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Table of ContentsFlow Coefficient .Operating Conditions .Specific Gravity.Pressure Drop Across the Valve.Flowing Quantity.Liquid Flow Equations .Liquid Pressure Recovery Factor .Combined Liquid Pressure Recovery Factor .Cavitation in Control Valves .Effect of Pipe Reducers .Equations for Nonturbulent Flow .Gas and Vapor Flow Equations .Multistage Valve Gas and Vapor Flow Equations .Ratio of Specific Heats Factor .Expansion Factor .Two-Phase Flow Equations .Choked Flow.Supercritical Fluids .Compressibility .Thermodynamic Critical Constants .3334456661112131414141516161719Engineering DataLiquid Velocity in Steel Pipe .Steam or Gas Flow in Steel Pipe .Commercial Wrought Steel Pipe Data .Temperature Conversion Table .Metric Conversion Tables .Useful List of Equivalents .References .21212426272929Particulars contained in this publication are for general information only and Masoneilan reserves the right to modify the contents without priornotice. No warranty either expressed or implied is either given or intended. 2004 Dresser, Inc. All rights reserved.2

ForewordThis handbook on control valve sizing is based on the useof nomenclature and sizing equations from ANSI/ISAStandard S75.01.01 and IEC Standard 60534-2-1.Additional explanations and supportive information areprovided beyond the content of the standards.The principal use of the equations is to aid in the selectionof an appropriate valve size for a specific application. Inthis procedure, the numbers in the equations consist ofvalues for the fluid and flow conditions and known valuesfor the selected valve at rated opening. With thesefactors in the equation, the unknown (or product of theunknowns, e.g., Fp CV) can be computed. Although thesecomputed numbers are often suitable for selecting a valvefrom a series of discrete sizes, they do not represent a trueoperating condition. Some of the factors are for the valveat rated travel, while others relating to the operating conditions are for the partially open valve.The sizing equations are based on equations for predictingthe flow of compressible and incompressible fluidsthrough control valves. The equations are not intended foruse when dense slurries, dry solids or non-Newtonianliquids are encountered.Original equations and methods developed by Masoneilanare included for two-phase flow, multistage flow, andsupercritical fluids.Once a valve size has been selected, the remainingunknowns, such as Fp, can be computed and a judgementcan be made as to whether the valve size is adequate. Itis not usually necessary to carry the calculations furtherto predict the exact opening. To do this, all the pertinentsizing factors must be known at fractional valve openings.A computer sizing program having this information in adatabase can perform this task.Values of numerical factors are included for commonlyencountered systems of units. These are United Statescustomary units and metric units for both kilopascal andbar usage.Flow Coefficient CVThe use of the flow coefficient, CV, first introduced byMasoneilan in 1944, quickly became accepted as theuniversal yardstick of valve capacity. So useful hasCV become, that practically all discussions of valvedesign and characteristics or flow behavior now employthis coefficient.through a given flow restriction with a pressure drop ofone psi. For example, a control valve that has a maximumflow coefficient, CV, of 12 has an effective port area inthe full open position such that it passes 12 gpm ofwater with one psi pressure drop. Basically, it is acapacity index upon which the engineer can rapidly andaccurately estimate the required size of a restriction inany fluid system.By definition, the valve flow coefficient, CV, is the numberof U.S. gallons per minute of water at 60 F that will passOperating ConditionsThere is no substitute for good engineeringjudgement. Most errors in sizing are due to incorrectassumptions as to actual flowing conditions. Generallyspeaking, the tendency is to make the valve too large tobe on the “safe” side (commonly referred to as“oversizing”). A combination of several of these “safetyfactors” can result in a valve so greatly oversized it tendsto be troublesome.The selection of a correct valve size, as determined byformula, is always premised on the assumption of fullknowledge of the actual flowing conditions. Frequently,one or more of these conditions is arbitrarily assumed. Itis the evaluation of these arbitrary data that reallydetermines the final valve size. No formulas, only goodcommon sense combined with experience, can solvethis problem.Specific GravityIn the flow formulas, the specific gravity is a square rootfunction; therefore, small differences in gravity have aminor effect on valve capacity. If the specific gravity is notknown accurately, a reasonable assumption will suffice.The use of .9 specific gravity, for example, instead of .8would cause an error of less than 5% in valve capacity.3

