75925837 Control Valve Sizing

Note: The source of the technical material in this volume is the ProfessionalEngineering Development Program (PEDP) of Engineering Services.

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Engineering EncyclopediaSaudi Aramco DeskTop Standards

Sizing Control Valves

Engineering Encyclopedia Instrumentation


Saudi Aramco DeskTop Standards

CONTENTS PAGE

MANUALLY SIZING CONTROL VALVES FOR LIQUID APPLICATIONS 1

The Importance Of Sizing 1

Undersizing Problems 1

Oversizing Problems 1

Fluid States 2

Fluid States And Sizing Equations 2

Scope Of Presented Equations 2

Guidelines For Capacity vs. Percent Of Rated Travel 3

Sizing For Maximum, Normal, And Minimum Flow Conditions 3

Tendency To Oversize Valves 3

Valve Manufacturer's Guidelines 3

Saudi Aramco Standards 4

Converting Degrees Rotation To Percent Travel 4

The Basic Liquid Flow Equation 5

Predicting Flow Through A Restriction 5

Solving For Required Valve Cv 5

ISA Standards 6

Recognized Valve Sizing Standards 6

ISA Forms Of The Basic Sizing Equation 6

Terms In The ISA Equation 8

Choked Flow 9

Limits Of The Basic Liquid Sizing Equation 9

Pressure And Velocity Profiles 10

Pressure Recovery 11

Fluid Vapor Pressure 12

Mechanics Of Choked Flow 13

Cavitation 15

Flashing 15




Implications Of Choked Flow For Sizing 15

Calculating the Allowable Pressure Drop 16

Valve Recovery Coefficient 16

Solving For DP Allowable 18

Implementing Choked Flow Equations 21

Piping Geometry 22

Significance Of Pipe Fittings In Valve Sizing 22

ISA Corrections For Swaged Lines 22

Piping Factors And Choked Flow 27

Limitations Of Calculated FLP 28

Alternate Methods For Calculating Swage Effects 30

Viscosity Corrections 31

Flow Regimes 31

Impact Of Flow Regime On Valve Sizing 32

Reynolds Numbers 32

ISA Equations For Non-Turbulent Flow 33

Other Viscosity Correction Methods 35

Summary Of Valve Sizing Equations 36

ISA Method 36

Equations Used By Fisher Controls And Others 38

COMPUTER SIZING CONTROL VALVES FOR LIQUID APPLICATIONS 39

Introduction to the Fisher Sizing Program 39

Benefits Of Computer Sizing Methods 39

Overview Of The Fisher Sizing Program (FSP 1.4) 39

Overview of Program Operation 40

Booting The Program 40

Project Information 40

Main Menu 40

Selecting Units 41

Selecting A Valve Sizing Method 42




Selecting Variables And Conditions 43

Valve Sizing Calculation Screen 44

Selecting Calculation Options 45

Other Important Operations 48

COMPUTER SIZING CONTROL VALVES FOR GAS AND STEAM APPLICATIONS49

Introduction 49

Differences In Compressible and Incompressible Fluid Flow 49

Use Of Computer Software 49

The ISA Sizing Equations For Compressible Fluids 49

Popular Standard 49

Saudi Aramco Standards 49

Alternate Forms Of The ISA Equation 49

Nomenclature 51

Numerical Constants 51

Basic Equation 52

Choked Flow 53

Expansion Factor: Y 56

Adapting The Equation For Use With Gasses Other Than Air 61

Real Gas Behavior 63

Piping Effects 65

Final Equation Form 67

Summary Of ISA Equation Terms 67

Computer Sizing Control Valves For Gasses Using The ISA Equations 68

Introduction 68

Valve Sizing Methods Available 68

Selecting The Desired Calculation Type 69

Overview Of Sizing Procedures 69

Selecting Options 70

The Fisher Universal Gas Sizing Equation 72

Introduction 72




Fisher And ISA Equation Comparison 72

Equation Basics 73

Equation Limits 74

Pressure Recovery And Critical Flow 75

Blending The Two Equations 76

The C1 Factor 78

Mechanics Of The Sine Term 80

Alternate Forms Of The Universal Sizing Equation 81

Solving for Cg 84

Comparison Of Fisher And ISA Gas Sizing Equations 85

Computer Sizing Control Valves For Gasses Using The Fisher ControlsEquations 86

Valve Sizing Methods Available 86

Selecting A Calculation Type 87

Overview Of Sizing Procedures 87

F3 Options 88

ENTERING VALVE SIZING DATA ON THE SAUDI ARAMCO ISS 91

Body And Flange Size 91

Control Valve Physical Size Information 91

Capacity Ratings 91

Capacity At Minimum, Normal, And Maximum Flow Conditions 91

Valve Travel At Minimum, Normal, And Maximum Flow Conditions 91

WORK AID 1: PROCEDURES THAT ARE USED TO MANUALLY SIZECONTROL VALVES FOR LIQUID APPLICATIONS 93

Work Aid 1A: Procedures That Are Used To Calculate The RequiredControl Valve Cv 93

Work Aid 1B: Procedures That Are Used To Calculate The AllowablePressure Drop (DPallow) 94

Work Aid 1C: Procedures That Are Used To Calculate The Effect OfPiping Factors On Cv 95




Work Aid 1D: Procedures That Are Used To Calculate The Effect OfLaminar Flow On Cv 96

WORK AID 2: PROCEDURES THAT ARE USED TO COMPUTER SIZECONTROL VALVES FOR LIQUID APPLICATIONS 97

Work Aid 2A: Procedures That Are Used To Computer Size ControlValves For Water Applications 97

Work Aid 2B: Procedures That Are Used To Computer Size ControlValves For Choked Flow 100

Work Aid 2C: Procedures That Are Used To Computer Size ControlValves For Fluids In The Sizing Database 101

Work Aid 2D: Procedures That Are Used To Computer Size ControlValves With Piping Factor Correction 103

Work Aid 2E: Procedures Used To Computer Size Control ValvesWith Viscosity Correction 105

Work Aid 2F: Procedures That Are Used To Computer Size ControlValves With Viscosity And Piping Factor Correction 108

Work Aid 2G: Procedures That Are Used To Computer Size ControlValves For Minimum, Normal, And Maximum FlowConditions 110

Work Aid 2G: Procedures That Are Used To Computer Size ControlValves For Minimum, Normal, And Maximum FlowConditions, cont'd. 112

WORK AID 3: PROCEDURES THAT ARE USED TO COMPUTER SIZECONTROL VALVES FOR GAS AND STEAMAPPLICATIONS 114

Work Aid 3A: Procedures That Are Used To Computer Size ControlValves For Ideal Gasses With The ISA Method 114

Work Aid 3B: Procedures That Are Used To Computer Size ControlValves For Real Gasses With The ISA Method 115

Work Aid 3C: Procedures That Are Used To Computer Size ControlValves For Vapors With The ISA Method 116

Work Aid 3D: Procedures That Are Used To Computer Size ControlValves For Steam With The ISA Method 117

Work Aid 3E: Procedures That Are Used To Computer Size ControlValves For Ideal Gasses With The Fisher Method 118

Work Aid 3F: Procedures That Are Used To Computer Size ControlValves For Real Gasses With The Fisher Method 119




Work Aid 3G: Procedures That Are Used To Computer Size ControlValves For Vapors With The Fisher Method 120

Work Aid 3H: Procedures That Are Used To Computer Size ControlValves For Steam With The Fisher Method 121

Work Aid 3I: Procedures That Are Used To Calculate The Effect OfCompressibility On Valve Size 122

Work Aid 3J: Procedures That Are Used To Computer Size ControlValves For All Flow Conditions 124

WORK AID 4: PROCEDURES THAT ARE USED TO ENTER VALVESIZING DATA ON THE SAUDI ARAMCO ISS 127

GLOSSARY 128




LIST OF FIGURES PAGE

Figure 1 Fluid States as A Function of Pressure And Heat Content 2Figure 2 Typical Vendor Recommendations For Percent Travel Versus

Flow 3Figure 3 Guidelines For Percent Travel At Various Flow ConditionsPer

Section 5.2 of SAES-J-700 4Figure 4 Units Constants For The ISA Liquid Sizing Equations 7Figure 5 Pressure And Flow Relationships 9Figure 6 Pressure And Velocity Profiles Around A Restriction 10Figure 7 Comparison Of High And Low Recovery Valves 11Figure 8 Fluid Vaporization When Pvc < Pv 12Figure 9 Pressure And Flow Relationships 13Figure 10 Pressure Profiles For Flashing And Cavitating Flows 14Figure 11 Generalized Relationship Of Pvc To Pv For High And Low

Recovery Valves At Different Pressure Drops 17Figure 12 Critical Pressure Ratios For Liquids Other Than Water 19Figure 13 Critical Pressure Ratios For Water 19Figure 14 Flow Limiting Influences Of Reducers And Expanders 23Figure 15 Piping Factor Effect Vs. Travel For Different Valve Styles 26Figure 16 R Values That Are Used In The Piping Factor Correction

MethodThat Is Included In Section 5.4 Of SAES-J-700 30Figure 17 Flow Profiles Of Laminar And Turbulent Flow Regimes 31Figure 18 Viscosity Conversion 34Figure 19 Valve Reynolds Number Vs. The Reynolds Number Factor FR 35Figure 20 Main Menu Of The Fisher Sizing Program 40




Figure 21 Screen That Appears When The Units Option Under Config Is Selected 41Figure 22 Drop-Down Menu That Lists Valve Sizing Methods 42Figure 23 Options For Variables To Solve For 43Figure 24 Calculation Screen For ISA Liquid Sizing 44Figure 25 Calculation Options 45Figure 26 Pull-Down Menu That Lists Units Options For Q 46Figure 27 Pull-Down Menu That Lists Fluids In The Sizing Database 47Figure 28 Table Of Values That Is Displayed When The F9 Key Is Pressed 48Figure 29 Numerical Constants For The ISA Gas Sizing Equations 51Figure 30 Gas Flow And Pressure Relationships 52Figure 31 Choked Flow As A Function Of xT 53Figure 32 Effects Of k On FKxT And qmax 55Figure 33 Pressure And Flow Relationships As x Increases From 0.02 To

xT 56Figure 34 Reduced Pressure PVC Leads To Reduced Fluid Density And

Reduced Flow 57Figure 35 Effect of Sonic Velocity On Flow 58Figure 36 Effect of Vena Contracta Enlargement 59Figure 37 Relationships Among x, FkxT, And Y 60Figure 38 Generalized Compressibility Chart 64Figure 39 Valve Sizing Method Options 68Figure 40 Available Calculation Types 69Figure 41 Valve Sizing Screen For The ISA Gas Valve Sizing Method 69Figure 42 Calculation Options For The ISA Gas Valve Sizing Method 70




Figure 43 Line-By-Line Units Options For Flow 71Figure 44 Actual Flow Versus Predicted Flow 74Figure 45 Critical Flow For Low And High Recovery Valves 75Figure 46 Predicting Low Flow And Critical Flow 76Figure 47 Tested Values Of Flow Compared To A Sine Curve 77Figure 48 Comparison of Cv, Cg, and C1 Values 79Figure 49 C2 Factor Versus k 82Figure 50 Comparison of ISA and Fisher Sizing Terms 85Figure 51 Valve Sizing Methods 86Figure 52 Selection Of A Calculation Type 87Figure 53 Valve Sizing Screen For The Fisher Real Gas Sizing Method 87Figure 54 Calculation Options For The Fisher Ideal Gas Sizing Method 88Figure 55 Calculation Options For The Fisher Real Gas Sizing Method 88Figure 56 Calculation Options For The Fisher Vapor Sizing Method 89Figure 57 Calculation Options For The Fisher Steam Sizing Method 89Figure 58 Pull-Down Menu Options For Temperature 90Figure 59 The Saudi Aramco ISS 92



Saudi Aramco DeskTop Standards 1

Manually sizing control valves for liquid applications

The Importance Of Sizing

While control valve selection is an "art," control valve sizing is closer to a "science". Valvesizing procedures are based on accepted mathematical equations that are used to model flowthrough ideal restrictions such as orifice plates and flow nozzles. While control valves do notalways resemble ideal restrictions, the mathematical models generally give useful results if thespecifier inputs accurate data. However, if the service conditions and fluid properties that areused as inputs to the sizing process are not accurate, the specifier may be led to the selectionof a control valve that is either undersized or oversized for the application.

Undersizing Problems

Limited Flow Capacity is the primary concern of control valves that are too small.Limited capacity may have economic impact, such as the inability to meet productionquotas. Limited capacity may result in process failure because of the inability tosupply needed fluids in sufficient quantity. Inadequate capacity can also result insafety hazards; for example, an undersized control valve that is used in a reliefapplication may allow upstream pressure to reach unsafe levels.

Oversizing Problems

Excessive Seat Wear is a common result of oversizing control valves. A valve withexcess capacity may spend most of its life throttling near the seat. Sustained throttlingwith the plug near the seat causes high velocity flow that impinges on and around theseating surfaces. Rapid wear and premature valve failure can result.Safety is also a key issue; for example, if an oversized valve feeds a relief system, therelief system may have insufficient capacity to control the excess input to the reliefsystem.Stable Control is another problem that is associated with oversized valves. Process gainis typically quite high when the valve closure member operates near the seat. The highgain can cause large changes in the process variable, which results in instability. Inaddition, any friction or deadband in the valve has a pronounced effect onperformance at extremely low valve lifts.Basic Economics are a concern because excess capacity generally comes at an increased,but unnecessary cost.




Fluid States

Fluid States And Sizing Equations

Fluid behavior, including flow rate as a function of pressure and temperature conditions,depends on the fluid state (i.e., whether the fluid is in a liquid, gas, vapor, or other state);accordingly, several different sizing equations are available that can be used to calculate theflow rate or to calculate the required control valve Cv. The chart below (see Figure 1)illustrates how a fluid state can change as a function of pressure and enthalpy (heat content).

Figure 1Fluid States As A Function Of Pressure And Heat Content

Scope Of Presented Equations

Many complexities are involved in predicting either valve capacity (Cv) or flow rate (q) whenthe fluid state is at or near any of the boundaries that are shown in Figure 1 above; therefore,this Module will present basic sizing methods for fluids that can be defined as liquids, idealgasses, and real gasses.




Guidelines For Capacity vs. Percent Of Rated Travel

Sizing For Maximum, Normal, And Minimum Flow Conditions

While it is sometimes tempting to select and size control valves for the maximum flowcondition only, it is equally important to calculate Cv requirements at normal and minimumflow conditions.Sizing for maximum flow ensures adequate capacity.Sizing for normal flow conditions allows the specifier to ensure that the valve will normallythrottle in a range of travel (or percentage of maximum valve Cv) that provides good controland sufficient reserve capacity.Sizing for minimum flow conditions allows the specifier to ensure that the valve is capable ofproviding stable control at the low-flow condition. Most valves are designed to provide goodcontrol down to about 10 percent of rated travel. Throttling below 10 percent travel can causesystem instability because of the high valve gain at low lifts, and it can cause high velocityflow that results in accelerated seat wear.

Tendency To Oversize Valves

In many engineering environments, several individuals or groups may have direct or indirectinput to the valve sizing process. All too often, each individual or group adds a 'safety margin'when providing information. Specifiers should remain aware that the most common controlvalve problem is the oversized valve, and they should strive to use actual service conditionswhen sizing control valves.

Valve Manufacturer's Guidelines

Most valve manufacturers use a rule of thumb that establishes acceptable percentages oftravel for the minimum, normal, and maximum flow conditions. The flow versus travelrecommendations that are shown in Figure 2 are common.

Flow Condition Percent Of Rated Travel

Minimum 10Normal 20-80

Maximum 90Figure 2

Typical Vendor Recommendations For Percent Travel Versus Flow




Saudi Aramco Standards

Section 5.2 of SAES-J-700 contains guidelines for the percentage of valve travel thatproduces the normal and maximum flow rates. The recommended percentages vary with theinherent valve characteristics as shown in Figure 3.

Flow Characteristic Percent Travel At NormalFlow

Percent Travel At MaximumFlow

Equal Percentage 80 93Linear 70 90

Modified Parabolic 75 90Figure 3

Guidelines For Percent Travel At Various Flow ConditionsPer Section 5.2 of SAES-J-700

Converting Degrees Rotation To Percent Travel

The guidelines for travel versus flow are expressed in percent travel and apply directly tosliding-stem valves; however, travel for rotary-shaft valves is expressed in degrees rotation. Inorder to apply the recommended percentages listed above to rotary-shaft control valves,percentages of travel must be converted to degrees rotation; for example, if the maximumacceptable travel for a given condition is 93 percent, the equivalent rotation is approximately84 degrees (0.93% x 90 degrees = 84 degrees).




The Basic Liquid Flow Equation

Predicting Flow Through A Restriction

Basic (Fisher) Flow Equation - Most sizing procedures are based on concepts andequations that are used to describe flow through orifice plates and flow nozzles. Themost common and basic form of the liquid flow equation is as follows:

Q CP

Gv=∆

(1)Where:

Q = The flow rate in gallons per minute (gpm).Cv = A coefficient that is assigned by valve manufacturers to describe how

much flow a specific valve will pass under standard conditions (i.e., thetest fluid is water with a specific gravity of 1.0, and the pressure dropacross the valve is 1 psi).

∆P = The pressure drop across the valve in psi; (∆P = P1-P2).G = The specific gravity of the fluid.

Major Assumption - In reality, the flow rate through a restriction is a function of thepressure drop between upstream pressure and the pressure at the limiting flow area ofthe restriction, which is called the vena contracta; however, Equation 1 provides thebasis for developing the complete equation.

Solving For Required Valve CvRearranging the equation to solve for the control valve Cv results in the base equation that isused for sizing valves for non-compressible fluids (liquids).

C QGPv =

∆ (2)




ISA Standards

Recognized Valve Sizing Standards

ISA - One organization that publishes standards that are widely accepted for controlvalve sizing is the Instrument Society of America (ISA). The ISA standard thatincludes the valve sizing equations is ANSI/ISA-S75.01-1985.Section 5.1 Of SAES-J-700 requires the use of the ISA equations for valve sizing, but italso allows the use of other methods that are based on the ISA equations.

ISA Forms Of The Basic Sizing Equation

The ISA forms of the basic equations that have been discussed to this point are:To Predict Flow - To predict flow, the basic form of the ISA equation is as follows:

q N Cp p

Gvf

=−

11 2 ( 3 )

To Calculate Control Valve Cv - To calculate the control valve Cv that is required to passa specified flow rate, the equation is as follows:

Cq

NG

p pv

f=−1 1 2

( 4 )

Where:q = The volumetric flow rate.N1 = A numerical constant for units of measurement (see Figure 4).Cv = The control valve flow coefficient.Gf = The liquid specific gravity at upstream conditions; the ratio of the fluid

density at the valve inlet to the density of water at 60 degrees F (15.6degrees C).

p1 = The upstream absolute pressure, psia.p2 = The downstream absolute pressure, psia.




Units Constants - The following table includes the values of some of the constants thatare used in the various forms of the ISA sizing equation.

