CompanyJ.OzolOmaha Public Power CompanyR.QuanceWalsh Inc.W.RahmeyerColorado State UniversityJ.ReedMasoneilan Division,McGraw-Edison CompanyG.RichardsJordan Valve Div.,Richards Industries,Inc.J.RosatoRawson CompanyH.SchwartzFlexible Valve Corporation*W.ScullLeslie CompanyF.SegerWillis Division,Smith International,Inc.J.SimonsenValtek,Inc.H.SonderreggerITT Grinnell CorporationN.SprecherDeZurikR.StanleyRetired*G.StilesFisher Controls International,Inc.R.TubbsCopes-VulcanW.WeidmanGilbert Commonwealth,Inc.R.WiddowsCashco,Inc.L.ZinckUnion Carbide Corporation*Deceased*One vote per company6ISA-S75.01-1985(R 1995)The following people served as members of ISA Committee SP75,who reaffirmed ISA-S75.01 in 1995:NAMECOMPANY*D.Buchanan,ChairmanUnion Carbide CorporationW.Weidman,Managing DirectorConsultantK.Schoonover,SecretaryCon-Tek*T.AbromaitisRed Valve,Inc.J.AddingtonFluid Controls InstituteH.BackingerJ.F.Kraus&CompanyG.BaenteliBechtelG.BarbConsultantH.BaumannH.D.Baumann Inc.K.BlackCashco,Inc.H.BogerMasoneilan/DresserG.Borden,Jr.ConsultantS.BoyleNeles-Jamesbury,Inc.R.BrodinFisher Controls International,Inc.F.CainValtek,Inc.C.CorsonFluor Daniel,Inc.*C.CrawfordUnion Carbide CorporationL.DriskellConsultant*J.DuhamelRed Valve Company,Inc.H.FullerConsultant*J.GeorgeRichards Industries,Inc.L.GriffithConsultantB.HartM.W.Kellogg CompanyF.HarthunConsultantB.HattonHoneywell,Inc.R.JeanesTU ElectricC.KoloboffChevron Research&Technology CompanyG.KovecsesYarway CorporationC.LangfordConsultantJ.LeistDow Chemical USAA.LibkeDeZurik Valve CompanyR.LouviereCreole Engineering Sales CompanyO.Lovett,Jr.Consultant/RetiredA.McCauley,Jr.Chagrin Valley Controls,Inc.H.MillerControl Components,Inc.T.MolloyCMESL.OrmanoskiFrick CompanyJ.OzolCommonwealth EdisonW.RahmeyerUtah State University*One vote per companyISA-S75.01-1985(R 1995)7J.ReedNorriseal*G.RichardsRichards Industries,Inc.A.SheaCopes-Vulcan,Inc.E.SkovgaardLeslie ControlsH.SondereggerGrinnell CorporationR.TerhuneCranmoorR.TubbsConsultantThis published standard was approved for publication by the ISA Standards and Practices Board on October 18,1995.NAMECOMPANYM.Widmeyer,Vice PresidentThe Washington Public Power Supply SystemH.BaumannH.D.Baumann Inc.D.BishopChevron USA Production CompanyP.BrettHoneywell,Inc.W.Calder IIICalder EnterprisesH.DammeyerThe Ohio State UniversityR.DieckPratt&WhitneyW.HollandSouthern Co.Services Inc.A.IversonLyondell Petrochemical CompanyK.LindnerEndress+Hauser GmbH+CompanyT.McAvinewMetro Wastewater Reclamation DistrictA.McCauley,Jr.Chagrin Valley Controls,Inc.G.McFarlandHoneywell Ind.Automation&ControlE.MontgomeryFluor Daniel,Inc.D.RapleyRapley Engineering ServicesR.ReimerRockwell Automation A-BR.WebbPacific Gas&Electric CompanyW.WeidmanConsultantJ.WeissElectric Power Research InstituteJ.WhetstoneNational Institute of Standards&TechnologyH.R.WiegleCanus CorpC.WilliamsEastman Kodak CompanyG.WoodGraeme Wood ConsultingM.ZielinskiFisherRosemount*One vote per companyISA-S75.01-1985(R 1995)9 Contents1 Scope.112 Introduction.112.1 Flow variables and fluid properties.113 Nomenclature.124 Incompressible fluid flow of nonvaporizing liquid.134.1 Equations for turbulent flow.144.2 Numerical constants N.144.3 Piping geometry factor Fp.154.4 Equations for nonturbulent flow.165 Incompressible fluid choked flow of vaporizing liquid.175.1 Liquid choked flow equations.185.2 Liquid pressure recovery factor FL.195.3 Combined liquid pressure recovery factor FLP.206 Compressible fluid flow of gas and vapor.206.1 Equations for turbulent flow.216.2 Numerical constants N.216.3 Expansion factor Y.226.4 Choked flow.236.5 Pressure drop ratio factor xT.236.6 Pressure drop ratio factor with reducers or other fittings xTP.236.7 Ratio of specific heats factor Fk.236.8 Compressibility factor Z.24AnnexesA Use of flow rate equations for sizing valves.25B Derivation of factors Fp and FLP.27C Control valve-piping system head changes.30D Representative values of valve capacity factors.33E Reynolds number factor FR.35F Equations for nonturbulent liquid flow.39G Liquid critical pressure ratio factor FF.43H Derivation of factor xTP.45I Control valve flow equations SI notation(International System of Units).47J References.4910ISA-S75.01-1985(R 1995)Figures1 Reynolds number factor.172 Liquid flow rate versus pressure drop for a typical valve (constant upstream pressure and vapor pressure).18C-1 Head changes in a control valve-piping system.32E-1 Reynolds number factor for valve sizing.36Tables1 Numerical constants for liquid flow equations.142 Numerical constants for gas and vapor flow equations.22C-1 Definitions of head terms.31D-1 Representative values of valve capacity factors.33E-1 Reynolds number factor FR for transitional flow.38ISA-S75.01-1985(R 1995)111 ScopeThis standard presents equations for predicting the flow of compressible and incompressible fluids through control valves.The equations are not intended for use when mixed-phase fluids,dense slurries,dry solids,or non-Newtonian liquids are encountered.In