Pressure Drop Across the ValveRemember one important fact, the pressure differentialabsorbed by the control valve in actual operation will bethe difference between the total available head and thatrequired to maintain the desired flow through the valve. Itis determined by the system characteristics rather than bythe theoretical assumptions of the engineer. In the interestof economy, the engineer tries to keep the control valvepressure drop as low as possible. However, a valve canonly regulate flow by absorbing and giving up pressuredrop to the system. As the proportion of the system dropacross the valve is reduced, its ability to further increaseflow rapidly disappears.On a simple back pressure or pressure reducingapplication, the drop across the valve may be calculatedquite accurately. This may also be true on a liquid levelcontrol installation, where the liquid is passing from onevessel at a constant pressure to another vessel at a lowerconstant pressure. If the pressure difference is relativelysmall, some allowance may be necessary for line friction.On the other hand, in a large percentage of controlapplications, the pressure drop across the valve will bechosen arbitrarily.Any attempt to state a specific numerical rule for such achoice becomes too complex to be practical. The designdrop across the valve is sometimes expressed as apercentage of the friction drop in the system, exclusive ofthe valve. A good working rule is that 50% of this frictiondrop should be available as drop across the valve. Inother words, one-third of the total system drop, includingall heat exchangers, mixing nozzles, piping etc., isassumed to be absorbed by the control valve. This maysound excessive, but if the control valve were completelyeliminated from such a system, the flow increase wouldonly be about 23%. In pump discharge systems, the headcharacteristic of the pump becomes a major factor. Forvalves installed in extremely long or high-pressure droplines, the percentage of drop across the valve may besomewhat lower, but at least 15% (up to 25% wherepossible) of the system drop should be taken.In some cases, it may be necessary to make an arbitrarychoice of the pressure drop across the valve becausemeager process data are available. For instance, if thevalve is in a pump discharge line, having a dischargepressure of 7 bar (100 psi), a drop of 0.7 to 1.7 bar(10 to 25 psi) may be assumed sufficient. This is trueif the pump discharge line is not extremely long orcomplicated by large drops through heat exchangersor other equipment. The tendency should be to use thehigher figure.On more complicated systems, consideration shouldbe given to both maximum and minimum operatingconditions. Masoneilan Engineering assistance is available for analysis of such applications.Flowing QuantityThe selection of a control valve is based on the requiredflowing quantity of the process. The control valve must beselected to operate under several different conditions.The maximum quantity that a valve should be required topass is 10 to 15% above the specified maximum flow.The normal flow and maximum flow used in sizecalculations should be based on actual operatingconditions, whenever possible, without any factors havingbeen applied.drop, and the minimum conditions are 25 gpm and 100 psidrop, the C V ratio is 16 to 1, not 8 to 1 as it would firstseem. The required change in valve CV is the product ofthe ratio of maximum to minimum flow and thesquare root of the ratio of maximum to minimum pressuredrop, e.g.,200 x 100 16125 x 25On many systems, a reduction in flow means an increasein pressure drop, and the CV ratio may be much greaterthan would be suspected. If, for example, the maximumoperating conditions for a valve are 200 gpm and 25 psiThere are many systems where the increase in pressuredrop for this same change in flow is proportionally muchgreater than in this case.4