Constant Units That Are Used In EquationsN w q p, ∆∆P d, D γγ1 νν

N1 0.0865 --- m3/h kPa --- --- ---0.865 --- m3/hr bar --- --- ---

1 --- gpm psia --- --- ---N2 0.00214 --- --- --- mm --- ---

890 --- --- --- in --- ---N4 76 000 --- m3/h --- mm --- centistokes

17 300 --- gpm --- in --- centistokesN6 2.73 kg/h --- kPa --- kg/m3

27.3 kg/h --- bar --- kg/m3

63.3 lb/h --- psia --- lb/ft3

Figure 4Units Constants For The ISA Liquid Sizing Equations.

The constant N1 is included in Equations 3 and 4 The constants N2 through N6 are used insupplemental equations that will be discussed later in this Module.




Terms In The ISA Equation

ISA Equation Compared To The Generic Equation - The ISA liquid flow sizing equation(Equation 6) differs in minor ways from the generic form of the equation (Equation 5),as shown below:

Generic: C Q

GP

v =∆ (5)

ISA: C

qN

Gp p

vf=

−1 1 2 (6)

Minor Differences - Note that the ISA equation uses:

• a lower case 'q' for flow rate.

• the term p1-p2 instead of ∆P to describe pressure drop across the valve.

• the term Gf instead of G for the specific gravity of the fluid.

• The term N1, which is a units constant. By selecting the proper constant, thespecifier may apply the equation by using either metric or Englishmeasurement units. Conversions are possible with the generic equation as well.

ISA vs. Generic Equation Similarities - Despite minor differences in nomenclature, the twoequation forms are algebraically identical, and as a result, they will give identicalresults. The only exception is the use of the N1 term (units constant) in the ISAequation; however, a units conversion factor can be applied to any sizing equation.Common Use Of Equation Forms - When reviewing sizing catalogs, technical articles, andother documentation, specifiers will commonly encounter both the ISA nomenclatureand minor departures from the ISA nomenclature that some valve manufacturersemploy.




Choked Flow

Limits Of The Basic Liquid Sizing Equation

Predicted Flow - The basic liquid sizing equations that have been discussed to this pointpredict an increase in flow for every increase in the square root of the pressure drop asshown in Figure 5 below. In reality, the relationship between pressure drop and flowrate only holds true for a limited range of conditions.Choked Flow - In every application, it is possible to reach a point at which increasingthe pressure drop by reducing P2 does not result in a proportional increase in flow. Atsome pressure drop limit, a condition of maximum flow is realized in spite of increasesin the pressure drop across the valve. The condition of maximum flow is known aschoked flow and is represented with Qmax or Qchoked.Predicting Qmax and ∆∆Pchoked - Equations have been developed that can be used topredict the value of Qmax (Qchoked) with relative certainty. The equations that are usedto predict choked flow make use of a computed value that is referred to either as∆Pchoked or ∆Pallow. When the computed value of ∆Pchoked or ∆Pallow is larger thanthe actual ∆P across the valve, the specifier knows that choked flow exists. Whenchoked flow does exist, the maximum pressure drop that can be used for sizingpurposes is the computed value of ∆Pchoked or ∆pallow.

Figure 5Pressure And Flow Relationships.




Pressure And Velocity Profiles

A plot that shows mean fluid pressure and mean velocity profiles at and around a controlvalve helps to explain the mechanics of choked flow. Refer to Figure 6.

Vena Contracta - Recall that as a fluid passes through a restriction such as a controlvalve, the flowstream continues to neck down to a minimum cross-sectional area. Thepoint of minimum cross-sectional area is known as the vena contracta. The venacontracta may be located at the control valve port, or it may be located downstream ofthe valve, depending on service conditions and valve style.Pressure And Velocity At The Vena Contracta - At the vena contracta, fluid velocityincreases to a maximum. In accordance with Bernoulli's equation, the increase invelocity is accompanied by a decrease in pressure. The low pressure at the venacontracta is referred to as Pvc.

Figure 6Pressure And Velocity Profiles Around A Restriction




Pressure Recovery

Pressure Recovery Defined - The difference between Pvc and P2 is referred to as pressurerecovery. P2 is a fixed value that is dictated by the process, while the pressure at thevena contracta (Pvc) is a function of valve style and geometry.High Recovery vs. Low Recovery Control Valves - Low recovery (globe style) controlvalves produce a relatively small pressure dip at the vena contracta. High recoveryvalves (ball and butterfly valves) produce a greater pressure dip at the vena contracta.Refer to Figure 7 below. Whether a valve is a high recovery or low recovery type has asignificant bearing on the pressure drop at which choked flow occurs.

Figure 7Comparison Of High And Low Recovery Valves




Fluid Vapor Pressure

Defined - All subcritical, single-species fluids have a vapor pressure (Pv). Vaporpressure is the pressure at which a fluid at a stated temperature will begin to changestate from the liquid to the vapor phase. The liquid-to-vapor change of state can bethought of as causing a liquid to boil by reducing the fluid pressure, as opposed toincreasing the fluid temperature.Pvc vs Pv - As the pressure at the vena contracta is reduced to the vapor pressure of thefluid (see Figure 8), the fluid will begin to vaporize. The fluid now consists of amixture of a liquid and vapor. The fluid is no longer incompressible (a liquid);therefore, the basic liquid flow equation is no longer valid.

Figure 8Fluid Vaporization When Pvc < Pv




Mechanics Of Choked Flow

Increasing Pressure Drop And Fluid Density - Once the Pvc has fallen below the Pv, furtherincreases in the pressure drop result in additional vapor bubble formation and a furtherreduction in the density of the fluid mixture. The decrease in fluid density offsets anyincrease in the velocity of the mixture; as a result, no additional mass flow is realized.Refer to Figure 9. Vapor formation and the subsequent reduction in fluid density helpto explain the phenomenon of choked flow.

Figure 9Pressure And Flow Relationships




Associated Phenomenon - Whenever the fluid pressure at the vena contracta falls belowthe fluid vapor pressure, one of two other phenomena will occur in conjunction withchoked flow. The fluid will either be cavitating or flashing, depending, as shown inFigure 10, on the value of P2.

Figure 10Pressure Profiles For Flashing And Cavitating Flows




Cavitation

Cavitation Defined - If downstream pressure (P2) recovers to a pressure that is greaterthan the local vapor pressure (Pv) of the fluid, the vapor cavities collapse and the fluidmixture reverts to a liquid. The entire liquid-vapor-liquid phase change is known ascavitation.Cavitation Damage results from the collapse of millions of tiny vapor cavities onboundary surfaces. Depending on cavitation intensity, proximity to critical surfaces,and time of exposure, the micro-jets and the shock waves that are associated with thecollapse of vapor cavities can produce extreme damage to valves and othercomponents. Cavitation damage has a characteristic appearance that is rough andcinderlike.Anti-Cavitation Trim is available for many valves to reduce or eliminate cavitationdamage. These special trim designs will be discussed in another module in this course.

Flashing

Flashing Defined - If downstream pressure remains at or below the local vapor pressureof the fluid, the vapor remains in the fluid stream, and the mixture is said to beflashing.Flashing Damage results from liquid droplets impinging on metal surfaces at highvelocity. Flashing damage has a smooth and polished appearance.Selection Of Valves For Flashing Fluids follows the same general strategy as valveselection for other erosive applications, including the selection of harder bodymaterials, hard trim, flow-down angle bodies, and replaceable liners.

Implications Of Choked Flow For Sizing

It is important for the specifier to identify the presence of choked flow. If the presence ofchoked flow is not identified and accounted for, the basic flow equation can grossly overpredict the flow capacity of the control valve. In addition, choked flow is always accompaniedby either flashing or cavitation, which must be considered during valve selection and sizing.




Calculating the Allowable Pressure Drop

All sizing methods include provisions for determining the onset of choked flow. The onset ofchoked flow is determined by calculating the maximum flow-producing pressure drop(∆Pallow or ∆Pchoked).

Valve Recovery Coefficient

Pressure Recovery Coefficient Defined - The valve pressure recovery coefficient (orsimply, recovery coefficient) plays a major role in calculating the ∆Pallow or the∆Pchoked. The recovery coefficient accounts for the influence of the valve's internalgeometry on its capacity at the choked flow condition. The equations that are includedin ISA Standard S75.01 use the term FL to express the recovery coefficient. Somemanufacturers also use the coefficient Km. Manufacturers determine the value of FLand/or Km for each valve style by test, and they publish the coefficients along withother sizing information.Equation For Determining The Valve Recovery Coefficient - The valve recovery coefficientrelates the valve pressure drop to the drop at the vena contracta as follows:

ISA: F

P PP PL

vc=

−−

1 2

1 (7)

Fisher: K

P PP Pm

vc=

−−

1 2

1 (8)Note that FL2 = Km.

Where:

FL = The valve recovery coefficient (ISA).Km = An alternate form of the valve recovery coefficient (Fisher Controls and

others).Pvc = The fluid pressure at the vena contracta.




Interpreting Values of Km or FL - Typically, values of Km and FL are much larger for lowrecovery globe style valves than for high recovery ball and butterfly valves. Refer toFigure 11 and note that high recovery valves tend to choke at lower pressure dropsthan low recovery valves do because high-recovery valves produce a greater pressuredip at the vena contracta. Low recovery valves produce a smaller drop at the venacontracta; therefore, more pressure drop can be taken across the valve before Pvcapproaches Pv.

Figure 11Generalized Relationship Of Pvc To Pv For High And Low

Recovery Valves At Different Pressure Drops

Recovery Coefficients For Globe Valves - Most manufacturers usually publish only onepressure recovery coefficient for each style and size of globe valve. The recoverycoefficient applies to all percentages of travel. Typical recovery coefficients for slidingstem valves are Km= 0.7 to 0.8 or FL = 0.8 to 0.9. (Remember that FL2 = Km)Recovery Coefficients Rotary-Shaft Valves - For ball, butterfly, and other high-efficiency(high recovery) valves, the value of the recovery coefficient can vary significantlywith the percent of valve travel; therefore, the recovery coefficient for a specific angleof opening must be used in the sizing equations. Typical values are Km = 0.4 to 0.6and FL = 0.6 to 0.8.




Solving For ∆P Allowable

Rearranging The Equation - The usefulness of the equations to calculate the recoverycoefficient (Equations 7 and 8) becomes more apparent when the equations arerearranged to solve for the flow limiting pressure drop, as shown in Equations 9 and10.

ISA: F

P PP P

Lvc

=−−

1 2

1 arranges to ∆Pchoked = FL2 (P1-Pvc) (9)

Fisher Controls: K

P PP Pm

vc=

−−

1 2

1 arranges to ∆Pallow = Km (P1-Pvc) (10)From the above, it becomes clear that the value of the recovery coefficient can be usedto predict ∆Pchoked for a specific set of service conditions.Problems In Determining Pvc - While Equations 9 and 10 allow the specifier to calculate∆Pchoked, the problem of how to determine the pressure at the vena contracta (Pvc)remains.Calculating Pvc - It has been theoretically established(1) that the Pvc at the choked flowcondition can be estimated as a nonlinear function of the fluid vapor pressuremultiplied by the value of the critical pressure ratio. This hypothesis is included in theAppendix of the ISA Standard S75.01 - 1985. The critical pressure ratio is identified inthe Fisher nomenclature as rc, and it is identified in the ISA nomenclature as FF.Refer to Equations 11 and 12.

Fisher: Pvc=rc Pv (11)ISA: Pvc=FF Pv (12)

Where:FF = rc = The critical pressure ratio.Pv = The vapor pressure of the fluid.

Although the value of rc (FF) is actually a unique function for each fluid and theprevailing conditions, it has been established that data for a variety of fluids can begeneralized, thereby allowing the use of rc (FF) in a wide range of sizing applications.The value of rc can be determined from plots or with the use of a simple equation.

1. Stiles, G.F., "Development of a Valve Sizing Relationship for Flashing and Cavitation Flow", proceedings of theFirst Annual Final Control Elements Symposium, Wilmington, Delaware, USA, Delivered May 14-16, 1970.




Determining The Value Of rc For Non-Water Liquids - For liquids other than water, the plotthat is shown in Figure 12 is used. The ratio of the fluid vapor pressure to the fluidcritical pressure is shown on the X axis. At the point where the vapor pressure tocritical pressure ratio intersects the curve, the critical pressure ratio (rc) is read fromthe Y axis.

1.0

0.9

0.8

0.7

0.6

0.50 .10 .20 .30 .40 .50 .60 .70 .80 .90 1.00

Vapor Pressure - PSIACritical Pressure - PSIA

Citi

cal P

ress

ure

Rat

io -

r c

A4148

Figure 12Critical Pressure Ratios For Liquids Other Than Water

Calculating The Value Of rc For Water - A special rc curve allows the straightforwarddetermination of rc for water (see Figure 13). Vapor pressure is shown on the X axis.At the point where the vapor pressure intersects the curve, the critical pressure ratio(rc) is read from the Y axis.

Crit

ical

Pre

ssur

e R

atio

--r c 1.0

0.9

0.8

0.7

0.6

0.50 500 1000 1500 2000 2500 3000 3500

Vapor Pressure---PSIAA4147

Figure 13Critical Pressure Ratios For Water




Locating Values - The vapor pressure and critical pressure of the fluid may besupplied to the valve specifier in a description of the process, or they may be found inany one of a number of references that give properties of fluids.Equation For rc - An equation has also been developed that allows the specifier tocalculate an approximate value of rc for a variety of fluids (1).

rc = FF = 0.96 - 0.28 (Pv/Pc )1/2 (13)Calculating ∆∆Pchoked (∆∆Pallow) - Because the pressure at the vena contracta (Pvc) can becalculated, the equations to calculate the flow-limiting pressure drop can becompleted. The ISA equations are as follows:

∆Pchoked = FL2 (P1-Pvc) (14)

and Pvc=FF Pv (15)

so ∆Pchoked = FL2 (P1-FF Pv) (16)The Fisher equations (as shown below) are similar in appearance and are functionallyidentical to the ISA equations.

∆Pallow = Km (P1-Pvc) (17)

and Pvc=rc Pv (18)

so ∆Pallow = Km (P1-rc Pv) (19)

Where:FL = The valve recovery coefficient, dimensionless (ISA).FF = The liquid critical pressure ratio factor, dimensionless (ISA).Pv = The liquid vapor pressure, psia.Pvc = The fluid pressure at the vena contracta, psia.Km = The valve recovery coefficient, dimensionless (Fisher and others).rc = The liquid critical pressure ratio, dimensionless (Fisher and others).

1. Reference ISA Standard S75.01-1985




Implementing Choked Flow Equations

ISA Sizing Equation For Choked Flow - The ISA standard includes the followingequations:

q N F Cp F p

GL vF v

fmax =

−1

1

and C

qN F

Gp F pv

L

f

F v=

−max

1 1 (20)Two options are available for use of the equations. If it is known that flow is choked,the equations that are shown above may be used directly. If it has not yet beendetermined if choked flow exists, the specifier may first calculate the ∆Pchoked byusing Equation 16. Then, the lesser of either the actual ∆P or the ∆Pchoked is used inthe basic sizing equations.

Cq

NG

p pvf=

−1 1 2 and q N C

p pGv

f=

−1

1 2

(21)Fisher Controls Sizing Equation - The standard procedure for use of the Fisher equation isto first calculate the allowable pressure drop with:

∆Pallow = Km (P1-rc Pv) (22)The smaller of either the ∆Pactual or the ∆Pallow is then used in the basic sizingequations.

C QGP

v =∆ and

Q CP

Gv=

∆

(23)Iterative Nature Of Sizing Calculations - The procedures that are used to calculate Cvthrough the use of the ∆Pallow are as follows:

1. Using an estimated value of Km(FL), calculate the ∆Pallow.

2. Use the lesser of the ∆Pallow or ∆Pactual to calculate the required Cv.

3. Select a valve size, and determine the percent of travel that will provide therequired Cv. Observe the actual Km (FL) of the selected valve size at the travelthat was just determined.

4. If the actual Km (FL) is different than the estimated Km (FL), use the actualvalue of Km (FL) to recalculate the ∆Pallow, and recalculate the required Cv.

5. Repeat steps 2 through 4 until the estimated Km (FL) is the same as the actualKm (FL).




Piping Geometry

Significance Of Pipe Fittings In Valve Sizing

ISA Standards For Testing Valve Cv - Valve manufacturers determine control valve Cvratings according to ISA test standards. These standards specify the use of test pipingthat is the same diameter as the nominal valve size. In many applications, the valvesize is smaller than the pipe size, and reducers and expanders (swages) are used.Swages can have a considerable effect on valve capacity.Fittings, Pressure Drop, And Flow Rate - The net effect of a reducer, an expander, or thecombination of a reducer and an expander is a reduction in the apparent pressure dropand a corresponding reduction in flow rate. The reduction in flow capacity that resultsfrom the use of swages results in decreased flow and increased valve Cv requirements.

ISA Corrections For Swaged Lines

Piping Geometry Factor FP - The ISA equation uses the piping geometry factor FP toaccount for the flow-limiting effect of swages. For maximum accuracy, FP values mustbe determined by test.Use of FP Factor - The piping geometry factor FP is included in the ISA equations asfollows:

q N F Cp p

GP v

f=

−1

1 2

(24)

Cq

N FG

p pvP

f=−1 1 2 (25)




ISA Standards For Calculating FP - The ISA standard states that when tested values of FPare not available, FP may be estimated as follows:

FP =Σ K Cv

2

N2 d 4 + 1

− 12

(26)Where:

FP = The piping geometry factor, dimensionless.

ΣK = The sum of all loss coefficients, dimensionless.

N2 = A dimensionless units constant for pipe and valve size (N2 = 890 forinches; N2 = 0.00214 for mm); see Figure 4.

d = The inside diameter of the valve inlet, specified in inches or mmaccording to the value of N2.

Calculating K - K is the algebraic sum of all the loss coefficients that influence flowthrough the fittings that are attached to the control valve. The coefficients are:

• Friction coefficients that account for turbulence and friction (K1 and K2)

• Bernoulli coefficients that account for pressure and velocity changes (KB1 andKB2)

Refer to Equations 26 and 27, and to Figure 14.ΣK K K K KB B= + + −1 2 1 2 (27)

Figure 14Flow Limiting Influences Of Reducers And Expanders




Resistance Coefficients K1 and K2 account for the pressure that is lost to turbulence andfriction in the inlet and outlet fittings respectively. K1 and K2 values may be found instandard piping references such as Crane Company's Flow of Fluids Through Valves,Fittings, and Pipe. Alternatively, K1 and K2 can be calculated by means of thefollowing equations:

K1 = 0. 5 1−d2

D12

2

and

K2 =1. 0 1−d2

D22

2

or when D1 = D2

K1 +K2 =1. 5 1−d2

D12

2

(28)

Where:

K1 = The resistance coefficient of the inlet fitting(s).

K2 = The resistance coefficient of the outlet fitting(s).

d = The inside diameter of the valve inlet.

D1 = The inside diameter of the upstream pipe.

D2 = The inside diameter of the downstream pipe.Equation 28 illustrates that the ratio of d to D (valve inlet diameter to pipe diameter) isthe key flow-limiting influence. As D increases relative to d, the flow limiting effectsincrease.Note that the combined equation (to solve for K1 + K2) can be used only when inletand outlet piping are the same size. Note also that all the K terms are dimensionless.