addition,the prediction of cavitation,noise,or other effects is not a part of this standard.2 IntroductionThe equations of this standard are based on the use of experimentally determined capacity factors obtained by testing control valve specimens according to the procedures of ANSI/ISA S75.02,“Control Valve Capacity Test Procedure”(see Annex JReferences).The equations are used to predict the flow rate of a fluid through a valve when all the factors,including those related to the fluid and its flowing condition,are known.When the equations are used to select a valve size,it is often necessary to use capacity factors associated with the fully open or rated condition to predict an approximate required valve flow coefficient(Cv).This procedure is further explained in Annex A.2.1 Flow variable and fluid propertiesThe flow rate of a fluid through a control valve is a function of the following(where applicable):a)Inlet and outlet conditions1)Pressure2)Temperature3)Piping geometryb)Liquid properties1)Composition2)Density3)Vapor pressure4)Viscosity5)Surface tension6)Thermodynamic critical pressurec)Gas and vapor properties1)Composition2)Density3)Ratio of specific heatsd)Control valve properties1)Size2)Valve travel3)Flow path geometry12ISA-S75.01-1985(R 1995)3 NomenclatureSymbolDescriptionCvValve flow coefficientdValve inlet diameterDInternal diameter of the pipeFdValve style modifierFFLiquid critical pressure ratio factor,dimensionlessFkRatio of specific heats factor,dimensionlessFLLiquid pressure recovery factor of a valve without attached fittings,dimensionlessFLPProduct of the liquid pressure recovery factor of a valve with attached fittings(no symbol has been identified)and the piping geometry factor,dimensionlessFPPiping geometry factor,dimensionlessFRReynolds number factor,dimensionlessFsLaminar,or streamline,flow factor,dimensionlessgLocal acceleration of gravityGfLiquid specific gravity at upstream conditions ratio of density of liquid at flowing temperature to density of water at 60F(15.6C),dimensionlessGgGas specific gravity(ratio of density of flowing gas to density of air with both at standard conditions,which is equal to the ratio of the molecular weight of gas to the molecular weight of air),dimensionlesskRatio of specific heats,dimensionlessKHead loss coefficient of a device,dimensionlessKBBernoulli coefficient,dimensionlessKiVelocity head factors for an inlet fitting,dimensionlessMMolecular weight,atomic mass unitsN1,N2,etc.Numerical constants for units of measurement usedp1Upstream absolute static pressure,measured two nominal pipe diameters upstream of valve-fitting assemblyp2Downstream absolute static pressure,measured six nominal pipe diameters downstream of valve-fitting assemblypPressure differential,p1 p2pcAbsolute thermodynamic critical pressureprReduced pressure,dimensionlesspvAbsolute vapor pressure of liquid at inlet temperaturepvcApparent absolute pressure at vena contractaqVolumetric flow rateqmaxMaximum flow rate(choked flow conditions)at a given upstream conditionISA-S75.01-1985(R 1995)13SymbolDescriptionRevValve Reynolds number,dimensionlessTrReduced temperature,dimensionlessTcAbsolute thermodynamic critical temperatureT1Absolute upstream temperature(in degrees K or R)U1Velocity at valve inletwWeight or mass flow ratexRatio of pressure drop to absolute inlet pressure(?p/p1),dimensionlessxTPressure drop ratio factor,dimensionlessxTPValue of xT for valve-fitting assembly,dimensionlessYExpansion factor,ratio of flow coefficient for a gas to that for a liquid at the same Reynolds number,dimensionlessZCompressibility factor,dimensionless1(gamma)Specific weight,upstream conditions(mu)Viscosity,absolute(nu)Kinematic viscosity,centistokes(rho)DensitySubscripts1Upstream conditions2Downstream conditionssNonturbulenttTurbulent4 Incompressible fluid flow of nonvaporizing liquidThe flow rate of a liquid through a given control valve at a given travel is a function of the differential pressure(p1 p2)when the liquid does not partially vaporize between the inlet and outlet of the valve.If vapor bubbles form either temporarily(cavitation)or permanently(flashing),this relationship may no longer hold.(Refer to Section 5 for choked flow equations that apply when extensive vaporization occurs.)In the transitional region between nonvaporizing liquid flow and fully choked flow,the actual flow rate is less than that predicted by either the equations in this section or those in Section 5.Cavitation that occurs in this transitional region can produce physical damage to the valve and/or to the downstream piping and equipment.14ISA-S75.01-1985(R 1995)4.1 Equations for turbulent flowThe equations for determining the flow rate of a liquid through a valve under turbulent,nonvaporizing flow conditions are:4.2 Numerical constants NThe numerical constants N are chosen to suit the measurement units used in the equations.Values for N are listed in Table 1.Table 1 Numerical constants for liquid flow equationsConstantUnits Used in Equat