Liquid Flow EquationsFlow of Non-vaporizing LiquidChoked Flow of Vaporizing LiquidThe following equations are used to determine therequired capacity of a valve under fully turbulent, nonvaporizing liquid flow conditions. Note Fp equals unityfor the case of valve size equal to line size.Choked flow is a limiting flow rate. With liquid streams,choking occurs as a result of vaporization of the liquidwhen the pressure within the valve falls below the vaporpressure of the liquid.Liquid flow is choked ifvolumetric flowIn this case, the following equations are used.mass flowvolumetric flowmass flowNomenclatureNumerical Constants for LiquidFlow EquationsCV valve flow coefficientN numerical constants based on units used(see Table 1)Fp piping geometry factor (reducer correction)Units Used in EquationsConstantwqp, pd, Dγ1-m3/hkPa--0.865-3m 3N0.0865FF liquid critical pressure factor 0.96 - 0.28FL liquid pressure recovery factor for a valveFLP combined pressure recovery and pipinggeometry factor for a valve with attached fittingsKi velocity head factors for an inlet fitting,dimensionlesspc pressure at thermodynamic critical pointq volumetric flow rateGf specific gravity at flowing temperature(water 1) @ 60 F/15.5 Cp1 upstream pressurepv vapor pressure of liquid at flowing temperaturep2 downstream pressurew weight (mass) flow rateγ 1 specific weight (mass density) upstreamconditionsN1N2N6Table 15

Liquid Pressure Recovery Factor FLThe liquid pressure recovery factor is a dimensionlessexpression of the pressure recovery ratio in a controlvalve. Mathematically, it is defined as follows:FL Liquid pressure recovery factors for various valve typesat rated travel and at lower valve travel are shown inproduct bulletins. These values are determined bylaboratory test in accordance with prevailing ISA andIEC standards.p1 - p2p 1 - p vcIn this expression, pvc is the pressure at the vena contractain the valve.Combined Liquid Pressure Recovery Factor FLPWhen a valve is installed with reducers, the liquid pressurerecovery of the valve reducer combination is not thesame as that for the valve alone. For calculations involvingchoked flow, it is convenient to treat the piping geometryfactor Fp and the FL factor for the valve reducer combinationas a single factor FLP. The value of FL for the combinationis then FLP /Fp where :p1 - p2F LP p 1 - p vcFpThe following equation may be used to determine FLP.F LP F LK i FL2Cv- 1/22N2 d4 1where Ki K1 KB1 (inlet loss and Bernoulli coefficients)Cavitation in Control ValvesCavitation, a detrimental process long associated withpumps, gains importance in control valves due to higherpressure drops for liquids and increased employment ofhigh pressure recovery valves (e.g. butterfly and ball valves).The pressure recovery in a valve is a function of its particular internal geometry. In general, the more streamlineda valve is, the more pressure recovery is experienced.This increases the possibility of cavitation.Cavitation, briefly, is the transformation of a portion ofliquid into the vapor phase during rapid acceleration of thefluid in the valve orifice, and the subsequent collapse ofvapor bubbles downstream. The collapse of vaporbubbles can produce localized pressure up to 100,000 psi(7000 bar) and are singly most responsible for the rapiderosion of valve trim under high pressure drop conditions.The pressure recovery factor, FL, is useful for valve sizingpurposes to predict limiting choked flow rate under fullycavitating conditions. However, the use of FL can bemisleading to predict limiting pressure drop at whichdamaging cavitation will result.An enhanced cavitation prediction method is described inthe ISA Recommended Practice ISA-RP75.23-1995“Considerations for Evaluating Control Valve Cavitation”.The recommended practice is based on the “Sigma”method, where sigma is defined as:It is, therefore, necessary to understand and to preventthis phenomenon, particularly when high pressure dropconditions are encountered.Cavitation in a control valve handling a pure liquid mayoccur if the static pressure of the flowing liquid tends todecrease to a value less than the fluid vapor pressure. Atthis point, continuity of flow is broken by the formation ofvapor bubbles. Since all control valves exhibit some pressure recovery, the final downstream pressure is generallyhigher than the orifice throat static pressure. When downstream pressure is higher than vapor pressure of the fluid,the vapor bubbles revert back to liquid. This two-stagetransformation is defined as cavitation.σ (P 1 – PV)(P 1 – P 2)The determination of sigma is based on cavitation energylevels, not on choked flow. Laboratory testing using highfrequency vibration data establishes sigma values. Thesesigma values then define different operational regimes fora specific product as illustrated below.6