Bernoulli Coefficients K KB B1 2and are used to compensate for changes in pressure thatresult from differences in flow stream area and fluid velocity. Each term is calculatedby means of the following equations:

KB1 =1−dD1

4

and KB2 = 1−d

D2

4

(29)Refer to Equations 27 and 29, and note that for equal size inlet and outlet piping, KB1and KB2 cancel out; therefore, only the terms K1 and K2 are needed.




Valve Geometry - Refer to Equation 30, and note the relationship between the valve Cvand the valve inlet diameter d.

FP =Σ K Cv

2

N2 d 4 + 1

− 12

(30)When isolated from the remainder of the equation, the Cv and d terms can be seen asan indicator of relative valve efficiency, (i.e., a large Cv and a small valve inletdiameter (d) indicates a high efficiency valve such as a ball or butterfly valve).

Relative Valve EfficiencyC

dv=2

(31)Note also that high recovery (high efficiency) valves will result in lower values of FP.Many experienced specifiers examine the ratio of the Cv to inlet diameter to determinewhether or not to account for swage effects. One rule of thumb is expressed by thefollowing:

IfC

daccount for piping factorsv

220≥ ,

(32)

IfC

dignore piping factorsv

2 20≤ , (FP = 1.0) (33)




Equation Analysis - Given the mathematical relationship of the Cv and d terms, it followsthat FP will have the largest impact on high efficiency (high recovery) valves such asrotary valves. Refer to Figure 15 and note that FP will have the greatest effect on flowwhen high efficiency valves are operated near their full rated capacity. Generallyspeaking, swage effects diminish rapidly as valve position is reduced to about 50% ofrated travel.For sliding-stem valves, the impact of swages on control valve sizing is generally inthe range of 2-5 percent. This margin of error is within the accuracy limits of the sizingequation; therefore, swage effects are commonly ignored for low recovery, sliding-stem valves.

Figure 15Piping Factor Effect Vs. Travel For Different Valve Styles




Piping Factors And Choked Flow

Calculating FLP - When a valve is used with swages, the pressure recovery coefficient(FL or Km) is not the same as the coefficient for the valve alone. Section 5.3 of ISAStandard S75.01-1985 describes the use of an additional coefficient FLP. FLP is acoefficient that is the product of the recovery coefficient that has been corrected forpiping factors (FL)P and the piping geometry factor FP as shown in the followingequations:

Cq

N F FG

p pv

P L P

f=−1 1 2( )

(34)and, combining terms:

F F FLP P L P= ( ) (35)therefore:

Cq

N FG

p pvLP

f=−1 1 2 (36)

Where:FP = The piping factor.(FL)P = FL corrected for piping factor.FLP = The combined coefficient for pressure recovery and piping factors.

The ISA Standard states that, for maximum accuracy, the value of FLP should bedetermined by test. The standard also states that if tested values are not available,reasonable accuracy can be achieved with the use of Equation 37.

FLP = FLKi FL

2 Cv2

N2 d4 + 1

− 12

(37)The new term Ki includes the loss coefficient (K1) and the Bernoulli coefficient (KB1)on the inlet side of the valve only.




FLP And Choked Flow - The factor FLP is used to calculate ∆Pchoked as shown inEquation 38.

∆Pchoked =FLPFP

2

P1 − FF Pv( )(38)

Note that the sizing equation (Equation 39) is modified to account for FLP only if flowis choked.

Cq

N FG

p pvLP

f=−1 1 2 (39)

Limitations Of Calculated FLPImprecise Results - For maximum accuracy, the value of FLP must be determined by test.The value of FLP that is calculated through the use of the ISA equation indicates onlyan approximation of swage effects, and it generally over-predicts the impact ofreducers and expanders. The lack of precision is caused by several factors, includingthe following:

• Difficulty in obtaining precise values for the K terms.

• The equations are based on liquid flow across abrupt transitions (as opposed tothe smooth transitions of most expanders and reducers).

• The combined effects of swages and specific valve geometry are not accountedfor.




Iterative Nature Of FP, FLP, And Cv Calculations - When calculating control valve Cvrequirements, the FP and FLP terms are used in the equation to size for Cv; however,the unknown Cv also appears in the equations to solve for FP and FLP. Refer toEquations 40 and 41.When ∆Pactual < ∆Pchoked:

Cq

N FG

p pvP

f=−1 1 2 but

FP =Σ K Cv

2

N2 d4 + 1

12

(40)When ∆Pactual > ∆Pchoked:

Cq

N FG

p pvLP

f=−1 1 2 but

FLP = FLKi FL

2 Cv2

N2 d4 + 1

12

(41)Therefore, several iterations of both equations must be performed as follows:

1. Using an estimated FL (Km) or FLP, calculate the required Cv.

2. Using the Cv that was calculated above, calculate FP or FLP.

3. Using the calculated value of FP or FLP and the actual FL (or Km) of theselected valve, solve for Cv again.

4. Using actual values for FL (Km) and the calculated values for Cv and FP orFLP, repeat steps 2 and 3 until the results converge on a final value of Cv.




Alternate Methods For Calculating Swage Effects

Swage Effects That Are Tested By Manufacturers - According to the ISA standard,maximum accuracy is achieved when the effect of fittings on valve Cv and FL (Km) isdetermined by test for each valve type and line-to-valve size ratio. Manymanufacturers publish rotary valve FL, Km, and Cv values that have been corrected forswage effects.Calculating Swage Effects With Sizing Software - Most valve sizing software includesoptions for calculating FP and FLP factors. The computer can quickly perform theiterations of the calculation that are necessary to arrive at useful (though approximate)results.Section 5.4 of SAES-J-700 states that when no specific vendor data is available for valvesthat are mounted between pipe reducers, a correction factor will be used. The standardincludes a table of correction factors (R) for D/d ratios (pipe diameter to valve size) of1.5 and 2.0 for a variety of valve styles. Refer to Figure 16. The R factors are appliedas follows:

Required Cv =Calculated Cv

R (42)

Valve Type D/d = 1.5 D/d = 2.0

R R

Globe Valves (Flow To Close) 0.96 0.94Globe Valves (Flow To Open) 0.96 0.94Angle Valves (Flow To Close) 0.85 0.77Angle Valves (Flow To Open) 0.95 0.91Ball Valves 0.84 0.80Butterfly Valves 90 Degrees Open 0.77 0.67Butterfly Valves 60 Degrees Open 0.91 0.85

Figure 16R Values That Are Used In The Piping Factor Correction Method

That Is Included In Section 5.4 Of SAES-J-700

R-Value Considerations - Because R factors are derived without consideration for valveCv or the percent of rated travel, the correction will not be as accurate as a correctionthat is calculated with the ISA method. (Recall the significance of Cv/d2). In spite ofthis consideration, the method can provide useful, if approximate, results.




Viscosity Corrections

Flow Regimes

The sizing equations that have been presented to this point are based on the assumption thatthe flowing fluid is turbulent, as opposed to laminar.

Laminar Flow - In laminar flow, the fluid flows in smooth, ordered layers. Refer toFigure 17 below. Fluid velocity is highest in the layers in the center of the pipe, whiledrag forces cause a reduction in the fluid velocity nearer the pipe wall. Laminar flow isalso referred to as viscous flow. Although effects other than fluid viscosity may causelaminar flow, most laminar flow occurs with high viscosity fluids.Turbulent Flow - In turbulent flow, the uniform layers disappear and the flowstream ismade up of turbulent eddies that occur randomly in the fluid stream as shown in Figure17. The flow profile is more blunt, and the velocity at the center of the pipe and thevelocity near the pipe wall are nearly equal.Transitional Flow - Between laminar and turbulent flow, a condition of transitional flowexists. The transitional flow regime has characteristics of both laminar and turbulentflow.

Laminar Flow Turbulent FlowA5615

Figure 17Flow Profiles Of Laminar And Turbulent Flow Regimes




Impact Of Flow Regime On Valve Sizing

Pressure Drop Vs. Flow Rate - The valve specifier's interest in flow regimes centers on therelationship between energy losses in the valve (pressure drop) and flow rate. Forturbulent flow, the standard sizing equation describes a relationship in which the flowrate is proportional to the square root of the pressure drop across the valve as follows:

For Turbulent Flow: Q P∝ ∆ (43)In the laminar flow regime, tests confirm that the flow rate is directly proportional topressure drop as described with the following:

For Laminar Flow: Q P∝ ∆ (44)For fluids in the laminar regime, either a larger valve or a larger pressure drop will berequired to produce a flow rate that is equal to the flow rate of a fluid flowing in theturbulent regime.Depending on the magnitude of the viscous effects, the flow rate of a fluid in thetransitional regime will fall somewhere between the flow rate of a fluid in the laminarregime and a fluid in the turbulent flow regime.

Reynolds Numbers

Inertial And Viscous Influences - The physical quantities that determine the flow regimecan be represented as a ratio of inertial to viscous forces. This ratio is a dimensionlessparameter that is known as the Reynolds number, R. To illustrate the concept, theReynolds number for a straight piece of piping is represented with the following:

RVD

=ρ

µ (45)Inertial influences are:

V - fluid velocityD - pipe inside diameterρ - fluid density

The viscous influence is:µ - fluid absolute viscosity




Influences On Reynolds Numbers - Note that a decrease in fluid velocity, pipe diameter, orfluid density will result in a lower Reynolds number and a tendency toward laminarflow. Also, note that increasing fluid viscosity will result in a lower Reynolds numberand a tendency toward laminar flow.

ISA Equations For Non-Turbulent Flow

Reynolds Number Factor FR - The ISA Standard uses a Reynolds number factor FR toaccount for the effects of viscous flow. The factor FR is included in the basic sizingequation as follows:

q N F Cp p

GR v

f=

−1

1 2

(46)

Cq

N FG

p pv

R

f=−1 1 2 (47)

The FR factor expresses the ratio of the nonturbulent flow rate to the turbulent flowrate that is predicted by the basic sizing equation. Note also that Equations 46 and 47do not include the piping correction factor FP. The effect of valve fittings and swageson nonturbulent flow is currently not well understood; therefore, when the ISAequations are used, the specifier may correct for piping factors or viscous effects, butnot for both.Reynolds Number Vs. Flow Regime - A chart that relates the valve Reynolds number to thevalue of FR helps to illustrate the effect that laminar flow can have on the calculatedflow rate or the control valve Cv. The plot that is shown in Figure 19 illustrates thatwhen the valve Reynolds is 12 000 or larger, the flow is fully turbulent; accordingly,there is no flow limiting effect and the value of FR is 1.0. As the Reynolds numberfalls below 12 000, the flow-limiting effects of laminar flow increase, and the value ofFR decreases.Section 5.5 Of SAES-J-700 requires an evaluation of viscous effects whenever theReynolds number is below 12 000.




Calculating FR - Calculating the value of FR is a two step process.

1. The first step is to calculate a valve Reynolds number, Rev, as shown below:

Rev =N4Fd q

υFL12 Cv

12

FL2 Cv

2

N2d4 +1

14

(48)Note that the equation is iterative because Rev, Cv, and FL are all unknown at thebeginning of the process. Estimates must be made for all values, and, then, severaliterations are performed to arrive at useful results.Note also the use of the term Fd. Fd is a valve style modifier. Currently, the ISAStandard recognizes only two values of Fd. A value of 0.7 is used for double portedglobe valves and for butterfly valves. For all other valve styles, Fd is 1.0.Kinematic viscosity, υ , is expressed in centistokes. If fluid viscosity is specified interms other than centistokes, it is necessary to convert the viscosity to centistokes withthe use of the methods that are shown in the table below:

Viscosity Expressed As: Convert to Centistokes by:

m2/s Multiply m2/s by 106

centipoise divide centipoise by Gf

Figure 18Viscosity Conversion

2. The calculated valve Reynolds number (Rev) is used to enter a plot (see Figure19) that relates Rev to a value of FR. The value of FR is used as shown inEquations 46 and 47.




Figure 19Valve Reynolds Number Vs. The Reynolds Number Factor FR

Other Viscosity Correction Methods

Viscosity Correction Nomograph - To avoid time-consuming calculations, valvemanufacturers provide simplified approaches to obtain low Reynolds number (viscousliquid) correction factors. Fisher Controls provides a simple nomograph that allows thespecifier to compensate for viscous effects when performing flow, pressure drop, andCv calculations. The nomograph uses known inputs of valve Cv, flow rate, and fluidviscosity to arrive at a Reynolds number NR. The value of NR is then used to identify acorrection factor Fv. Fv is used to correct the initial Cv calculation to arrive at acorrected value of Cvr (Cv required ). For purposes of selecting an appropriately sizedcontrol valve, the value of Cvr is used instead of Cv.

Cvr = Fv Cv (49)

Where:

Cvr = The Cv that has been adjusted for fluid viscosity.

Fv = A correction factor, dimensionless, from the Fisher nomograph.

Cv = The uncorrected Cv.Sizing Software such as the Fisher Sizing Program and other sizing programs includeoptions that automatically check for the effects of viscous (laminar) flow. The specifierenters the fluid viscosity along with other service conditions, and the softwareperforms all of the necessary calculations.




Summary Of Valve Sizing Equations

ISA Method

Basic Flow Equation - For nonchoking, turbulent fluids, Cv is calculated with:

Cq

NG

p pvf=

−1 1 2 (50)Choked Flow Sizing Equation - To determine if choked flow exists, the specifiercalculates the ∆Pchoked, compares ∆Pchoked to the actual ∆P, and uses the lesser of thetwo drops for sizing purposes. The ∆Pchoked is calculated as follows:

∆Pchoked = FL2 (P1 - FF Pv) (51)If choked flow exists (∆Pactual > ∆Pchoked), the required valve Cv is calculated with theuse of the following equation:

Cv =qmaxN1FL

Gfp1 −FFpv (52)

Alternatively, the basic flow equation (Equation 50) may be used for choked flowsizing if the ∆Pchoked is used as the sizing pressure drop.Piping Correction For Non-Choked Flow Applications - In applications where the flow is notchoked, the flow limiting effect of piping reducers and expanders is calculated with theuse of the piping correction factor FP as follows:

Cq

N FG

p pvP

f=−1 1 2 where

FP =Σ K Cv

2

N2 d4 + 1

− 12

(53)




Piping Correction For Choked Flow Applications - To compensate for piping factors underconditions of choked flow, a single coefficient FLP is used to compensate for bothchoked flow and piping factors as follows:

Cq

N FG

p pvLP

f=−

max

1 1 2 where

FLP = FLKi FL

2 Cv2

N2 d4 + 1

− 12

(54)Viscosity Corrections FR - The effect of nonturbulent (laminar) flow is included in thesizing equation with the Reynolds number factor, FR, as shown in Equation 55.

Cq

N FG

p pvR

f=−1 1 2 (55)

The value of FR is determined by first calculating the valve Reynolds number with theuse of Equation 56 and, then, locating a value of FR from the chart that was shownpreviously in Figure 19.

Rev =N4Fd q

υFL12 Cv

12

FL2 Cv

2

N2d4+1

14

(56)Only one of the correction factors FR or FP may be used.




Equations Used By Fisher Controls And Others

Basic Flow Equation - The basic flow equation that is used by many manufacturers (referto Equation 57) is similar in form to the ISA equation.

Q CP

Gv=∆

(57)Checking for Choked Flow - The potential for choked flow is investigated by calculatingthe ∆Pallow and comparing the result with the actual ∆P across the valve. If the actual∆P is greater than the ∆Pallow, choked flow exists and the ∆Pallow is used as the sizingpressure drop in Equation 57.The ∆Pallow is calculated with:

∆Pallow = Km (P1-rc Pv) (58)Km values are published in manufacturers' literature. The value of rc can be foundfrom tables or calculated with a simple equation.Piping Corrections - The effect of reducers and expanders on valve capacity isdetermined by testing each type and size of valve with different line-to-body sizeratios. Corrected Cv's are then published for rotary valves. Corrected values of Km arealso published. The effect of reducers and expanders on globe valve capacity andrecovery characteristics is negligible; therefore, no corrections are published or arenecessary.Viscosity Corrections - During a manual sizing procedure, viscosity corrections are easilymade with the use of a nomograph that relates valve Cv, flow rate, and viscosity to acorrection factor Fv. The Cv required (CVR) is calculated by taking the product of thecorrection factor times the calculated Cv (i.e., CVR = Fv Cv).




Computer sizing control valves for liquid applications

Introduction to the Fisher Sizing Program

Benefits Of Computer Sizing Methods

Valve specifiers generally make use of available sizing software that runs on PC's. The manyadvantages of computer sizing include the following:

• Ease and speed of computation

• Computational accuracy

• Elimination of need to remember numerous sizing equations

• The ability to construct a database of fluids and fluid properties

• The ability to save data and sizing calculations on disk

• The ability to generate various reports and specification sheets

Overview Of The Fisher Sizing Program (FSP 1.4)

Sizing Equations - The sizing software that is used in this Module has the ability toperform sizing calculations according to the ISA sizing equations and the equationsthat are used by Fisher Controls and by other manufacturers. The ability to performcalculations with the use of either method will be helpful in demonstrating varioussizing approaches.Generic Sizing Engine - The Fisher Sizing Program uses accepted equations, does notrely on proprietary valve specifications, and calculates results that are useful duringthe selection of any valve - regardless of manufacturer - provided that valve recoverycoefficients are expressed in terms of FL or Km. The flexibility of the softwarebecomes most apparent in special sizing applications.Other Capabilities - The program allows the specifier to select a system of units, to builda database of common fluids and fluid properties, and to print both standard andcustom reports and specification sheets; however, only those features that directlyrelate to valve sizing will be discussed in this Module. Participants with ongoingresponsibility for valve sizing will benefit from exploring other options that areincluded in this software.




Overview of Program Operation

Booting The Program

After the PC is set to the appropriate directory, the program is launched by typing theexecutive (exec) file "FSP" and, then, pressing the ENTER key.

Project Information

After launching the program, a main menu and identification screen appears as shown inFigure 20. This screen allows for specifier identification, project identification, equipment tagnumber, and other information.

Figure 20Main Menu Of The Fisher Sizing Program

Main Menu

A menu at the top of this screen lists several different sizing activities and functions. Thespecifier selects a specific sizing activity by moving the cursor to the desired selection andpressing the ENTER key or by pressing the capitalized letter of the desired activity.

Valve is selected to size control valves, calculate flow rate, or calculate pressure drop.

Ssact is selected to size sliding-stem actuators.

Rotact is selected to size rotary-shaft actuators.

sTroking is selected to calculate actuator stroking time.




rEport is selected to print a report of the service conditions, fluid properties, and theresults of the sizing calculations.sPecsheet - is selected to print out a standard or custom specification sheet.File is selected to import or export text files to or from a specification sheet.Other is selected to gain access to a notepad and other miscellaneous options.Config is selected to change units from English to metric, to select printers, to setatmospheric pressure, and to establish other system and sizing defaults.eXit is selected to quit the program.

Selecting Units

The specifier may select the default engineering units by selecting Config from the main menuand, then, selecting the Units option. See Figure 21. Each entry may be changed individuallyby highlighting it and pressing ENTER. Also, notice the option at the bottom of the screen tomake all units either English (by pressing the F2 key) or metric (by pressing the F3 key).Pressing the F10 key exits this screen.