Cavitation Prediction “Sigma” RegimesFour different operational regimes for each product andlift position.Characteristics of the different cavitationregimes are:Incipient Cavitation: Onset of cavitation Detect using high frequency vibration measurement Very local phenomenon Transient: random “ticks” sound Low level cavitation: usually not damaging Occurs prior to loss of capacityσi Inceptionσc Constantσmv Maximum VibrationRegime envelopes vary for each product and lift, andare based on laboratory testing.σmr Manufacturer’s Recommended LimitConstant Cavitation: More regular cavitation events Lower frequency sound and vibration sensed:“rumbling” sound Some damage to surfaces may occur: dependentupon valve and trim styles, and materialsA series of tests have to be run on multiple valve sizes,and at multiple upstream pressures to establish performance curves for each product line.Maximum Cavitation: Highest vibration amplitude: sounds like “marbles” or“gravel” Vigorous, large scale cavitation Predicted by steady flow pressure distribution ( FL) Very high damage potentialManufacturer’s Recommended Limit: Valve style dependent Provided by manufacturer from combination of:- Application experience- Laboratory testing (Cavitation damage testing ofaluminum parts) Varies with:- Size- Pressure Other application considerations:- Materials, usage duration and frequency, fluidproperties- Fluid velocity Testing required for each product line:- Sigma curves established for each lift point- Minimum of two valve sizes of like geometry testedto establish size scaling factors- Minimum of two upstream pressures used to establish pressure scaling factors- The use of these two scaling factors allowsthe application of a particular valve geometry atvarious pressures and sizes while allowing thesame cavitation energy levels to occur7

Factors Impacting Cavitation DamageValve SizeLarger valves increase the extent of the cavitatingregion. Larger and more damaging bubble size.Driving PressureHigh pressure is more damagingQuantified by exponent ‘a’Damage is proportional to: (P1Damage Scales with:– P2) a‘a’ exponent is from testing at multiple P1 levelsScaling varies with valve Style and GeometryAdditional Factors Impacting Cavitation Damage: (Not scaled by ISA- RP75.23) Hardness: This is the most important quality, the abilityto resist surface pressures. The higher the hardnessthe greater the resistance. Temperature effects material properties, highertemperatures decrease material yield strength levels.Fluid Properties Fluid Surface Tension- Higher tension, higher collapse energy, more damaging.- Water has very high surface tension.- Ammonia also has high surface tension. Fluid with multiple constituents- Multiple vapor pressures are less damaging as onlya portion of the liquid cavitates at service condition.- Hydrocarbon mixtures are less damaging. Fluid with non-condensable gases- Favorable: Gas “cushions” bubble implosion, reducing overpressure and damage.- Unfavorable: Cavitation inception occurs “earlier”, athigher application “sigma” over a larger region.Presence of gas or solid particles ‘foster’ the formationof bubbles. Temperature- Impacts gas solubility and degree of cushioning(favorable).- Pressure of vaporization, (unfavorable), higher temperature, higher Pv, increased cavitation possibility.Higher temperature decreases surface tension(favorable).Cavitation Can Worsen Corrosion and ChemicalAttack on Materials Cavitation weakens material facilitating corrosion attack(and visa versa). Cavitation expedites removal of weakened material. Cavitation removes protective oxide layers, greatlyaccelerating additional material removal.Additional Considerations:Some designs can allow a degree of cavitation to occur,however, by controlling the location and energy levels,damage is avoided (Cavitation Containment Designs). Forthese designs the following considerations, alongwith the Sigma index, are also important and additionallimitations are applied: Valve Materials of Construction In most instances, ALL MATERIALS WILL EVENTUALLY FAIL! Stain-Hardening: Material toughens as it plasticallydeforms, this is a positive trait. Ductility: Ability to deform vs. fracture. Ductile materialsexhibit greater resistance than brittle materials.8Inlet and inter-stage pressure levelsValve body velocityTrim velocitySound power levels