Figure 21Screen That Appears When The Units Option Under Config Is Selected




Selecting A Valve Sizing Method

When the menu item Valve is selected, the specifier is presented with several options for sizinggasses, liquids, and vapors. Each option uses different equations within the computerprogram. The three available methods for liquid sizing are shown in Figure 22 and aredescribed below.

Figure 22Drop-Down Menu That Lists Valve Sizing Methods

ISA Liquid - When the ISA Liquid method is selected, the software uses the ISA sizingequations.Fisher Liquid - When the Fisher Liquid method is selected, the software uses the samefundamental equations that are used in the ISA method, except that the terms Km andrc are used instead of FL and FF, respectively. In the Fisher Liquid method, there is nooption for calculating FP because piping effects are included in the valve Cv's that arepublished by Fisher Controls.Fisher Water - The Fisher Water method takes advantage of the fact that the SG(specific gravity) and Pv (vapor pressure) for water can be calculated from otherinformation that is entered by the specifier. The Fisher Water method saves timebecause it eliminates the need for the specifier to input values for SG and Pv; however,there is an option that allows manual entry of SG for special circumstances.




Selecting Variables And Conditions

Selecting Variables To Solve For - After a sizing method has been selected, the specifierselects the variable to solve for. Refer to Figure 23. The choices are as follows:

• Valve Sizing and LpA (noise prediction)

• Velocity

• LpA vs. Q (Noise prediction at various flow rates)

• Cv Simple (for estimating Cv with no corrections for choked flow, viscosity,piping, etc.)

Selecting Conditions - On the same screen, the specifier selects whether the sizingcalculations will be performed for the minimum, normal, or maximum flowconditions, or for some other condition (identified by the column header 'OTH').Copying Conditions - The software performs calculations for one service condition (min,norm, max, or OTH) at a time, and the active condition is indicated with a check mark.Parameters for one condition can be copied to another to eliminate redundant entry ofinputs. Copying parameters from one condition to another is performed by pressing thecursor keys until the cursor is on the target condition, pressing ALT C, and selectingthe condition from which data will be copied.

Figure 23Options For Variables To Solve For




Valve Sizing Calculation Screen

Selecting the Valve Sizing and LpA option of the ISA Liquid sizing method brings up the actualsizing screen (shown in Figure 24). This screen is divided into several sections.

Figure 24Calculation Screen For ISA Liquid Sizing

Liquid Properties And State - This section is where the specifier enters the fluid and fluidproperties such as the fluid critical pressure (Pc), vapor pressure (Pv), and specificgravity (SG).Service Conditions - In this section, the specifier enter pressure, flow, and temperatureinformation.Intermediate Results - Any intermediate results such as the calculated values of FF, FR,Rev, or FP are displayed in this area.Valve Specification - In this section, the specifier enters any needed valve data such asthe value of FL. When pipe and valve size are required for calculating FP or FR, theyare also entered in this section.Calculated Results - After all data have been entered, the specifier presses the functionkey F2 to calculate the required valve Cv. The results of the sizing calculations appearin the Calculated Results section. In addition to valve Cv, other important informationsuch as the ∆Pchoked is also shown.




Selecting Calculation Options

The F3 Options Key - At any time, the specifier may choose from several different sizingoptions (see Figure 25) by pressing the function key F3. Options are toggled byhighlighting the appropriate line and pressing ENTER. The option that is visible whenthe option menu is stored (by pressing the ESCAPE key) is the option that will be usedin sizing. The options menu for the ISA liquid sizing method includes the following:

• Line 1: Solve for Cg, Cs, or Cv - Other options: Solve For Flow Rate, SolveFor Pressure Drop

• Line 2: LpA (SPL) OFF - Option: Calculate LpA (SPL)

• Line 3: Omit Fp - Other options: Calculate Fp, input Fp

• Line 4: Viscous Correction OFF - Option: Viscous Correction ON

• Line 5: Pipe: Size/Sched - Option: Pipe: Diameter/Thickness

• Line 6: Input Pv - Option: Calculate Pv (Note that the software can onlycalculate the Pv for fluids for which data have been included in the permanentdatabase; for other fluids, the specifier must enter the Pv.)

• Line 7: Warnings ON - Option: Warnings OFF

Figure 25Calculation Options




As various options are selected, the fields for inputs and for calculated results willchange; for example, if the Viscous Correction option is set to ON, the program willrequire the specifier to input fluid viscosity and valve inlet diameter. In addition, thecalculated values of Rev and FR will be displayed in the Intermediate Results section.Line-By-Line Units Selection - F8 Key - The specifier may change units of measurement forany input parameter by placing the cursor on that parameter and pressing F8. PressingF8 produces a sub-menu that lists all possible choices. Refer to Figure 26. A choice ismade by positioning the cursor on the desired unit and pressing the ENTER key. Theoption that is visible when the option menu is stored (by pressing the ENTER key) isthe option that is used in the program.

Figure 26Pull-Down Menu That Lists Units Options For Q




Pull-Down Menus - F4 Key - Pull-down menu options for several of the input fields canbe accessed by pressing the F4 key; for example, if the cursor is on the field for"Liquid", pressing the F4 key brings down a menu of several different options asshown in Figure 27. Fluids that are preceded with a tilde character (∼) are included in afixed database. The fixed database also includes sufficient data to allow automaticcalculation of the fluid vapor pressure at the service conditions. The fixed databasecannot be edited; however, the software does allow the specifier to construct a separatedatabase of fluids and fluid properties that can be edited.

Figure 27Pull-Down Menu That Lists Fluids In The Sizing Database




Other Important Operations

For basic operation of the software, knowledge of a few special keystrokes is helpful.Escape Key - The escape key serves several functions. When menus are present,pressing the ESCAPE key has the effect of selecting an option and, then, returning tothe calculation screen. Pressing the escape key also allows the specifier to stepbackwards through the various screens.Clearing An Entry Field - F5 - Pressing the F5 key clears the field at the cursor location.Clearing An Entire Screen - ALT F5 - To clear all data on the screen, the specifier pressesthe ALT key together with the F5 key.On-Line Help - F1 - The first time F1 is pressed, a context sensitive help screen appears.The help screen displays information about the procedure that was being performedwhen F1 was pressed. Pressing F1 again brings up an index of topics for which on-linehelp is available. A topic is selected by moving the cursor and, then, pressing theENTER key.Table Of Values - F9 - Pressing F9 displays a table of input parameters and calculatedresults for all flow conditions as shown in Figure 28 below.

Figure 28Table Of Values That Is Displayed When The F9 Key Is Pressed




Computer Sizing control valves for gas and Steam applications

Introduction

Differences In Compressible and Incompressible Fluid Flow

Valve sizing for compressible fluids (gasses and vapors) differs from sizing for non-compressible fluids (liquids) in several ways. The most important difference is that the densityof a gas or vapor cannot be assumed to be constant as it passes through the valve. Instead,density is a strong function of pressure and temperature conditions; therefore, the equationsthat are used to size control valves use several additional terms to account for fluid density.

Use Of Computer Software

Because of the complexity of the sizing equations that are used for compressible fluids,specifiers typically make use of computer programs to perform sizing calculations; however,to ensure the use of proper sizing techniques, specifiers should develop an understanding ofthe terms that are used in the sizing equations.

The ISA Sizing Equations For Compressible Fluids

Popular Standard

The equations that are included in Section 6 of ISA Standard S75.01 are broadly acceptedboth by valve manufacturers and by valve users. The ISA equations are used in virtually allindustries, and they are endorsed in most world areas.

Saudi Aramco Standards

Section 5.1 of SAES-J-700 states that valve sizing procedures shall be based on the equationsthat are included in the ISA standard that is referenced above. Section 5.1 of SAES-J-700 alsoallows the use of vendor-supplied, computer-based sizing software that is based on the ISAequations.

Alternate Forms Of The ISA Equation

The specifier may select from many forms of the ISA equation. The choice of equation formdepends on:

• whether the objective is to calculate fluid flow rate or valve Cv

• whether fluid flow is expressed in terms of volumetric flow or mass flow

• the terms that are used to express fluid density

• the units of measurement (SI or English unit systems)




Mass Flow - To solve for mass flow (w), equations that account for fluid density withspecific weight (γ) or molecular weight (M) are used. These equations are sometimesreferred to as the 'vapor' forms of the equation.

w N F C Y xpp v= 6 1 1γ or

w N F C p YxMT Z

p v= 8 11 (59)

Volumetric Flow - To solve for volumetric flow (q), either specific gravity (Gg) ormolecular weight (M) can be used to account for fluid density.

q N F C p Yx

G T Zp vg

= 7 11 or

q N F C p Yx

MT Zp v= 9 11 (60)

Control Valve Cv - For valve sizing, the equations above are rearranged to solve for Cv.When the fluid flow rate is specified in terms of mass flow (w) and density is specifiedin terms of specific weight () or in terms of molecular weight (M), Cv is calculatedwith the use of one of the following equations:

Cw

N F Y xpv

p=

6 1 1γ or

Cw

N F p YT ZxMv

p=

8 1

1

(61)When the flow rate is specified in terms of volumetric flow (q) and fluid density isspecified in terms of specific gravity (Gg) or molecular weight (M), Cv is calculatedwith the use of one of the following equations:

Cq

N F p Y

G T Z

xvp

g=7 1

1

or

Cq

N F p YMT Z

xvp

=9 1

1

(62)Units Systems - The various N terms in the equations allow the specifier to use thedesired engineering units such as psi or bar for pressure, and scfm or kg/m3 for flowrate.




Nomenclature

The terms that are used in Equations 59 through 62 are described below.

Cv control valve flow coefficientFp piping geometry factor; dimensionlessGg gas specific gravity; dimensionless (i.e., density of gas to density of air at reference

conditions, or ratio of molecular weight of a gas to molecular weight of air)M molecular weight; atomic mass unitsNx constants for units of measure; see table belowpX p1 = static fluid pressure upstream of the valve; p2 = static fluid pressure downstream

of the valve; see the table below for unitsT1 absolute temperature of fluid at valve inlet; degrees K or Rw mass flow rate; kg/h or lb/h - see the table below for units

x pressure drop ratio ∆ p p1 ; dimensionlessY expansion factor; dimensionlessZ compressibility factor; dimensionless

1 specific weight of the fluid at valve inlet; see the table below for units

Numerical Constants

The values of the various N terms are shown below.

Constant UnitsN w q* p1, p2, ∆∆p γγ T1 d, D

N5 0.00241 - - - - - - - - - - - - - - - mm1000 - - - - - - - - - - - - - - - in

N6 2.73 kg/h - - - kPa kg/m3 - - - - - -27.3 kg/h - - - bar kg/m3 - - - - - -63.3 lb/h - - - psia lb/ft3 - - - - - -

N7 4.17 - - - m3/h kPa - - - K - - -417 - - - m3/h bar - - - K - - -

1360 - - - scfh psia - - - °R - - -N8 0.948 kg/h - - - kPa - - - K - - -

94.8 kg/h - - - bar - - - K - - -19.3 lb/h - - - psia - - - °R - - -

N9 22.5 - - - m3/hr kPa - - - K - - -2250 - - - m3/hr bar - - - K - - -7320 - - - scfh psia - - - °R - - -

* cubic feet per hour at 14.73 psia and 60 degrees F, or cubic meters per hour at 101.3 kPa and 15.6degrees C

Figure 29Numerical Constants For The ISA Gas Sizing Equations




Basic Equation

To help develop an understanding of the ISA sizing equations, the complete equation forvolumetric flow (Equation 63) will be stripped to its most basic form, and each term will beexplained as it is added to the basic equation.

q N F C p Yx

G T Zp vg

= 7 11

(63)Flow Rate: A Function Of Pressure Drop Ratio - Recall that for liquid flow, q is a functionof the square root of the pressure drop, as shown below.

q CP

Gv=∆

(64)Similarly, gas flow is a function of pressure conditions and Cv. Over a limited set ofconditions, tests show that the basic relationship between gas flow, Cv, and pressureconditions is as follows:

q C p xv= 1 (65)Where:

xP

p=

∆1 (66)

Equation 65 predicts a flow rate that is a linear function of x as shown in Figure 30.

Figure 30Gas Flow And Pressure Relationships




Choked Flow

Overview Of Choked Flow - The equation that was just shown predicts an increase in flowfor every increase in the value of x; however, when the value of the square root of xbecomes greater than about 0.02, the observed increases in flow rate become less thanthe equation predicts. Refer to Figure 31. Ultimately, there is a point of choked flow.At the choked flow condition, increases in x (by reducing downstream pressure) do notproduce any increase in flow rate. Choking occurs when the jet stream at the venacontracta achieves sonic velocity. The choked flow rate is associated with a flowlimiting value of x, which is known as xT.Pressure Drop Ratio Factor xT - The flow limiting value of x (refer to Figure 31) is calledthe pressure drop ratio factor, or xT (T stands for terminal). The value of xT is relatedto valve style and geometry; therefore, valve manufacturers determine xT values bytest, and they publish them in sizing catalogs and other documents. The values of xTare different for every different valve style and size. xT values also change as afunction of the percentage of valve travel.

Figure 31Choked Flow As A Function Of xT




xT And The Ratio Of Specific Heats Factor - Manufacturers test valves for xT values atstandard conditions and with standard fluids. The test fluid is air. To make the value ofxT meaningful with fluids other than air, the sizing equations account for properties offlowing fluids that are different than the properties of air. One of the significant fluidproperties of any compressible fluid is its specific heat ratio, which is expressed as k. krepresents the ratio of a fluid's specific heat at a constant pressure to its specific heat ata constant volume. When a valve is used with a fluid other than air, the value of xTvalue should be corrected for the specific heat of the flowing gas. The correction factoris called the ratio of specific heats factor and it is referred to as Fk. Fk is simply thespecific heat ratio for the flowing gas (k) divided by the specific heat ratio (k) of air,which is 1.4. Refer to Equation 67.

Fk

k =14. (67)

Where:Fk = The ratio of specific heats factor.k = The specific heat ratio of the flowing gas.1.4 = The specific heat ratio (k) of air at standard conditions.

To correct the value of xT for the ratio of specific heats of the flowing gas, the value ofxT becomes FkxT. The value of xT that is used in any sizing equation should be limitedto the value of FKxT.Locating k Values - k values are included in many standard references such as the GasProcessor's Handbook, and they are also included in the fluid databases of manysizing programs. Specifiers should note that k values vary with service temperature,and that these values can change dramatically (generally increase) at hightemperatures.




Use Of FKxT - To prevent overpredicting flow or undersizing valves, the value of x thatis used in any of the sizing equations must not exceed the value of FKxT. Refer toEquation 68.

q C p xv= 1 becomes q C p F xv K T= 1 (68)Effect Of Fk on XT - Refer to Figure 32 and note that larger values of k result in highervalues of FKxT, and vice versa. The values of qmax are similarly affected. Note that theeffects that are shown are exaggerated to help illustrate the concept.

Figure 32Effects Of k On FKxT And qmax

Us Of FK In Valve Sizing - Many hydrocarbon gasses and vapors have k values that rangefrom 1.2 to 1.5 at moderate temperatures. k values in this range typically have a verysmall impact on valve sizing; therefore, many specifiers ignore the specific heatcorrection when k is between 1.2 and 1.5, and they assume that FK is equal to 1.0.




Expansion Factor: Y

Application of x and xT - At the beginning of this discussion, the basic gas flow equationwas presented as:

q C p xv= 1 , where x

pp

=∆

1 (69)

It has been shown that the x can be used to predict flow when x < 0.02, that chokedflow can be predicted when x is limited to xT, and that xT can be further modified toaccount for the thermodynamic properties of the fluid. Refer to Equation 70.

q C p F xv K T= 1 (70)

The equations above do not express the non-linear relationship between x and q inthe region where x>0.02 and x<Fk xT. Refer to Figure 33.

q Versus x When x > 0.02 and x < FKxT - The expansion factor, Y, is included in the ISAequations to account for the relationship of q to x when x > 0.02 and x < FKxT. Theexpansion factor (Y) helps to account for the following:

• Changes in fluid density that result from increased fluid velocity and reducedfluid pressure at the vena contracta.

• The effect of vena contracta enlargement.

These conditions are discussed in the following sections.

Figure 33Pressure And Flow Relationships As x Increases From 0.02 To xT




Density Changes - As the value of x increases, fluid velocity at the vena contracta increases andfluid pressure decreases. See Figures 33 and 34. The reduction in local fluid pressure causesthe fluid to expand, which results in a reduction in fluid density. Because fluid densitydecreases with each incremental increase in x, incremental increases in x no longer produceproportional increases in flow rate.

Figure 34Reduced Pressure PVC Leads To Reduced Fluid Density And Reduced Flow




Vena Contracta Enlargement - When the fluid velocity becomes sonic, a shock wave iscreated that limits velocity to a maximum (terminal) value. Flow rate becomes afunction of sonic (terminal) velocity and the effective flow area at the vena contracta.Refer to Figures 33 and 35.

Figure 35Effect of Sonic Velocity On Flow




After the fluid attains sonic velocity, a decrease in P2 may produce a limited increasein flow rate, depending on the valve style. The increase in flow rate occurs because anincrease in x reduces backpressure and causes the vena contracta to move upstream tothe valve throat as shown in Figure 36. The flow area at the valve throat is typicallylarger than the flow area of an unconstrained vena contracta that is located in thepiping downstream of the control valve; therefore, some increase in flow rate mayoccur.

Figure 36Effect of Vena Contracta Enlargement

Inclusion Of Y In Sizing Equations - The ISA equation accounts for the conditions listedabove by means of the expansion factor Y. The Y term is used in the sizing equationas follows:

q C p Y xv= 1 (71)




Calculating Y - Y can be taken as a linear function of x. The equation to calculate Y isas follows:

Yx

F xK T= −1

3 (72)Relationships of x, xT, Fk, And Y - The relationships between the values of x, xT, and Yare best shown graphically as in Figure 37. Note that the value of Y will always fall ina range between 0.67 and 1.0.

Figure 37Relationships Among x, FkxT, And Y

Basis For Y - For compressible fluids, the expansion factor can be defined as the ratio ofthe flow coefficient for a gas to the flow coefficient for a liquid. When the value of Yis 1.0, there is no difference in the liquid and gas flow coefficients. Values of Y thatare less than 1.0 indicate a flow limiting effect due to density changes that result fromfluid expansion.In other words, as x approaches zero (very low pressure drop ratios), flow resemblesthat of an incompressible fluid (a liquid); accordingly, fluid expansion has a smalleffect on flow, and Y approaches 1.0. As x approaches xT, the fluid becomes lessdense. The expansion factor Y becomes smaller to account for the reduction in density.As x approaches xT, Y approaches 0.67, thereby signaling the maximum flow-limitingeffect of fluid expansion and the presence of choked flow.




Dimensionless Terms - Refer to Equation 72 and note that all of the terms that are used tocalculate Y are dimensionless; therefore, Y is also dimensionless.Equation Development - At this point of discussion, the flow equation takes the form:

q C p Y xv= 1 (73)This equation:

• predicts flow at low pressure drop ratios (p x1 )

• predicts critical flow (with the use of xT)

• predicts the effect of density changes that result from fluid expansion due tolow pressure at the vena contracta.

Adapting The Equation For Use With Gasses Other Than Air

Ideal Gasses - The equation that has been discussed to this point (Equation 73) is basedon the flow of air at standard conditions. It can be generalized for any gas at anytemperature with a simple modification to account for fluid specific gravity andtemperature as shown in Equation 74.

q C p Yx

G Tv

g= 1

1(74)

Where:Gg = The specific gravity of the flowing gas; the ratio of the density of the gas

at the valve inlet to the density of air, where both the flowing gas and thereference fluid (air) are at standard conditions of 60 degrees F and 14.7psia.

T1 = The absolute temperature of the fluid at the valve inlet in degrees Rankineor in Kelvin.




The manner in which fluid density is included in the gas sizing equations is differentthan the method that is used for liquid sizing. Recall that for liquid sizing, fluid densityis included in the equation as the actual SG of the liquid at the valve inlet; that is, theSG of the liquid must be corrected for temperature before the sizing equations areused.For gas sizing, the fluid density that is used in the sizing equations is the fluid densityat standard conditions (i.e., 14.7 psia and 60 degrees F). The sizing equation correctsthe density for the flowing conditions according to the ideal gas law, which states that:

pV = RT (75)Where:

p = The absolute fluid pressure, psia.V = The specific volume (e.g., m3/kg, ft3/lb, etc.).R = A gas constant that is unique for each fluid.T = The fluid's absolute temperature, Kelvin, degrees Rankine, etc.

The relationships that are shown in Equation 75 are valid only for gasses that followthe ideal gas law.Note also that the correction is not necessary when the mass flow forms of theequation are used, and density is expressed in terms of specific weight () at the valveinlet (e.g., lbs/ft3, kg/m3, etc.).




Real Gas Behavior

Real Versus Ideal Gasses - Many gasses and vapors do not behave according to ideal gaslaw of pV = RT, and those gasses that do not exhibit ideal gas behavior are referred toas real gasses. The most significant aspect of real gas behavior is that specific volume(V) may not change as a linear function of either temperature or pressure, i.e.:

VRTp

≠(76)

Non-linear changes in the relationships between p, V, and T are a result of aphenomenon known as compressibility. Valve specifiers are interested incompensating for the effects of fluid compressibility because of the direct relationshipof fluid specific volume to fluid density and because of the impact of fluid density onflow and Cv calculations. To obtain precise results when calculating Cv or flow rates,the compressibility factor Z must be included in any equation where the specificweight is a computed value. The correction for fluid compressibility is not necessarywhen density is expressed in terms of specific weight at the valve inlet (e.g., lbs/ft3,kg/m3, etc.).Compressibility Factor Z - For real gasses at a specific set of service conditions, theeffects of compressibility can be calculated with the use of the compressibility factor,Z.

pV = ZRT (77)The compressibility factor is included in the basic flow equation to correct for thebehavior of a non-ideal gas as follows:

q C p Yx

G T Zvg

= 11 (78)

Note that a compressibility factor of 1.0 indicates ideal gas behavior (i.e., there are nocompressibility effects), whereas a lower value of Z (e.g., Z= 0.8) would indicate atendency toward incompressible (liquid) flow. Also, note that lower values of Z willresult in an increase in flow (q).Application Of Z Factor - The correction for fluid compressibility is not necessary whenthe flowing gas displays ideal gas behavior or when fluid density is expressed in termsof specific weight.




Calculating Z - Z can be determined in many ways. One popular approach is to calculatethe reduced pressure (pr) and the reduced temperature (Tr) and, then, to locate thevalue of Z from a generalized compressibility chart (refer to Figure 38). As shown inEquation 79, the reduced pressure (pr) is the ratio of inlet pressure to the fluid criticalpressure, and the reduced temperature (Tr) is the ratio of inlet temperature to the fluidcritical temperature. All values are expressed in absolute units.

ppp

rc

= 1

and T

TT

rc

= 1

(79)

To determine the value of Z, the value of pr is located on the X axis. At the pointwhere pr intersects the appropriate Tr plot, the value of Z is read at the Y axis of thechart.

Figure 38Generalized Compressibility Chart

Maximum Impact Of Z - Refer to Figure 38 and note that compressibility effects becomemost significant when the inlet pressure approaches the fluid critical pressure (i.e., aspr approaches 1.0), and/or as the inlet temperature approaches or falls below the fluidcritical temperature.




Piping Effects

Piping Factor FP - When expanders and reducers are used, the piping factor FP isincluded in the equation as shown below:

q F C p Yx

G T Zp vg

= 11 (80)

The following equation is used to calculate Fp. The equation is the same equation thatis used for liquids.

Fp =Σ K Cv

2

N2 d4 + 1

− 12

(81)XT Plus Piping Factor FP = xTP - The value of XT is also affected by inlet reducers.Outlet expanders are considered as part of the valve for purposes of determining XT.When the factor XT is modified to account for an inlet reducer, it becomes xTP, and itis calculated with the following:

xTP =xT

Fp2

xT Ki Cv2

N5d4 + 1

−1

(82)Where:

Ki = The inlet loss coefficients only (K1 + KB1).Effect of XTP On Valve Sizing - The use of inlet reducers rarely affects the value of xTsignificantly; therefore, it is often ignored, except in the case of large, highly efficientvalves. Experienced specifiers often ignore the effect of inlet reducers on xT exceptwhen the ratio of Cv to d (ratio of valve capacity to valve size) becomes very large (asit does with ball and butterfly valves), and the valve inlet is much smaller than the pipesize. In these situations, the value of x that is used in the sizing equations should belimited to the value of xTP.




Calculating XTP - The equation that is used to calculate control valve Cv through the useof the xTP factor (see Equation 83) is highly iterative. Note that the equation tocalculate Cv requires the terms Fp and xTP; however, the equations that are used tocalculate Fp and xTP both include the Cv term. Therefore, an estimated value of Cvmust be calculated (without consideration of Fp and with the use of xT instead of xTP).The estimated Cv is then used to initially solve for both Fp and xTP. The calculatedvalues Fp and xTP are then used to solve for Cv. Several iterations of the equationsmust be solved until the solutions converge on a useful result. Generally speaking,only two or three iterations are necessary to arrive at a useful result. When successiveiterations of the calculations result in very small differences in the calculated Cv, thespecifier knows that accuracy has been achieved

Cq

N F p Y

G T Z

xv

p

g

TP=

7 1

1

(83)

but

Fp =Σ K Cv

2

N2d4 + 1

− 12

and

xTP =xT

Fp2

xT Ki Cv2

N5d4 + 1

−1

(84)

Although manual sizing involves the use of many calculations, the necessarycalculations are performed easily and quickly with personal computers and appropriatesoftware.




Final Equation Form

Numerical Constants - The final term in the ISA equation is the term N7, or the unitsconstant. The specifier selects a units constant that allows use of either the metric orthe English units system.

q N F C p Yx

G T Zp vg

= 7 11

(85)

Solving For Cv - For purposes of valve sizing, Equation 85 is arranged to solve for Cv asfollows:

Cq

N F p Y

G T Z

xvp

g=7 1

1

(86)

Summary Of ISA Equation Terms

Following is a quick review of terms in the equation.

q flow rate (scfh, lbs/hr, kg/hr depending on the units constant, N7)

N2 units constant that is used in the equation to calculate Fp; N2 allows pipe and valveinside diameters to be expressed in mm (N2=0.00214) or in inches (N2=890); refer toFigure 4

N5 units constant that is used in the equation to calculate XTP; N5 allows pipe and valveinside diameters to be expressed in mm (N2=0.00214) or in inches (N2=890); refer toFigure 29

N7 units constant to determine units for pressure, flow, and temperature measurements;refer to Figure 29

Fp piping geometry factor, dimensionless

Cv control valve flow coefficient

p1 inlet pressure, absolute

Y expansion factor. Y

xF xk T

= −13 where Fk = ratio of specific heats factor

Gg gas specific gravity (ratio of the density of the flowing gas to the density of air, withboth at standard conditions)

T1 inlet temperature, absolute

Z compressibility factor, dimensionless

x pressure drop ratio ( ∆P p/ 1); limited to xT for choked flow, FKxT to account forspecific heat ratio, and xTP to correct for piping factors




Computer Sizing Control Valves For Gasses Using The ISA Equations

Introduction

The procedures that are used to operate the Fisher Sizing Program when sizing control valvesfor compressible fluids are similar to the procedures that are used with the liquid sizingmethod. The major differences are the required inputs, the entries in the Intermediate Resultssection, and the results that are displayed in the Calculated Results section.

Valve Sizing Methods Available

When the main menu item Valves is selected, the specifier is presented with several sizingoptions as shown in Figure 39. The ISA options are as follows:

ISA Gas - Selecting the ISA Gas method causes the software to use the equations inwhich fluid density is expressed in terms of SG or M.ISA Vapor - Selecting the ISA Vapor method causes the software to use the equations inwhich fluid density is expressed in terms of specific weight (e.g., lbs/ft3. kg/m3, etc.)The Vapor method calculates the most accurate results with the fewest inputs.

Figure 39Valve Sizing Method Options




Selecting The Desired Calculation Type

After a valve sizing method has been selected, the specifier selects the type of calculation thatwill be performed. Refer to Figure 40. Choices include valve sizing, fluid velocitycalculations, and various noise calculations.

Figure 40Available Calculation Types

Overview Of Sizing Procedures

Valve Sizing Screen - Selecting the Valve Sizing & LpA option brings up the sizingscreen. This screen is divided into several sections as shown in Figure 41 below.

Figure 41Valve Sizing Screen For The ISA Gas Valve Sizing Method




Fluid And Service Conditions - In this section, the specifier enters the fluid type, and fluidproperties such as critical pressure, critical temperature, and Fk. Service conditions arealso entered in this section.Intermediate Results - Any intermediate results that the software calculates are displayedin the Intermediate Results section. Examples include the calculated values of Y and Z.Valve Specification - In this section, the specifier enters any needed valve data such as xTand sizing data for the valve and piping if piping corrections are necessary.Calculated Results - After all fluid properties, service conditions, and valve data areentered in the appropriate locations, the specifier presses the function key F2 tocalculate the required control valve Cv. The results of the sizing calculations appear inthe calculated results section. In addition to valve Cv, other important information suchas the ∆Pchoked and the pressure drop ratio (x) is also shown.

Selecting Options

F3 Options - During the sizing procedure, the specifier may choose from severaldifferent sizing options by pressing the function key F3. The options menu for the ISAGas method is shown in Figure 42. Options are toggled by highlighting the appropriateline and pressing enter. The option that is visible when the option menu is stored (bypressing the escape key) is the option that will be used.

Figure 42Calculation Options For The ISA Gas Valve Sizing Method




F3 Options For The ISA Gas Sizing Method - Options for the gas sizing method are asfollows:Line 1: Solve for Cg, Cs, or Cv. Other options: Solve For Flow, Solve For dP(pressure drop)

Line 2: Calculate Z. Option: Input Z

Line 3: Calculate Fp. Other options: Input Fp & Xtp, Omit Fp & Xtp

Line 4: LpA (SPL) OFF. Option: Calculate LpA (SPL)

Line 5: Pipe: Size/Sched. Option Pipe: Diameter/Thickness

Line 6 Warnings ON. Option: Warnings OFFF3 Options For The ISA Vapor Sizing Method - Options for the vapor sizing method are thesame as for the gas method, except that there is no option for calculating Z. Recall thatcompressibility effects are not considered when the vapor form of the equation.Options And Input Fields - As various options are selected, the input fields on the sizingscreen will change; for example, if the option to calculate Z is selected, the softwarewill require values for critical pressure and temperature, and it will display thecalculated value of Z.Units-Selection - As explained previously, engineering units can be changed globallythrough the selection of Units from the Config heading on the main menu. The specifiermay also change units for any input parameter by placing the cursor on that parameterand pressing F8. Pressing F8 produces a sub-menu (refer to Figure 43) of availableoptions.

Figure 43Line-By-Line Units Options For Flow




The Fisher Universal Gas Sizing Equation

Introduction

Many valve specifiers use the Fisher Universal Gas Sizing Equation as an alternative to theISA equations. The Fisher Universal Gas Sizing Equation gained popularity immediately afterits introduction in 1951 because it was easier to use than other techniques that were availableat that time. During this era, specifiers sized valves manually, either by calculation or withslide rules. At a later date, the programmable calculator gained popularity for valve sizing.The Universal Gas Equation was easily adapted for use with the programmable calculatorbecause of its straightforward, non-iterative nature. Today, control valve specifiers size valveswith computers and sizing software; accordingly, equation complexity is less of an issue.

Fisher And ISA Equation Comparison

While the Fisher and ISA equations differ in many ways, they both model the gas flowprocess in a similar fashion and they give nearly identical results. With rare exception, anydiscrepancies in calculated results are within the limits of accuracy of any sizing technique. Invirtually all instances, either equation will direct the specifier to the same valve size.Key differences between the Fisher and ISA equations include the following:

• For gasses and vapors, the Fisher equation uses the flow coefficient Cg, rather than Cv.Cg relates critical flow to absolute inlet pressure.

• The Fisher equation uses a sine term to account for fluid expansion in the regionbetween linear flow and choked flow. This approach eliminates the need to calculatethe value of an expansion factor (Y).

• Terms to account for the influences of piping factors, compressibility, and specificheat ratios other than 1.0 are not included in the basic equation; instead, they areconsidered on an as-needed basis.

The Fisher Universal Sizing equation for an ideal gas is as follows:

Q =520GTZ

Cg P1C2 SIN3417C1C2

∆P

P1

Degrees (87)




Equation Basics

To gain an understanding of equation mechanics and the terms that are used in the equation,the equation will be discussed by starting with its most basic form.

Basic Liquid Flow Equation - All early efforts to derive a useful gas sizing equation beganwith the basic liquid sizing equation (see Equation 88).

Q CP

GGPM v( ) =

∆

(88)Adding A Constant To Change From GPM To SCFH - The first step in adapting theequation for use with compressible fluids is to add a conversion factor to change unitsfrom gallons-per-minute to cubic-feet-per-hour. In addition, specific gravity is relatedin terms of pressure, which is more meaningful for gas flow. Refer to Equation 89.Note that the ratio of ∆P to P1 is known as the pressure drop ratio and that the pressuredrop ratio is identical to the x term in the ISA equation. The result is as follows:

Q C PP

Pscfh v=59 64 1

1.

∆

(89)Provisions For Any Specific Gravity And Temperature - With the inclusion of a modificationthat is based upon Charles' Law for gasses, the equation is generalized to account forany gas at any temperature as shown in Equation 90.

Q C PP

P GTscfh v= 59 64520

11

.∆

(90)Where:

520 = The product of the specific gravity and the absolute temperature of air atstandard conditions (i.e., the specific gravity is 1.0 and the temperature is520 degrees Rankine, which corresponds to 60 degrees F).

G = The specific gravity of the flowing gas at standard conditions (60 degreesF and 14.7 psia).

T = The temperature of the flowing gas in degrees Rankine.




Equation Limits

Pressure Drop Ratio Limits - Equation 90 predicts a flow rate that is a linear function ofthe square root of the pressure drop ratio (the same as the flow rate that is predicted bythe x term in the ISA equation); however, at pressure drop ratios that are greater thanapproximately 0.02, tests show smaller and smaller incremental increases in actualflow for every incremental increase in the pressure drop ratio. Refer to Figure 44.Critical Flow - Tests also indicate a point of critical flow, which is the same as chokedflow in ISA terminology. Critical flow is defined as the point where increasing thepressure drop ratio by reducing downstream pressure does not produce any increase inflow rate.

Figure 44Actual Flow Versus Predicted Flow




Pressure Recovery And Critical Flow

The next challenge was to determine a method that could be used to predict the critical flowrate. As it turns out, critical flow is a function of valve geometry. A comparison of plots thatrelate critical flow to the pressure drop ratio for two different valve styles illustrates theconcept. Refer to Figure 45. Note that the two valves have identical Cv ratings, but one of thevalves is a high recovery type and the other valve is a low recovery type.

Figure 45Critical Flow For Low And High Recovery Valves

Low Recovery Valves (or globe style valves) reach critical flow at a pressure drop ratioof approximately 0.5.High Recovery Valves reach critical flow at much lower pressure drop ratios.Flow Coefficient Cg and Critical Flow - Because of the problems in using Cv to predictcritical flow in both high and low recovery valves, Fisher Controls developed astandard for testing flow capacity with air as well as with water. From these tests, a gassizing coefficient Cg was defined that relates gas critical flow to the absolute inletpressure. Cg is experimentally determined for each valve style and size; therefore, Cgcan be used to accurately predict critical flow (using air as a test fluid) with thefollowing:

Q C Pcritical g= 1 (91)To make the critical flow equation useful for any gas at any temperature, thecorrection factor that was shown previously is applied:

Q C PGT

critical g= 1520

(92)




Blending The Two Equations

Impracticality Of Using Two Equations - At this point, Fisher had two equations. SeeFigure 46.Equation A (see Equation 93) accurately predicted flow at very low pressure dropratios only. Note that this equation uses the flow coefficient Cv.

Q C PP

P GTv=59 64520

11

.∆

(93)Equation B (see Equation 94) predicted critical flow only. Note that this equation usesthe flow coefficient Cg.

Q C PGT

critical g= 1520

(94)Although the equations provided utility, neither equation accounted for the transitionregion between low flow conditions and critical flow; i.e.,when ∆P/P1 > 0.02 and Q < Qcritical. In addition, the process of using two equationsand two flow coefficients was inefficient.

Figure 46Predicting Low Flow And Critical Flow




Tests And Data Plotting - To arrive at a single equation, Fisher Controls completed anextensive testing procedure to analyze flow versus pressure relationships in the regionbetween low pressure drop ratios and critical (choked) flow. Tests were performed onhigh recovery valves, low recovery valves, and valves that can be called intermediaterecovery valves. Test results were normalized with respect to critical flow, and datawas plotted.Sine Curve - Analysis revealed that the test points in the transition region between lowflow and critical flow fell on a curve that closely approximates the first quarter cycleof a standard sine curve. See Figure 47 below.

Figure 47Tested Values Of Flow Compared To A Sine Curve

Combining The Equations - Capitalizing on this finding, Fisher Controls used a sinefunction to mathematically model flow in the transition region. The sine functioneffectively blends Equation 93 and Equation 94 into one, as shown in Equation 95.Note that the result of the sine function must be limited to a maximum of 90 degreesso that the equation does not predict decreasing flow after critical flow is achieved.

Q =520GT

CgP1SIN3417

C1

DP

P1

Degrees (95)




The C1 Factor

Note the inclusion of the C1 factor in Equation 96.

Q =520GT

CgP1SIN3417

C1

∆P

P1

Degrees (96)

Role of C1 - The role of C1 is to allow the use of a single sizing coefficient (Cg) in auniversal equation that combines the equation that is used to calculate the flow ofincompressible fluids (Equation 97) with the equation that is used to calculate thecritical flow of a gas (Equation 98). A fundamental obstacle in blending Equations 97and 98 is that the liquid flow equation uses the flow coefficient Cv, while the gas flowequation uses the flow coefficient Cg.