Calculation MethodCalculation Example1. Calculate Applications using Service ConditionsConditions: Water, P1 275 psia, P2 75 psia, PV 4.0CV req’d 21, 3 inch Pipe Line1. σ 1.362. Try 2 Inch Camflex @ CV 21, F-T-O3. σmr 1.15 @ CV 212. Calculate Operating CV3. From Product Rating @ CV Find4. Scale4. Scaleσmrσmr to Service conditions4.1 SSE σmr to Service Conditions 1.0964.1 Calculate Size Scaling Effect SSE4.2 PSE dr Ref. Valve Sized Application Valve Sizeb Size Scaling Exponent4.34.2 Calculate Pressure Scaling Effect PSE5. As 1.49σV (σmr )1.096 - 1 1.49 1 σ(1.36) σV(1.39), 1.39– Valve is Not Acceptable –Try 3 Inch Camflex in the 3 Inch Line@ CV 21, σmr 1.06New SSESSE 1.156 Reference from TestingPSE 1.494.3 σmr Scaled to Service Conditions and Valve Sizeσv (σmr)SSE - 1 PSE NewσVσV (σmr )1.156 - 1 1.49 1 1 5. IF σ / σV Valve is OK for ApplicationIF σ σV Valve is Not Acceptable for the ApplicationAs 1.34σ(1.36) σV(1.34), – Valve is Acceptable –Note: Also Check Body Velocity on CamflexNote: See Nomenclature page 109

Calculation Flow ChartCalculationSizing FromService ConditionsCalculationσv for Valve @Service ConditionsCalculationCapacityCvCalculationService ConditionsσSelect ProductProductFlow Characteristic,W/Size & PressureScaling Exponents(a & b),and Rated σmr @Cv/TravelCalculationSize & PressureScaling FactorsSSE/PSEFrom Ref. To ServiceAcceptance CriteriaAdditional CheckCalculations IfRequiredσ / σv ---- Acceptableσ σv ---- Not Acceptable Velocity ChecksNomenclatureaEmpirical characteristic exponent for calculating PSEσbA characteristic exponent for calculating SSE; determined from reference valve data for geometricallysimilar valves.σcCVValve flow coefficient, CV q(Gf / P)1/2dValve inlet inside diameter, inchesdrValve inlet inside diameter of tested referencevalve, inchesFLLiquid pressure recovery factorP1Valve inlet static pressure, psiaP2Valve outlet static pressure, psiaσiσmrσmvPSE Pressure Scale EffectPvAbsolute fluid vapor pressure of liquid at inlettemperature, psiaSSE Size Scale Effect10Cavitation index equal to (P1-PV)/(P1-P2) at serviceconditions, i.e., σ (service)Coefficient for constant cavitation; is equal to(P1-PV)/ P at the conditions causing steadycavitation.Coefficient for incipient cavitation; is equal to(P1-PV)/ P at the point where incipient cavitationbegins to occur.Coefficient of manufacturer’s recommended minimum limit of the cavitation index for a specified valveand travel; is equal to minimum recommended valueof (P1-PV)/ P.Coefficient of cavitation causing maximum vibration as measured on a cavitation parameter plot.