Liquid Flow Q C P

PP GT

v=59 64520

11

.∆

(97)

Gas Flow

QGT

C Pg=520

1

(98)Equations 97 and 98 could have been combined in their original forms; however, thespecifier would have to supply both the Cv coefficient and the Cg coefficient. Duringthe development of the Fisher equation, the decisions were made that a singlecoefficient would be used and that a factor to account for the differences in liquid andgas flow through a particular valve would be included in the equation. The factor C1 isused for this purpose. As shown in Equation 99, C1 is defined simply as the ratio ofthe gas flow coefficient, Cg to the liquid flow coefficient, Cv.

CC

Cg

v1=

(99)




Differences In Gas And Liquid Capacity - In order to better understand the significance ofthe C1 term, consider a comparison of the Cg and Cv flow coefficients for a highrecovery valve, and the Cg and Cv flow coefficients for a low recovery valve that areshown in Figure 48.Liquid flow (Cv) is heavily influenced by valve geometry (i.e., whether the flow pathis tortuous or streamlined). Gas flow (Cg) is largely a function of the flow area of thevalve. The difference in the factors that determine capacity for liquid flow and for gasflow explain why two valves with identical Cg's can have substantially different Cv's(and why two valves with identical Cv's can have substantially different Cg's).

TYPICAL C1 VALUES FOR HIGH AND LOW RECOVERY VALVES

High Recovery Valve Low Recovery Valve

Cg = 4680 Cg = 4680

Cv = 254 Cv = 135

C1 = Cg/Cv = 4680/254

=18.4

C1 = Cg/Cv =4680/135

=34.7

Figure 48Comparison of Cv, Cg, and C1 Values

Locating C1 Values - Manufacturers that use C1 values determine them by test, and theypublish them in sizing catalogs along with other sizing information. For globe valves,the value of C1 is the same at all percentages of travel. For rotary-shaft control valves,the value of C1 depends on the degrees of rotation.




Mechanics Of The Sine Term

Concept - A close look at the sizing equation reveals that the quantity of the sinefunction is essentially used as a multiplier with the simple equation for critical flow.Refer to Equation 100.

Q =520GT

CgP1 SIN3417

C1

∆P

P1

Degrees

(100)Predicts Qcritical Serves as a multiplier

Low Pressure Drop Ratio Example - Assuming a C1 value of 35 and a pressure drop ratioof 0.02, the value of the bracketed terms is as follows:

SIN3417

35

0. 02

Degrees

=SIN 98 × 0.141[ ]Degrees = SIN 13 0 225= .

(101)The flow rate that is predicted by the critical flow equation is multiplied by 0.225;therefore, the calculated value of Q will be relatively small.Higher Pressure Drop Ratios - As the pressure drop ratio increases, the sine function, atthe end of the first quarter cycle, tends towards its maximum value of 1.0. If the resultof the sine function is 1.0, the equation is functionally reduced to the equation forcritical flow as illustrated in the following equation.

If

Q =520GT

CgP1SIN3417

C1

∆P

P1

Degrees and

∆PP1

1 0= .102)

then SIN

341735

1

≈ SIN 90° =1. 0

and Q

GTC Pg=

5201

(103)Intermediate Pressure Drop Ratios - At intermediate pressure drop ratios, the sine functionmodels flow in the transition region between low flow and critical flow.




Alternate Forms Of The Universal Sizing Equation

Ideal (Perfect) Gas Law Assumptions - The equation that has been discussed to this point isbased on the ideal gas laws. As was discussed previously, real gas behavior can differmarkedly from ideal behavior.Real Gasses - The real gas form of the Fisher equation uses two correction factors. Thecorrections are for compressibility and for the ratio of specific heats. Both correctionsare similar to the real gas corrections that are used in the ISA sizing equations.

The Z Factor And Real Gas Compressibility - When the compressibility of a real gasdoes not follow the ideal gas law of pV = RT, the term Z is used to correct theideal gas equation.

pV = ZRT (104)The value of Z can be determined from generalized compressibility charts(refer back to Figure 38) after establishing the reduced pressure andtemperature with the use of the following equations:

PPP

and TTTreduced

actual

criticalreduced

actual

critical= =

(105)The Z term is included in the equation as follows:

Q =520GTZ

Cg P1SIN3417

C1

∆P

P1

Degrees (106)




C2 And The Ratio Of Specific Heats - In the Fisher equation, allowance is made forthermodynamic properties (the ratio of specific heats) with the term C2. C2serves the same function as the Fk factor in the ISA equations. C2 is included inthe equation as follows:

Q =520GTZ

Cg P1C2 SIN3417C1C2

∆P

P1

Degrees (107)

In the ISA equation, the Fk factor suggests a linear relationship between k andFk (i.e., Fk = k/1.4). This relationship is typically valid for k values between 1.2and 1.6 only. The Fisher equation uses a somewhat more precise correction.Although C2 values are found to be a strong function of k, the relationship isnot precisely linear. For a specific value of k, the specific value of C2 can bedetermined from the chart that is shown in Figure 49.

Figure 49C2 Factor Versus k




Density Form Of Equation (Mass Flow/Vapor) - When the specific weight (weight per unitof volume) of the fluid at the valve inlet is known, a more generalized form of theequation can be used. The density form of the equation, (see Equation 108) eliminatesthe need to correct for the effects of pressure and temperature on density, and it alsoeliminates the need for the Z term.

Q =1. 06 d1P1 Cg SIN3417

C1

∆P

P1

Degrees (108)

Where:Q = Gas, steam, or vapor flow (lbs/hr, kg/hr, etc.).d1 = The density of the gas at the valve inlet (lbs/ft3, kg/m3, etc.).

The density form of the equation is commonly used for steam and other vaporapplications.Special Steam Equation (Below 1000 PSIG) - Because steam applications are quitecommon, a special form of the equation, which is shown in Equation 109, is alsoavailable.

QLB/HR =Cs P1

1+ 0. 00065 Tsh

SIN3417

C1

∆P

P1

Degrees (109)

Where:Cs = The steam sizing coefficient.Tsh = The degrees of superheat (degrees F).

Note that Equation 109 uses the flow coefficient Cs (s is for steam). Fisher Controlspublishes Cs values for most valves. The relationship between Cs, Cg, and Cv is asfollows:

CC

sg=

20 therefore C C xg s= 20

(110)Note also that Equation 109 can be used only for steam below 1000 psig.




Solving for Cg

Rearranging The Equations - While the equations have been discussed in forms thatpredict flow rate, any of the equations that are used to predict flow can be arranged tosolve for the required control valve Cg as shown in Equation 111.

Cg =Qscfh

520GTZ

P1C2 SIN3417C1C2

∆PP1

Degrees (111)

Initial Assumptions For C1 Values - When solving for Cg, the specifier must initiallyselect a valve style and estimate a value of C1. After calculating Cg and selecting aspecific valve type and size, the actual C1 values for the selected valve are used in theequation to ensure maximum accuracy. Specifiers typically use initial (estimated) C1values of approximately 35 for standard globe style valves, and C1 values ofapproximately 15 to 20 for ball and butterfly valves.Converting Cg To Cv - It may occasionally be desirable to convert a flow coefficientfrom Cg to Cv; for example, it may be useful to size non-Fisher valves by means of theFisher Sizing Program, or it may be useful to convert Cg to Cv for comparative studiesof capacity or other valve attributes. Recall that C1 is calculated as follows:

CC

Cg

v1=

(112)Therefore, after a Cg has been calculated, it can be converted to Cv as follows:

CC

Cvg=1 (113)




Comparison Of Fisher And ISA Gas Sizing Equations

Both the ISA and the Fisher equations model the same process and typically produce nearlyidentical results. Although minor differences in the calculated flow coefficient may occur, theuse of either equation will virtually always lead the specifier to the same valve size. The tablebelow summarizes how the two equations account for various aspects of flow through thecontrol valve.

Parameter ISA Equation Fisher Equation

Flow equationq N F C p Y

xG T Zp v

g= 7 1

1Q =

520GTZ

Cg P1 C2 SIN3417C1C2

∆PP1

Degrees

Flow Coefficient Cv (water test) Cg (air test) C

C

Cvg=1

Flow when∆P p/ .1 0 02≤ C

Ppv∆

1 (liquid equation)C

Ppv∆

1 (liquid equation)

Critical Flow ForSpecific ValveStyle

p xT1

Published xT tested bymanufacturer

p1 CgPublished Cg tested at criticalflow

Fluid Expansion Y x Sine function

Piping Factor FP factor

Calculated by specifier ortested and published bymanufacturer

Swaged capacities for rotary-shaft valves published in sizinginformation

Can use FP

Compressibility

(real gasses)Z

pVRT

= ZpVRT

=

Thermodynamicbehavior (k)

Fk xT C2

Figure 50Comparison of ISA And Fisher Sizing Terms




Computer Sizing Control Valves For Gasses Using The Fisher Controls Equations

Valve Sizing Methods Available

When the main menu item Valves is selected, the specifier is presented with several sizingmethods as shown in Figure 51. The available methods are:

Fisher Ideal Gas - The Fisher Ideal Gas method assumes ideal gas behavior; accordingly,the corrections for compressibility (Z) and for non-ideal thermodynamic properties(C2) are not used. In this sizing method, Z is assumed to be 1.0, and k is assumed to be1.4. Fluid density is expressed in terms of SG or M.Fisher Real Gas - The Fisher Real Gas method includes options for the use of Z factorsand C2 coefficients. This method is similar to the ISA Gas method.Fisher Vapor - The Fisher Vapor method is similar to the ISA Vapor method except thatthere is no option for the piping factor correction. Fluid density is entered in terms oflbs/ft3 or kg/m3, and there are options for the use of Z and C2 factors. The vapormethod is also commonly used for steam.Fisher Steam - The Fisher Steam method uses the special equation for steamapplications under 1 000 psig.

Figure 51Valve Sizing Methods




Selecting A Calculation Type

After a specific valve sizing method has been selected, the specifier can choose the type ofinformation that is being sought. As shown in Figure 52, choices include valve size, fluidvelocity, and various noise calculations.

Figure 52Selection Of A Calculation Type

Overview Of Sizing Procedures

Valve Sizing Screen - Selecting the Valve Sizing & LpA option brings up the actualsizing screen, which is illustrated in Figure 53. The sizing screen is divided into fourdistinct sections.

Figure 53




Valve Sizing Screen For The Fisher Real Gas Sizing Method




F3 Options

Fisher Ideal Gas - As shown in Figure 54 below, there are no sizing options for the IdealGas Method that affect how the flow coefficient is determined.

Figure 54Calculation Options For The Fisher Ideal Gas Sizing Method

Fisher Real Gas - The calculation options for the Fisher Real Gas Method (see Figure55) present the specifier with several choices for the use of Z and C2 factors. Thechoices are as follows:• Input Z, omit C2• Input Z, calculate C2 (C2 is calculated from k)• Calculate Z, C2 (Z is calculated from Pc and Tc)

Figure 55Calculation Options For The Fisher Real Gas Sizing Method




Fisher Vapor - As shown in Figure 56, there are no sizing options for the Fisher VaporMethod that affect the calculation of the flow coefficient.

Figure 56Calculation Options For The Fisher Vapor Sizing Method

Fisher Steam - The only option in the Fisher Steam Method is the choice of whether thespecifier will input steam temperature or assume that the steam is saturated. See Figure57.

Figure 57Calculation Options For The Fisher Steam Sizing Method




Options And Input Fields - As various options are selected, the input fields on the sizingscreen will change; for example, if the option to calculate Z is selected, the softwarewill require values for critical pressure and temperature. Refer to Figure 58.Units-Selection - As explained previously, engineering units can be changed globally byselecting Units from the Config heading on the main menu; in addition, the specifiermay change the units for any input parameter by placing the cursor on that parameterand pressing F8. Figure 58 illustrates the available units options for fluid temperature.

Figure 58Pull-Down Menu Options For Temperature




eNTERING VALVE SIZING DATA ON THE SAUDI ARAMCO ISS

To complete a Saudi Aramco Instrument Specification Sheet (ISS), the specifier mustcalculate and enter information that describes both the physical size of the valve andinformation that describes the capacity of the valve. For purposes of illustration, thediscussion that follows is based on the ISS for globe and angle control valves (Refer to SaudiAramco Form 8020-711-ENG.)

Body And Flange Size

Control Valve Physical Size Information

Body And Port Size - After a particular valve size is selected, the body size and port sizeare entered on line 49.Flange Sizes and Ratings - The inlet flange size, rating, and style are specified on line 50.The outlet flange size, rating, and style and rating are specified on line 51.Face-To-Face Dimensions - are entered on line 72. The face-to-face dimension for aparticular valve style and size is included in the appropriate valve specificationbulletin.

Capacity Ratings

Capacity At Minimum, Normal, And Maximum Flow Conditions

Cv At Minimum, Normal, And Maximum Flow Conditions is specified on lines 62 through64.Maximum Rated Cv of the valve is specified on line 65.Percent of Rated Cv At Min, Norm, and Max Flow Conditions is also entered on lines 62through 64. Each value is simply the calculated Cv at each flow condition divided bythe maximum rated Cv of the selected valve.

Valve Travel At Minimum, Normal, And Maximum Flow Conditions

Throttling Range is shown on line 66. The lower value of the range is defined by thepercent of valve travel that provides the minimum Cv requirement, and the upper valueof the range is the percent of valve travel that provides the maximum Cv requirement.Valve Opening At Normal Flow is the percent of valve travel that provides the required Cvat normal flow conditions.




Figure 59The Saudi Aramco ISS




WORK AID 1: PROCEDURES THAT ARE USED TO MANUALLY SIZECONTROL VALVES FOR LIQUID APPLICATIONS

Work Aid 1A: Procedures That Are Used To Calculate The Required Control Valve Cv

1. Use the following ISA and Fisher equations to solve for Cv.

Fisher:C Q

GPv =

∆

ISA:C

qN

Gp p

vf=

−1 1 2

To determine the appropriate value N1, refer to the table below.

Constant Units That Are Used In EquationsN w q p, ∆∆P d, D γγ1 νν

N1 0.0865 --- m3/h kPa --- --- ---0.865 --- m3/hr bar --- --- ---

1 --- gpm psia --- --- ---

2. Refer to Fisher Catalog 10 or to other manufacturer's catalog and locate theappropriate pages for the valve types that are described in the Exercise. For each valvetype, browse through the Cv table and locate a valve size that will provide the requiredcapacity. Ensure that you select a valve size that will provide the required Cv at apercentage of travel that is consistent with the guidelines that are given in Section 5.2of SAES-J-700. The guidelines are summarized in the table below.

Extrapolate the degrees of rotation or the percent of travel that provides the requiredCv.

For rotary-shaft valves, convert the degrees of rotation to percent of travel by dividingthe degrees of rotation that provide the required Cv by 90 degrees.Guidelines For Percent Travel At Various Flow Conditions Per Section 5.2 of SAES-J-700

Flow Characteristic Percent Travel At NormalFlow

Percent Travel At MaximumFlow

Equal Percentage 80 93Linear 70 90Modified Parabolic 75 90




Work Aid 1B: Procedures That Are Used To Calculate The Allowable Pressure Drop(∆Pallow)

Perform the following procedures to complete Exercise 1B.

1. Locate the required fluid properties from the Fisher Control Valve Handbook asfollows:

SG Properties of Water table, page 135

Pv Properties of Water table, page 135 (given as Saturation Pressure)

Pc Physical Constants of Various Fluids table, page 134

2. Using the following equation, calculate the ∆Pallow.∆Pallow = Km (P1-rc Pv)

Locate the values that are required to solve the equation as follows:

Km Use the value that is listed in the Exercise under the heading "ValveSpecifications."

P1 Use the value that is listed in the Exercise under the heading "ServiceConditions."

Pv Use the value that was recorded during step 1. of this Exercise.

rc Refer to Fisher Catalog 10, section 2, page 10, Figure 1.

3. Using the Fisher Sizing equation that is included in Work Aid 1A, calculate therequired Cv. Use the lesser of the actual ∆P or the ∆Pallow.

Refer to the page in Fisher Catalog 10 that lists the Cv's for the selected valve andselect the smallest valve size that will provide the required Cv at a percentage of travelthat is consistent with the guidelines that are given in Section 5.2 of SAES-J-700 (referto Work Aid 1A). Extrapolate and record the percent of travel at which the Cvrequirements are met. Note and record the Km of the selected valve.

4. Using the value of Km that was determined in step 2, recalculate the ∆Pallow.

5. Using the new value of ∆Pallow, recalculate the required Cv.

6. Select a valve size that will meet the Cv requirements.

7. Extrapolate and record the percent of travel at which Cv requirements are met.




Work Aid 1C: Procedures That Are Used To Calculate The Effect Of Piping Factors OnCv

Perform the following procedures to complete Exercise 1C.

1. Locate the appropriate pages in Fisher Catalog 10 for the valve that is described in theExercise. Ensure that you locate the page for the line-to-body size ratio that is given inthe Exercise. Browse through the Cv column and locate a valve that provides themaximum Cv at less than the percent of travel guideline that is included in Section 5.2of SAES-J-700. Note: For rotary valves, the percentages of travel that are listed inSection 5.2 of SAES-J-700 can be converted to degrees of rotation as follows:

% travel x 90 degrees

2. Refer to Section 5.4 of SAES J-700. Locate the value of R for the valve type that isdescribed in the Exercise. Calculate the required Cv through use of the followingequation:

Re quired Cv =Calculated Cv

R

Using the required Cv that was just calculated, refer to the appropriate page in FisherCatalog 10, and select a valve size. Note: The required Cv has already been corrected;therefore, ensure that you select a valve size from the page for the 1:1 line-to-bodysize ratio. Also, ensure that the selected valve provides the maximum required Cv at atravel that is consistent with the guidelines that are listed in Section 5.2 of SAES-J-700. (Refer to the note in step 1, above.)




Work Aid 1D: Procedures That Are Used To Calculate The Effect Of Laminar Flow On Cv

Perform the following procedures to complete Exercise 1D.

1. Without attempting to compensate for fluid viscosity, calculate the required Cv for theapplication that is described. Use the following equation.

C QGPv =

∆

2. To compensate for viscous effects, locate the Viscosity Correction Nomograph inFisher Catalog 10, Section 2, pages 26 and 27 and follow the instructions that areincluded in the nomograph. Use the value of Cv that was calculated in step 1.