Effect of Pipe ReducersBernoulli CoefficientsWhen valves are mounted between pipe reducers,there is a decrease in actual valve capacity. The reducerscause an additional pressure drop in the system by actingas contractions and enlargements in series with thevalve. The Piping Geometry Factor, Fp, is used toaccount for this effect.Σ4dK B2 1 - D24SummationΣK K 1 K 2 K B1 - K B2Piping Geometry FactorFp dD1K B1 1 -1C v2 ΣK 1 - /2N2 d4When inlet and outlet reducers are the same size, theBernoulli coefficients cancel out.Pipe Reducer EquationsLoss CoefficientsinletΣoutletNomenclatureCV valve flow capacity coefficientdK 2 pressure loss coefficient for outlet valve end inside diameterreducer, dimensionlessD1 inside diameter of upstream pipeK B1 pressure change (Bernoulli) coefficientD2 inside diameter of downstream pipeFp piping geometry factor, dimensionlessK1 pressure loss coefficient for inletfor inlet reducer, dimensionlessK B2 pressure change (Bernoulli) coefficientfor outlet reducer, dimensionless K K1 K2 KB1 - KB2, dimensionlessreducer, dimensionless11

γEquations for Non-turbulent FlowLaminar or transitional flow may result when the liquidviscosity is high, or when valve pressure drop or CV issmall. The Valve Reynolds Number Factor is used in theequations as follows :The valve Reynolds number is defined as follows :Re v22 N 41F d q 1 FL C v 1ν FL/ C v / N 2 d42volumetric flowmass flowCv qN1 FRCv N6 FRGfp1 - p2wp1 - p21/42The Valve Reynolds Number Rev is used to determinethe Reynolds Number Factor FR. The factor FR can beestimated from curves in the existing ISA and IECstandards, or by calculation methods shown in the standards. Iteration is required in the method shown in theIEC standard.γ1νNumerical Constants for LiquidFlow EquationsNomenclatureCV valve flow capacity coefficientd nominal valve sizeFd valve style modifier, dimensionlessFL Liquid pressure recovery factor volumetric flow rateRev valve Reynolds number, dimensionlessw weight (mass) flow rateγ mass density of liquidν kinematic viscosity, centistokeswqp, pd, Dγ1-m3/hkPa--0.865-3m /hbar--1.00-gpmpsia--0.00214---mm----in-76000-3m 363.3lb/h-psia-lb/ft3NFR Reynolds number correction factor, dimensionlessGf specific gravity at flowing temperature(water 1) @ 60 F/15.5 C p valve pressure dropqUnits Used in EquationsConstant0.0865N1N2N4890.02.73N6Table 212

Gas and Vapor Flow EquationsGas expansion factorvolumetric flowPressure drop ratioor*mass flow*Ratio of specific heats factor**The IEC 534-2 equations are identical to the aboveISA equations (marked with an *) except for the following symbols:ork (ISA) corresponds to γ (IEC)γ 1 (ISA) corresponds to ρ1 (IEC)Numerical Constants for Gas andVapor Flow EquationsNomenclatureCVFkFPp1p2qN Gg valve flow coefficientratio of specific heats factor, dimensionlesspiping geometry factor (reducer correction)upstream pressuredownstream pressurevolumetric flow ratenumerical constant based on units(see table below)gas specific gravity. Ratio of gas densityat standard conditionsabsolute inlet temperaturegas molecular weightpressure drop ratio, p/p1 Limit x Fk xTgas compressibility factorxgas expansion factor, Y 1 3 Fk x TT1MxZY xTγ1 pressure drop ratio factor (Gamma) specific weight (mass density),upstream conditions weight (mass) flow rate gas specific heat ratiowkUnits Used in arkg/m-lb/h-psialb/ft3--3m -K7320.0-scfhpsia-R0.948N9p, p63.31360.0N8q*27.34.17N7w*q is in cubic feet per hour measured at 14.73 psia and 60 F,or cubic meters per hour measured at 101.3 kPa and 15.6 C.Table 313

Multistage Valve Gas and Vapor Flow Equationsvolumetric flowCv G g T1 ZxqN 7 Fp p1 Y Mor, limit xM Fk xTCv qN 9 Fp p1 Y MM T1 Zxmass flowwCv N 6 Fp Y Mx p1 γ1FM Multistage Compressible Flow Factor(FM 0.74 for multistage valves)orCv N8wFp p1 Y MXM Pressure drop ratio factor formultistage valvesT1 Zx MRatio of Specific Heats Factor FkFor valve sizing purposes, Fk may be taken as having alinear relationship to k. Therefore,The flow rate of a compressible fluid through a valve isaffected by the ratio of specific heats. The factor Fkaccounts for this effect. Fk has a value of 1.0 for air atmoderate temperature and pressures, where its specificheat ratio is about 1.40.Expansion Factor YThe factor xT accounts for the influence of 1, 2 and 3;factor Fk accounts for the influence of 4. For all practicalpurposes, Reynolds Number effects may be disregardedfor virtually all process gas and vapor flows.The expansion factor accounts for the changes in densityof the fluid as it passes through a valve, and for thechange in the area of the vena contracta as the pressuredrop is varied. The expansion factor is affected by all ofthe following influences :1.2.3.4.5.As in the application of orifice plates for compressibleflow measurement, a linear relationship of the expansionfactor Y to pressure drop ratio x is used as below :Ratio of valve inlet to port areaInternal valve geometryPressure drop ratio, xRatio of specific heats, kReynolds Number14

Two-Phase Flow EquationsUse the actual pressure drop for pf and pg, but with thelimiting pressure drop for each individually as follows :Two-phase flow can exist as a mixture of a liquid with anon-condensable gas or as a mixture of a liquid with itsvapor. The flow equation below applies where the twophase condition exists at the valve inlet. p f F L2 (p 1 - F F p v)The flow equation accounts for expansionγof the gas orγvapor phase, and for possible vaporization γof the liquidγphase. It utilizes both the gas and liquid limiting sizingpressure drops. p g F k x T p 1The use of this flow equation results in a required CVgreater than the sum of a separately calculated CV forthe liquid plus a CV for the gas or vapor phase. Thisincreased capacity models published two-phase flowdata quite well.The flow equation for a two phase mixture entering thevalve is as follows.Note : Fp equals unity for the case of valve size equal toline size.Cv wN6 FpFor the hypothetical case of all liquid flow ( ff 1), the flowequation reduces to the liquid flow equation for mass flow.fgff p f γf p g γg Y 2For the hypothetical case of all gas or vapor flow (fg 1),the flow equation reduces to the gas and vapor flowequation for mass flow.NomenclatureNumerical Constants for LiquidFlow EquationsCV valve flow coefficientff weight fraction of liquid in two-phase mixture,dimensionlessγγfg weight fraction of gas (or vapor) in two-phasemixture, dimensionlessFF liquid critical pressure factor 0.96 - 0.28Fk FL Fp p1 pv pf pg w xT Y Units Used in EquationsConstantp, pd, ft3w2.73pvpcN6ratio of specific heats factor, dimensionlessliquid pressure recovery factorγpiping geometry factor (reducercorrection)γupstream pressurevapor pressure of liquid at flowing temperaturepressure drop for the liquid phasepressure drop for the gas phaseweight (mass) flow rate of two-phase mixturepressure drop ratio factorxgas expansion factor, Y 1 -Table 43 Fk x Tγ f specific weight (mass density) of the liquidphase at inlet conditionsγ g specific weight (mass density) of the gas orvapor phase at inlet conditions15γ1qN

Choked Flow (Gas and Vapor)If all inlet conditions are held constant and pressure dropratio x is increased by lowering the downstream pressure,mass flow will

sizing factors must be known at fractional valve openings. A computer sizing program having this information in a database can perform this task. This handbook on control valve sizing is based on the use of nomenclature and sizing equations from ANSI/ISA Standard S75.01.01 and IEC Standard 60534-2-1. Additional explanations and supportive .

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