Work Aid 2: Procedures That Are used to Computer size con trol valves forliquid Applications

Work Aid 2A: Procedures That Are Used To Computer Size Control Valves For WaterApplications

1. Use the following procedures to complete part 1.

a. If necessary, press ESCAPE to return to the main menu.

b. From the main menu, select Valve.

c. Press and hold the ALT key and press F5 to clear all sizing inputs.

d. Select the Fisher Water method.

e. From the menu that appears, select the Cv Simple method.

f. Ensure that the engineering units on the calculation screen match the units thatare used to describe the application. If the units do not match for any field,move the cursor to that field, press the F8 key, and select the desired units.Press ESCAPE.

g. Enter the pressure drop (dP). dP = P1 minus P2.

h. Locate the SG of water at 100 degrees F from the table on page 135 of theFisher Control Valve Handbook. Enter the value of SG in the appropriate field.

i. Enter the flow rate.

j. Press F2 to calculate the valve sizing information. Record the values that arerequested in the Exercise.


a. Press ESCAPE.

b. Select the Valve Sizing and LpA option.

c. Press F3 and ensure that the options are selected as follows:

• Solve for Cg, Cs, or Cv

• LpA (SPL) OFF

• Calculate SG




• Cavitation Check OFF

• Warnings OFF

d. Ensure that all of the fluid properties and the service conditions are accuratelyentered.

e. Enter an estimated value of Km. Select a value from the table below.Typical Values Of Km and FL

Valve Style Typical Km Typical FLGlobe And Angle 0.75 .87

Rotary-Shaft 0.45 0.67

f. Press F2 to calculate the valve sizing information. Record the values that arerequested in the Exercise.


a. Press ESCAPE twice.

b. Select the Fisher Liquid method.

c. Select the Valve Sizing and LpA option.

d. Press F3 and ensure that the Input Pv option is selected.

e. Enter the value of Pv that was recorded during step 2 above.

f Obtain the value of Pc from the table on page 134 of the Control ValveHandbook

g. Ensure that all service conditions and fluid properties are accurately entered.

h. Press F2 to calculate the valve sizing information. Record the values that arerequested in the Exercise.


a. Press ESCAPE twice.

b. Select the ISA Liquid method.

c. Select the Valve Sizing and LpA option.




d. Determine an estimated value of FL through the use of the equation thatfollows or by selecting a value from the table below.

Estimated FL = Estimated Km

Typical Values Of Km and FLValve Style Typical Km Typical FL

Globe And Angle 0.75 .87Rotary-Shaft 0.45 0.67

e. Enter the estimated FL.

f. Ensure that all service conditions and fluid properties are accurately entered.

g. Press F2 to calculate the valve sizing information. Record the values that arerequested in the Exercise.




Work Aid 2B: Procedures That Are Used To Computer Size Control Valves For ChokedFlow

Use the following procedures to complete Exercise 2B.

1. Return to the main menu.

2. From the main menu, select Valve.

3. From the menu that appears, select the Fisher Liquid method.

4. Press and hold the ALT key and press F5 to clear any sizing inputs.

5. Select the Valve Sizing and LpA option.

6. Press F3 and ensure that the option Input Pv is selected.

7. Enter the fluid name as "HC liquid."

8. Enter the fluid properties and the service conditions.

9. Enter the estimated Km. (Refer to the table in step 4 of Work Aid 2A.)

10. Press F2 to calculate the valve sizing information.

11. Refer to the appropriate page in Catalog 10 and select a valve size that will provide themaximum Cv at a percentage of travel that is consistent with the guidelines that arelisted in Section 5.2 of SAES-J-700. (Refer to the table in Work Aid 1A).

12. Record the information that is requested under the heading "Initial Calculations andValve Selection."

13. Using the Km of the initially selected, recalculate the valve sizing information. Notethat the calculated Cv may now allow the selection of a smaller valve. To determine ifa smaller valve will pass the required flow, use the Km of the smaller valve torecalculate the sizing information.

14. Record the information that is requested under the heading "Final Calculations andValve Selection."




Work Aid 2C: Procedures That Are Used To Computer Size Control Valves For Fluids InThe Sizing Database


a. Return to the main menu.


c. From the menu that appears, select the Fisher Liquid method.

d. Press and hold the ALT key and press F5 to clear any sizing inputs.

e. Select the Valve Sizing and LpA option.

f. Press F3 and ensure that the option Input Pv is selected.

g. Enter the fluid name as "Liquid Propane."

h. Refer to page 130 of the Fisher Control Valve Handbook, and locate the valuesof Pc, Pv, and SG for the liquid. Enter these values in the proper fields on thecalculation screen. Note: The value of Pv that is included in the table is for thefluid at a temperature of 100 degrees F; however, this value of Pv will be usedbecause it is the only value that is available.

i. Enter all of the service conditions.

j. Enter an estimated value of Km. (Refer to the table in part 4 of Work Aid 2A.)

k. Press F2 to calculate the valve sizing information. Record the information thatis requested under the heading Calculated Results.


a. Place the cursor on the appropriate fields and press the F5 key to clear thevalues that were previously entered for Pv and Pc.

b. Press F3 and select the Calculate Pv option.

c. Place the cursor in the Fluid field and press F4 to display a list of fluids. Fromthe pull-down menu, select Propane.

d. Press F2 to calculate the valve sizing information. Record the information thatis requested under the heading Calculated Results.





a. Without clearing the calculation screen, change the temperature and the SG toto the values that are stated in part 3.

b. Press F2 to calculate the valve sizing information. Record the information thatis requested under the heading Calculated Results.


a. Without clearing the calculation screen, change the Km to 0.75.

b. Press the F2 key to calculate the valve sizing information. Record, under theheading Calculated Results on the Exercise Sheet, the information that isrequested.




Work Aid 2D: Procedures That Are Used To Computer Size Control Valves With PipingFactor Correction


a. Press ESCAPE to return to the menu that gives choices of sizing methods.

b. Select the Fisher Water sizing method.

c. Press and hold the ALT key, and press the F5 key to clear all sizing inputs.

d. Select the Valve Sizing and LpA option.

e. Press F3. Ensure that the option Calculate SG is selected.

f. Enter the service conditions.

g. Enter an estimated value of Km. (To determine an estimated Km, refer to thetable in step 4 of Work Aid 2A).

h. Press F2 to calculate the valve sizing information. Record the calculated Cv.


a. Locate the page in Fisher Catalog 10 that describes the valve that is specified.Ensure that you locate the page that lists capacities for the appropriate line-to-body size ratio.

b. Select a valve size that provides the maximum required Cv at a percentage oftravel (or degrees of rotation) that is consistent with Section 5.2 of SAES-J-700. (Refer to the table in part 2 of Work Aid 1A.)

c. Record the information that is requested in the Exercise.


a. Locate the page in Fisher Catalog 10 that describes the valve that is specified.Ensure that you use the page that lists capacities for the appropriate line-to-body size ratio.

b. Select a valve size that provides the maximum required Cv at a percentage oftravel (or degrees of rotation) that is consistent with Section 5.2 of SAES-J-700. (Refer to the table in part 2 of Work Aid 1A.)

c. Record the information that is requested in the Exercise.






b. Select the ISA Liquid sizing method.

c. From the menu that appears, select the Valve Sizing and LpA option.

d. Press F3. Ensure that the options Calculate FP, Viscous Correction OFF, and InputPv, are selected.

e. Ensure that fluid properties and the service conditions are accurately entered.

f. Enter an estimated FL. Determine an estimated value of FL through the use ofthe equation that follows or by selecting a value from the table below.

Estimated FL = Estimated KmTypical Values Of Km and FL

Valve Style Typical Km Typical FLGlobe And Angle 0.75 .87

Rotary-Shaft 0.45 0.67

g. Enter an assumed valve inlet size, d. Use the valve size that was previouslyselected.

h. Enter the appropriate values for D1 and D2.

i. Press F2 to calculate the valve sizing information. Record the value of Cv.

j. Select an appropriate valve size. Note: Because the calculated Cv includes thenecessary correction for piping factors, ensure that you select a valve size fromthe table that lists capacities for a 1:1 line-to-body size ratio. Also, ensure thatyou select a valve size that is consistent with the percentage of travel guidelinesthat are listed in Section 5.2 of SAES-J-700. (Refer to the table in part 2 ofWork Aid 1A.)




Work Aid 2E: Procedures Used To Computer Size Control Valves With ViscosityCorrection



b. Select the Fisher Liquid sizing method.

c. Press and hold the ALT key, and press F5 to clear any sizing inputs.


e. Press F3. Ensure that the options Viscous Correction OFF and Input Pv areselected.

f. Enter the fluid name.

g. Ensure that the engineering units that are displayed on the calculation screenmatch the units that are used in the description of the application. If necessary,change the units for any field by moving the cursor to the field, pressing F8,and selecting the desired units.

h. Enter the fluid properties and the service conditions.

i. Enter an estimated value of Km. (Refer to the table in part 4 of Work Aid 2A.)

j. Press F2 to calculate the valve sizing information.

k. Locate the page in Fisher Catalog 10 that describes the valve that is specified inthe Exercise.

l. Select a valve size that satisfies the Cv requirement according to the travelguidelines that are given in Section 5.2 of SAES-J-700. (Refer to the table inpart 2 of Work Aid 1A.)

m. Record the requested values.





a. Do NOT clear the calculation screen.

b. Press F3. Ensure that the options Input Pv, and Viscous Correction ON areselected.

c. Ensure that the engineering units that are displayed on the calculation screenmatch the units that are used in the description of the application. If necessary,change the units for any field by moving the cursor to the field, pressing F8,and selecting the desired units.

d. Ensure that all fluid properties and service conditions are accurately entered.

e. Press F2 to calculate the valve sizing information.

f. Refer to the appropriate page in Fisher Catalog 10, and select a valve size thatsatisfies the Cv requirement according to the travel guidelines that are given inSection 5.2 of SAES-J-700. (Refer to the table in part 2 of Work Aid 1A.)

g. Record the requested values.


a. Do NOT clear the calculation screen.

b. Press ESCAPE twice to return to the sizing methods menu.

c. Select the ISA Liquid sizing method.

d. From the menu that appears, select the Valve Sizing and LpA option.

e. Press F3. Ensure that the options Omit FP, Viscous Correction ON, and Input Pv areselected.

f. Note that the software may have calculated a value of FL from the Km that wasincluded in the previous calculation. If the software has not calculated thisvalue, calculate FL from the value of Km that was used previously; i.e., FL =square root of Km. Alternatively, an estimated value of FL may be obtainedfrom the table that is included in part 4 of Work Aid 2A.




g. Enter the appropriate value of Fd for a globe valve. To view a Help Screen thatexplains Fd values, press the F1 key twice, press "v" to view a list of valvesizing Help Screens, select Valve Sizing: Sizing Parameters, and press PageDown until the explanation of Fd appears. (Note that for most globe valves, Fd= 1.0).

h. Assume that the valve size is equal to the line size, and enter an appropriatevalue for d.

i. Press F2 to calculate the valve sizing information, and note the Cv.

j. Refer to Fisher Catalog 10, and ensure that the valve size that is assumed abovecan provide the required capacity. If it appears that a smaller valve can providethe need capacity, change the value of d, calculate Cv, and again refer to thesizing tables. Ensure that you select a valve that is consistent with theguidelines in Section 5.2 of SAES-J-700 (see the table in part 2 of Work Aid1A).




Work Aid 2F: Procedures That Are Used To Computer Size Control Valves WithViscosity And Piping Factor Correction

1. Use the following procedures to complete part 1.Calculating Cv with Viscous Correction

a. Press ESCAPE until the valve sizing method menu appears.


c. Clear all values by pressing ALT-F5.


e. Press F3. Ensure that the options Omit FP, Viscous Correction ON and Input Pv areselected.

f. Ensure that the engineering units that are displayed on the calculation screenmatch the units that are used in the description of the application. If necessary,change the units for any field by moving the cursor to the field, pressing F8,and selecting the desired units.

g. Enter the fluid properties and the service conditions.

h. Enter an estimated value of FL. An estimated value of FL can be obtained fromthe table in part 4 of Work Aid 2A.

i. Enter the appropriate value of Fd. Refer to step g. in part 3. of Work Aid 2E.

j. Assume that the valve size is equal to the line size, and enter the appropriatevalue for d.

k. Press F2 to calculate the valve sizing information, and note the Cv.

l. Refer to the appropriate page in Fisher Catalog 12, and select a control valvesize that provides the required Cv at a percentage of travel that is consistentwith Section 5.2 of SAES-J-700. Refer to the table in part 2 of Work Aid 1A.

m. Record the selected valve size and the degrees of rotation at which the valvewill provide the maximum Cv requirement.




Calculating Cv with Piping Factor Correction

a. Press F3. Ensure that the options Calculate FP and Viscous Correction OFF areselected.

b. Initially assume that the required valve size is equal to line size, and enter theappropriate value of d.

c. Enter the appropriate values for D1 and D2.

d. Press F2 to calculate the valve sizing information, and note the Cv.

e. Refer to the appropriate page in Fisher Catalog 12, and select a control valvesize. Evaluate the assumed valve size as well as smaller sizes. If a smaller thaninitially selected valve size appears to have sufficient capacity, recalculate thevalve sizing information with the use of the appropriate value of d and theactual value of FL.

f. Record the selected valve size and the degrees of rotation at which the valveprovides the maximum Cv requirements.


a. If the calculations that consider piping factors lead to the selection of one valvesize and the calculations that consider the effects of laminar flow lead to theselection of another valve size, select the larger valve.




Work Aid 2G: Procedures That Are Used To Computer Size Control Valves ForMinimum, Normal, And Maximum Flow Conditions

Use the following procedures to complete Exercise 2G.Setup



c. Press ALT-F5 to clear all of the data.

d. With the cursor on the Valve Size and LpA Option, press F3 and ensure that the optionsare set to LpA (SPL) OFF, Omit FP, Viscous Correction OFF, Pipe: Size, Sched., Input Pv, andWarnings OFF. Note that the FP option will not be used to initially select a valve size.

Initial Sizing

a. Select the MIN (minimum) condition. Enter the fluid properties and the serviceconditions. To determine an estimated value of FL, browse through the FL values thatare listed on the Catalog 12 page that describes the selected valve type. Select a valueof FL that is typical for the valve type and size.

b. Press F2 to calculate the valve sizing information.

c. Press ESCAPE. On the screen that appears, move the cursor to the NRM (normal)flow condition column.

d. Press ALT-C. From the menu that appears, select 1 to copy the sizing informationfrom the minimum flow calculation screen to the normal flow calculation screen. PressENTER.

e. Change the pressure and flow conditions to the values that are given for the normalflow condition.

f. Press F2 to calculate the valve sizing information.

g. Press ESCAPE. On the screen that appears, move the cursor to the MAX (maximum)flow condition column.

h. Press ALT-C. From the menu that appears, select 2 to copy the sizing informationfrom the normal flow calculation screen to the maximum flow calculation screen.Press ENTER.




i. Change the pressure and flow conditions to the values that are given for the maximumflow condition.


Display The Calculated Results And Select A Valve Size

a. Press F9 to display a table of calculated values.

b. Note the minimum and maximum Cv values. Refer to the Catalog 12 page for theselected valve. Locate the smallest valve size that can provide the maximum Cvaccording to the guidelines in Section 5.2 of SAES-J-700 (refer to the table in part 2 ofWork Aid 1A).




Work Aid 2G: Procedures That Are Used To Computer Size Control Valves ForMinimum, Normal, And Maximum Flow Conditions, cont'd.

Intermediate Sizing With The Calculate FP Option

a. Press ESCAPE twice to return to the menu screen from which the Valve Sizing AndLpA calculations are selected.

b. Press F3 and select the Calculate FP option. (Note that selecting an option from thisscreen invokes the option for all calculation screens (MIN, NRM, and MAX);selecting an option from a particular sizing screen invokes the option for that specificcondition only.)

c. Select the minimum flow condition. Enter the appropriate values for d, D1, and D2.Press F2 to calculate the valve sizing information.

d. Repeat the step immediately above for the normal and the maximum flow conditions.

e. Press F9 to display a table of calculated Cv's that have been corrected for pipingfactors. Refer to the appropriate Catalog 12 page, and compare the corrected Cv's thatare displayed on the screen to the Cv's that are published for the initially selectedvalve. Ensure that the selected valve can provide the Cv's that are required at theminimum and maximum flow conditions according to the guidelines in Section 5.2 ofSAES-J-700 (refer to the table in part 2 of Work Aid 1A). Record the valve size asrequested on the Exercise Sheet.

Final Sizing and Selection

a. Select the minimum flow condition sizing screen and note the calculated Cv.

b. Refer to the appropriate page in Catalog 12 and estimate the degrees of rotation atwhich the Cv requirement will be met.

c. Extrapolate a value of FL for the degrees of rotation that were estimated in step b.Enter the extrapolated value of FL in the appropriate field on the sizing screen, andpress F2 to calculate the valve sizing information.

d. If the Cv that was calculated in step c. is different than the Cv that was calculated instep b., the degrees of rotation at which the required Cv is obtained will be differentand the value of FL may have also changed; therefore, steps b. and c. must berepeated. If the Cv's that were calculated in steps b. and c. are the same (or nearly thesame), record the information that is requested on the Exercise Sheet, and proceed tothe next step.




e. Select the normal flow condition and note the value of the calculated Cv. Performsteps b., c., and d. for the normal flow condition.

f. Select the maximum flow condition and note the calculated Cv. Perform steps b., c.,and d. for the maximum condition.

g. Ensure that you have recorded all the information that is requested on the ExerciseSheet.

h. If it is necessary to review the calculated results, press F9.




work aid 3: Procedures that are used to Computer size control valves forgas and steam applications

Work Aid 3A: Procedures That Are Used To Computer Size Control Valves For IdealGasses With The ISA Method

Perform the following procedures to complete Exercise 3A.

a. If necessary, press ESCAPE to return to the main menu.


c. From the menu that appears, select the ISA Gas method.


e. Press F3, and select the Input Z option.

f. Enter the service conditions, the fluid properties, and the value of xT.

• Note that Fk = k divided by 1.4. If k is unknown, enter 1.0 for FK.

• Because Tc and pc are not included in the description of the fluid properties, Zcannot be calculated; therefore, enter a value of 1.0 for Z.

g. Press F2 to calculate the valve sizing information.

h. Record the values that are requested in the Exercise.




Work Aid 3B: Procedures That Are Used To Computer Size Control Valves For RealGasses With The ISA Method

Perform the following procedures to complete Exercise 3B.Note: It is not necessary to clear the existing sizing inputs.

a. Press ESCAPE to return to the sizing method menu.

b. From the menu that appears, select the ISA Gas method.


d. Press F3, and select the Calculate Z option.

e. Ensure that the correct information is entered in the fields for the service conditions,fluid properties, and the value of xT. Remember that Fk = k divided by 1.4.


g. Record the values that are requested in the Exercise.




Work Aid 3C: Procedures That Are Used To Computer Size Control Valves For VaporsWith The ISA Method

Perform the following procedures to complete Exercise 3C.


b. From the menu that appears, select the ISA Vapor method.


d. Ensure that the engineering units on the calculation screen match the units that areused to describe the service conditions. If the units do not match for any field, movethe cursor to that field, press the F8 key, and select the desired units.

e. Enter the fluid properties, the service conditions, and xT. Remember that FK = k/1.4.






Work Aid 3D: Procedures That Are Used To Computer Size Control Valves For SteamWith The ISA Method

Perform the following procedures to complete Exercise 3D.


b. From the menu that appears, select the ISA Vapor method.


d. Press and hold the ALT key, and press F5 to clear all sizing inputs.

e. Ensure that the engineering units on the calculation screen match the units that areused to describe the service conditions. If the units do not match for any field, movethe cursor to that field, press the F8 key, and select the desired units.

f. Using the chart in Fisher Catalog 10, Section 2, page 39, determine the density of thesteam.

g. Enter the fluid properties, the service conditions, and the value of xT.

h. Press F2 to calculate the valve sizing information.

i. Record the values that are requested in the Exercise.




Work Aid 3E: Procedures That Are Used To Computer Size Control Valves For IdealGasses With The Fisher Method

Perform the following procedures to complete Exercise 3E.

1. Fisher Ideal Gas sizing method

a. Press ESCAPE to return to the main menu.


c. From the menu that appears, select the Fisher Ideal Gas method.


e. Press and hold the ALT key, and press F5 to clear any sizing inputs.

f. Ensure that the engineering units on the calculation screen match the units thatare used to describe the service conditions. If the units do not match for anyfield, move the cursor to that field, press the F8 key, and select the desiredunits.

g. Enter the required service conditions, the fluid properties, and the value of C1.

h. Press F2 to calculate the valve sizing information.

i. To convert the Cg to Cv, divide the value of Cg by the value of C1.

j. Record the values that are requested in the Exercise.

2. Fisher Real Gas sizing method

Note: It is not necessary to clear the existing sizing inputs.


b. From the menu that appears, select the Fisher Real Gas method.


d. Press F3. If there is insufficient to calculate Z and C2, select the option Input Z,Omit C2.

e. Enter the service conditions, the fluid properties, and the value of C1.

f. To ignore the effects of real gas compressibility, enter a value of 1.0 for Z.


h. To convert Cg to Cv, divide Cg by C1.





Work Aid 3F: Procedures That Are Used To Computer Size Control Valves For RealGasses With The Fisher Method

Perform the following procedures to complete Exercise 3F.

1. Fisher Real Gas sizing methodNote: It is not necessary to clear the existing sizing inputs.




d. Press F3, and select the Calculate Z, C2 option.

e. Enter the service conditions, the fluid properties, and the value of C1.


g. To convert Cg to Cv, divide Cg by C1.





Work Aid 3G: Procedures That Are Used To Computer Size Control Valves For VaporsWith The Fisher Method

Perform the following procedures to complete Exercise 3G.

1. Fisher Vapor sizing method


b. From the menu that appears, select the Fisher Vapor method.


d. Ensure that the service conditions and the value of C1 are entered correctly.


f. To convert Cg to Cv, divide Cg by C1.





Work Aid 3H: Procedures That Are Used To Computer Size Control Valves For SteamWith The Fisher Method

Use the following procedures to complete Exercise 3H.

1. Fisher Vapor sizing method


b. From the menu that appears, select the Fisher Vapor method.


d. Ensure that the service conditions and C1 are entered correctly.


f. To convert Cg to Cv, divide Cg by C1.


2. Fisher Steam sizing method


b. From the menu that appears, select the Fisher Steam method.


d. Ensure that the service conditions and C1 are entered correctly.


f. To convert Cs to Cg, multiply Cs by 20.

g. To convert Cg to Cv, divide Cg by C1.





Work Aid 3I: Procedures That Are Used To Calculate The Effect Of Compressibility OnValve Size

Use the following procedures to perform the sizing calculations for Exercise 3I.

1. Fisher Ideal Gas sizing method

a. Press ESCAPE to return to the valve sizing method menu.

b. From the menu that appears, select the Fisher Ideal Gas method.


d. Press and hold the ALT key, and press F5 to clear any sizing inputs.

e. Move the cursor to the Gas entry field, and press F4. From the menu thatappears, select N-Butane.

f. Enter the service conditions and the value of C1.




2. Fisher Real Gas sizing method




d. It is not necessary to clear existing sizing inputs.

e. Press F3, and select the Calculate Z, C2 option.

f. Ensure that the sizing inputs are entered correctly.







3. ISA Gas sizing method


b. From the menu that appears, select the ISA Gas method.


d. It is not necessary to clear existing sizing inputs.

e. Press F3, and select the Calculate Z option.

f. Ensure that the sizing inputs are entered correctly.






Work Aid 3J: Procedures That Are Used To Computer Size Control Valves For All FlowConditions

Setup


b. Select the ISA Gas sizing method.

c. Press ALT-F5 to clear all data.

d. With the cursor on the Valve Sizing and LpA Option, press F3 and ensure that the optionsare set to Input Z, Omit FP and xTP, LpA (SPL) OFF, and Warnings OFF. Note that the FPoption will not be used to initially select a valve size.

e. If it is necessary to change engineering units for any of the input fields, ensure that thescreen that is displayed is the screen from which Valve Sizing and LpA are selected.Press F8 to display a list of sizing parameters. Move the cursor to the parameters forwhich units must be changed. To display a list of options for a particular parameter,place the cursor on the parameter, and, then, press ENTER. Move the cursor to thedesired option, and press ENTER. After the units for the appropriate parameters havebeen selected, press ESCAPE.

Initial Sizing

a. Select the MIN (minimum) condition and enter the required sizing inputs. Assumeideal gas behavior; i.e., set Fk to 1.0, and set Z to 1.0. To determine an estimated xT,browse through the xT values that are listed on the Catalog 12 page that describes theselected valve and select a value of xT that is typical for the selected valve type.

b. Press F2 to calculate the valve sizing information.

c. Press ESCAPE. On the screen that appears, move the cursor to the NRM (normal)flow condition column.

d. Press ALT-C. From the menu that appears, select 1 to copy the sizing informationfrom the minimum flow calculation screen to the normal flow calculation screen. PressENTER.

e. Change the pressure and the flow conditions to the values that are included in theapplication description.





g. Press ESCAPE. On the screen that appears, move the cursor to the MAX (maximum)flow condition column.

h. Press ALT-C. From the menu that appears, select 2 to copy the sizing informationfrom the normal flow calculation screen to the maximum flow calculation screen.Press ENTER.

i. Change the pressure and the flow conditions to the values that are included in theapplication description.


Display The Calculated Results And Select A Valve Size

a. Press F9 to display a table of calculated values.

b. Note the minimum and maximum Cv values. Refer to the appropriate Catalog 12 page,and locate the smallest valve size that can provide the required Cv at the maximumflow condition. Ensure that you observe the percentage of travel guidelines that areincluded in Section 5.2 of SAES-J-700. Refer to the table in part 2 of Work Aid 1A.

Intermediate Sizing With The Calculate FP Option

a. Press ESCAPE twice to return to the menu screen from which the Valve Sizing AndLpA calculations are selected.

b. Press F3 and select the Calculate FP option. (Note that selecting an option from thisscreen invokes the option for all calculation screens (MIN, NRM, and MAX);selecting an option from a particular sizing screen invokes the option for that specificcondition only.)

c. Select the minimum flow condition. Enter the appropriate values for d, D1, and D2.Press F2 to calculate the Cv.

d. Repeat step c. for both the normal and maximum flow conditions.

e. Press F9 to display a table of calculated Cv's that have been corrected for pipingfactors. Refer to the appropriate Catalog 12 page, and compare the corrected Cv's thatare displayed on the screen to the Cv's that are published for the initially selectedvalve. Ensure that the initially selected valve has adequate capacity and that itconforms to the guidelines in Section 5.2 of SAES-J-700 (refer to the table in part 2 ofWork Aid 1A). Record the valve size on the Exercise Sheet.




Final Sizing and Selection

a. Select the minimum flow condition. Note the calculated Cv.

b. Refer to appropriate page in Catalog 12, and estimate the percentage of travel at whichthe Cv requirement will be met.

c. Extrapolate a value of xT for the percent travel that was estimated in step b. Enter theextrapolated value of XT in the appropriate field on the sizing screen, and press F2 tocalculate the sizing information.

d. If the Cv that was calculated in step c. is different than the Cv that was calculated instep b., the percent of travel at which the required Cv is obtained will be different andthe value of XT may have also changed; therefore, steps b. and c. must be repeated. Ifthe Cv's that were calculated in steps b. and c. are the same (or nearly the same),record the information that is requested and proceed to the next step.

e. Select the normal flow condition and note the value of the calculated Cv. Performsteps b., c., and d. for the normal flow condition.

f. Select the maximum flow condition and note the calculated Cv. Perform steps b., c.,and d. for the maximum condition.

g. Ensure that you have recorded the information that is requested on the Exercise Sheet.Press F9 to review the calculated results if necessary.




WORK AID 4: PROCEDURES THAT ARE USED TO Enter Valve Sizing Dataon the saudi Aramco ISS

Enter the information on the ISS as follows:Line 49: Enter the valve body size and the valve port size.Line 50: Enter the inlet flange size, the inlet flange ANSI Class rating, and the flange

style (enter the abbreviation RF for a raised-face flange style).Line 51: Enter outlet flange size, the ANSI Class rating, and the flange style.Line 61: Circle the entry that indicates whether flow tends to close or open the valve.Line 62: Enter the minimum flow Cv. Divide the Cv at the minimum flow condition by

the maximum Cv rating of the valve. Enter the result as a percentage.Line 63: Enter the normal flow Cv. Divide the Cv at the normal flow condition by the

maximum Cv rating of the valve. Enter the result as a percentage.Line 64: Enter the maximum flow Cv. Divide the Cv at the maximum flow condition by

the maximum Cv rating of the valve. Enter the result as a percentage.Line 65: Enter the maximum Cv rating of the valve.Line 66: Enter the percentages of travel at which the valve provides the Cv's that are

required at the minimum and maximum flow conditions.Line 67: Enter the percentage of travel at which the valve provides the Cv that is

required at the normal flow condition.Line 72: Refer to the appropriate specification bulletin and determine the face-to-face

dimension of the selected valve. Enter the dimension on the ISS, and circle theappropriate units of measurement (mm or inches).




GLOSSARYγγ1 Specific weight of the fluid at the valve inlet.∆∆Pallow Pressure drop at which choked flow limits flow to Qmax; same

as ∆Pchoked.∆∆Pchoked Pressure drop at which choked flow limits flow to Qmax; same

as ∆Pallow.C1 Term that is used in the Fisher Gas Sizing Equation to account

for differences in liquid and gas coefficients for high and lowrecovery valve types.

C2 Term that is used in the Fisher Gas Sizing Equation to accountfor the ratio of specific heats. C2 serves the same function as Fkin the ISA equations.

capacity Rate of flow through a valve under stated conditions.cavitation In liquid service, the noisy and potentially damaging

phenomenon that accompanies bubble formation and collapsein the flowstream.

centipoise Unit of measure of viscosity (Cs).centistokes Unit of measure of viscosity (Cp).Cg Gas flow coefficient that is used by Fisher Controls.choked flow Maximum flow rate through a restriction. Choked flow results

in liquid flows as pressure reductions cause decreases in fluiddensity and thus offset any increase in velocity. In gasses,choked flow is achieved when fluid velocity is sonic.

compressibility Condition that occurs in gasses as increasing pressure compactsmolecules of the flowing gas.

critical flow Condition when gas flow is at sonic velocity and furtherreductions in downstream pressure produce no increase in flowrate.

critical pressure The pressure of the liquid-vapor point.critical pressure ratio Ratio that is used in liquid sizing to calculate Pvc and allowable

pressure drop (∆Pchoked).critical temperature Temperature of the liquid-vapor critical point (i.e., the

temperature above which the fluid has no liquid-vaportransition.

Cs Steam flow coefficient that is used by Fisher Controls.Cv Flow coefficient that is commonly used for liquids.Cvr Cv required; a value of Cv that has been corrected to account

for the effects of fluid viscosity on the calculated Cv. This termis used in conjunction with the Fisher Controls nomograph thatis used to determine viscosity corrections.

D Term that represents nominal pipeline diameter.d Term that represents nominal valve size (generally the valve

inlet diameter).D1 Diameter of the piping that is connected to the valve inlet.




D2 Diameter of the piping that is connected to the valve outlet.density Weight per unit of volume of a fluid. May be given as relative

density (specific gravity SG, molecular weight M, or in termsof specific weight (weight per unit of volume, such as kgs/m3,lbs/ft3, etc.).

downstream Any point that is located away from a reference point in thedirection of fluid flow.

∆∆P The pressure drop. in psi, across the valve (∆P = P1-P2).Fd Valve style modifier that is used in ISA equation to calculate

valve Reynolds number.FF ISA term for critical pressure ratio; same as rc, which is used by

Fisher and others.FL Term that is used in ISA equations to describe valve recovery

coefficient. Similar to Km, which is used by Fisher.FLP FL corrected for piping factor.flashing A phenomenon that is observed in liquid service when the

pressure of the fluid falls below its vapor pressure and it doesnot recover to a pressure above its vapor pressure. Flashingcommonly produces, in control valve components, damage thathas the appearance of erosion damage (smooth, polishedcavities on the affected components).

flow characteristic Relationship between flow through the valve and percent ofrated travel as the latter is varied from 0 to 100 percent. Thisterm is a special term. It should always be designated as eitherinherent flow characteristic or installed flow characteristic.Common flow characteristics are linear, equal percentage, andquick opening.

flow coefficient (Cv) The number of U.S. gallons per minute of 60 degree F waterthat will flow through a valve with a pressure drop of onepound per square inch.

flow rate The amount (mass, weight, or volume) of fluid flowing througha regulator per unit of time.

FLP ISA term that represents a recovery coefficient (liquid flow)that is corrected for piping factors.

FR Reynolds number factor that is used in the ISA equations.FP Piping factor that is used in the ISA equations.Fv Viscosity correction factor that is used by Fisher Controls to

compensate for the effects of viscous flow. The value of Fv isdetermined from a nomograph, and it is applied as follows: Cvr(Cv required) = FvCv, where Cv is an initially calculated value.

fluid Substance in a liquid, gas, or vapor state.fluid expansion Expansion that results from a decrease in pressure as a gas

flows through a control valve.FP ISA term that represents the piping factor. See Piping Factor.




FSP Fisher Sizing ProgramG The specific gravity of the fluid. Identical to the SG and the

ISA terms Gf and Gg.Gf Liquid specific gravity at upstream conditions; ratio of fluid

density at flowing temperature to density of water at 60 degreesF (15.6 degrees C).

Gg Gas specific gravity; ratio of density of gas at flowingconditions to density of air at reference conditions; ratio ofmolecular weight of a gas to molecular weight of air;dimensionless.

high-recovery valve A valve design that dissipates relatively little flow-streamenergy because of streamlined internal contours and minimalflow turbulence. Valves, such as rotary-shaft ball and butterflyvalves, are typically high-recovery valves. In these designs, thepressure dip at the vena contracta is larger than in low-recoveryvalves.

ideal gas A gas that obeys the ideal gas law of pV=RT.ISA Instrument Society of America.Km Liquid flow valve recovery coefficient that is used by Fisher

Controls; similar to FL in ISA equations.laminar flow A flow regime characterized by smooth, ordered layers. The

layers in the center of the pipe have the highest velocity, whiledrag forces result in reduced velocity nearer the pipe wall.Laminar flow is also referred to as viscous flow. The termviscous flow is somewhat of a misnomer because effects otherthan fluid viscosity can cause laminar flow.

low-recovery valve A valve design that dissipates a considerable amount offlowstream energy because of turbulence created by thecontours of the flowpath. Globe valves are typical. In thesedesigns, the pressure dip at the vena contracta is not as great asin high-recovery valves.

M molecular weight, atomic mass units.Nx Used in ISA equations, N terms are numerical constants that

allow the use of the equations with different engineering units.p1 Fluid pressure upstream of the valve.p2 Fluid pressure downstream of the valve.piping factor Ratio of flow through a valve with swaged connections to flow

through a valve with a 1:1 line-to-body size ratio. Representedin the ISA equations with term FP.

pr The reduced pressure, determined by dividing the actualpressure of the fluid (psia) by the fluid's critical pressure psia).The value of Pr and the value of Tr (the reduced temperature)may be used to determine the value of the compressibilityfactor, Z.




pressure Force exerted per unit of area.pressure differential The difference in pressure between two locations in a fluid

system.pressure drop The difference between upstream pressure and downstream

pressure that represents the amount of flow stream energy thatthe control valve must be able to withstand.

pressure drop ratio Ratio of inlet pressure P1 to pressure drop across the valve.pressure drop ratiofactor

The limiting value of x that is used in the ISA sizing equations.Referred to with xT (t stands for terminal). The value of xT isrelated to valve style and geometry. It is determined by test andpublished with other valve sizing information.

pressure drop, allowable The pressure drop at which choked flow limits flow to Qmax.This term is used by Fisher Controls and others. It is equivalentto the term "choked pressure drop" that is used in the ISAequations.

pressure drop, choked The pressure drop at which choked flow limits flow to Qmax.This term is used in the ISA equations. It is equivalent to theterm "allowable pressure drop" that is used by Fisher andothers.

PSI or psi Pounds per square inch.Pv For a liquid, the pressure of the vapor in equilibrium with the

liquid.Pvc Pressure at the vena contracta.Q or q flow rateR Gas constant that is used in the equation to describe pressure,

volume, and temperature relationships of ideal gasses. R =1545/molecular weight (M) of the fluid.

Rev Reynolds number for valve.rated Cv The value of Cv at the rated full-open position.ratio of specific heatfactor

The factor that is used in the ISA gas sizing equations toaccount for thermodynamic fluid behavior. It is represented byFk. Fk is equal to the ratio of the specific heat for the flowinggas to the specific heat of air, which is 1.4 (i.e., Fk = k/1.4).

rc A term that is used by Fisher Controls and others to representthe critical pressure ratio. The term rc is equivalent to the termFF in the ISA sizing equations. The critical pressure ratio andthe fluid vapor pressure (Pv) are used to estimate the fluidpressure at the vena contracta according to: Pvc = rc Pv.

real gas A gas for which deviations form the ideal gas law are taken intoaccount.

SG specific gravitysonic velocity The upper velocity limit of a flowing gas. It is equal to the

speed of sound in the flowing gas.




specific gravity Measure of density, generally expressed as SG or M. See SGand M.

specific heat ratio Represented with the term k. The ratio of the amount of heatthat is required to raise a mass of material 1 degree intemperature to the amount of heat that is required to raise anequal mass of a reference substance (usually water) 1 degree intemperature. Both measurements are made at a specifictemperature and at constant volume or pressure.

swage A piping expander or reducer that allows the installation of acontrol valve in a pipeline whose diameter is greater than thediameter of the control valve inlet and outlet fittings.

T or T1 Temperature of the fluid at the valve inlet.throttling range The range defined by the percent valve travel that provides the

minimum Cv requirement and the percent valve travel thatprovides the maximum Cv requirement.

Tr The reduced temperature, determined by dividing the actualtemperature of the fluid by the fluid's critical temperature. Thevalue of Tr and the value of Pr (the reduced pressure) may beused to determine the value of the compressibility factor, Z.

transitional flow A flow regime with characteristics of both laminar andturbulent flow.

travel The amount of movement (linear or rotational) of the valveclosure member between the closed and open positions,generally expressed in degrees of rotation for rotary-shaftvalves and in percent of travel for sliding-stem valves.

turbulent flow A flow regime characterized by turbulent eddies that occurrandomly in the fluid stream. Fluid velocity at the center of thepipe and the velocity near the pipe wall are nearly equal.

vena contracta The location where cross-sectional area of the flowstream is atits minimum size, where fluid velocity is at its highest level,and fluid pressure is at its lowest level. (The vena contractanormally occurs just downstream of the actual physicalrestriction in a control valve.)

w Mass flow rate (lbs/hr, kg/s, etc.)x Pressure drop ratio ( ∆P p/ 1 ); limited to value of xT for choked

flow and xTP to correct for piping factors, dimensionless.xT Flow limiting pressure drop that is used in ISA gas sizing

equations.

Y Expansion factor Y

xF xk T

= −13 , where Fk = ratio of specific

heats.Z Compressibility factor; dimensionless.




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75925837 Control Valve Sizing