Fisher CV Sizing Info

Catalog 12Section 2 tab

Printed in U.S.A. on recycled paper.!Fisher Controls International, Inc., 1995, 1999;All Rights Reserved

November 1999Page 2-1

Catalog 12Fisher, and Fisher-Rosemount are marks owned by Fisher Controls Inter-national, Inc. or Fisher-Rosemount Systems, Inc. All other marks are theproperty of their respective owners.

Introduction

Standardization activities for control valve sizing can betraced back to the early 1960’s when an American tradeassociation, the Fluids Control Institute, published sizingequations for use with both compressible and incom-pressible fluids. The range of service conditions thatcould be accommodated accurately by these equationswas quite narrow, and the standard did not achieve ahigh degree of acceptance. In 1967, the Instrument Soci-ety of America (ISA) established a committee to developand publish standard equations. The efforts of this com-mittee culminated in a valve sizing procedure that hasachieved the status of American National Standard. Lat-er, a committee of the International ElectrotechnicalCommission (IEC) used the ISA works as a basis to for-mulate international standards for sizing control valves.(Some information in this introductory material has beenextracted from ANSI/ISA S75.01 standard with the per-mission of the publisher, the instrument Society of Amer-ica.) Except for some slight differences in nomenclatureand procedures, the ISA and IEC standards have beenharmonized. ANSI/ISA Standard S75.01 is harmonizedwith IEC Standards 534-2-1 and 534-2-2. (IEC Publica-tions 534-2, Sections One and Two for incompressibleand compressible fluids, respectively.)

In the following sections, the nomenclature and proce-dures are explained, and sample problems are solved toillustrate their use.

Sizing Valves for Liquids

Following is a step-by-step procedure for the sizing ofcontrol valves for liquid flow using the IEC procedure.Each of these steps is important and must be consideredduring any valve sizing procedure. Steps 3 and 4 con-cern the determination of certain sizing factors that mayor may not be required in the sizing equation dependingon the service conditions of the sizing problem. If one,two, or all three of these sizing factors are to be includedin the equation for a particular sizing problem, refer to

the appropriate factor determination section(s) located inthe text after the sixth step.

1. Specify the variables required to size the valve as fol-lows:

D Desired design: refer to the appropriate valve flow co-efficient table in this catalog.

D Process fluid (water, oil, etc.), and

D Appropriate service conditions

q or w, P1, P2 or "P, T1, Gf, Pv, Pc, and #

The ability to recognize which terms are appropriate for aspecific sizing procedure can only be acquired throughexperience with different valve sizing problems. If any ofthe above terms appears to be new or unfamiliar, refer tothe table 1 for a complete definition.

2. Determine the equation constant N. N is a numericalconstant contained in each of the flow equations to pro-vide a means for using different systems of units. Valuesfor these various constants and their applicable units aregiven in table 2.

Use N1, if sizing the valve for a flow rate in volumetricunits (gpm or m3/h).

Use N6 if sizing the valve for a flow rate in mass units(lb/h or kg/h).

3. Determine FP, the piping geometry factor.

FP is a correction factor that accounts for pressurelosses due to piping fittings such as reducers, elbows, ortees that might be attached directly to the inlet and outletconnections of the control valve to be sized. If such fit-tings are attached to the valve, the FP factor must beconsidered in the sizing procedure. If, however, no fit-tings are attached to the valve, FP has a value of 1.0 andsimply drops out of the sizing equation.

For rotary valves with reducers (swaged installations)and other valve designs and fitting styles, determine theFP factors by using the procedure for Determining FP,the Piping Geometry Factor on page 3.

ANSI/ISA/IEC Valve Sizing

Introduction and Sizing Valves for Liquids



Catalog 12

Table 1. Abbreviations and TerminologySymbol Definition Symbol Definition

Cv Valve sizing coefficient P2 Downstream absolute static pressure

d Nominal valve size PC Absolute thermodynamic critical pressure

D Internal diameter of the piping PV Vapor pressure absolute of liquid at inlet temperature

FD Valve style modifier, dimensionless "P Pressure drop (P1-P2) across the valve

FF Liquid critical pressure ratio factor, dimensionless "Pmax(L) Maximum allowable liquid sizing pressure drop

FK Ratio of specific heats factor, dimensionless "Pmax(LP)Maximum allowable sizing pressure drop withattached fittings

FL Rated liquid pressure recovery factor, dimensionless q Volume rate of flow

FLP

Combined liquid pressure recovery factor and pipinggeometry factor of valve with attached fittings (whenthere are no attached fittings, FLP equals FL),dimensionless

qmaxMaximum flow rate (choked flow conditions) at givenupstream conditions

FP Piping geometry factor, dimensionless ReV Valve Reynolds number, dimensionless

FR Reynolds number factor, dimensionless T1Absolute upstream temperature (degrees K ordegree R)

GF

Liquid specific gravity (ratio of density of liquid atflowing temperature to density of water at 60_F),dimensionless

w Mass rate of flow

GG

Gas specific gravity (ratio of density of flowing gas todensity of air with both at standard conditions(1), i.e.,ratio of molecular weight of gas to molecular weightof air), dimensionless

x Ratio of pressure drop to upstream absolute staticpressure ("P/P1), dimensionless

k Ratio of specific heats, dimensionless xT Rated pressure drop ratio factor, dimensionless

K Head loss coefficient of a device, dimensionless YExpansion factor (ratio of flow coefficient for a gas tothat for a liquid at the same Reynolds number),dimensionless

M Molecular weight, dimensionless Z Compressibility factor, dimensionless

N Numerical constant $1 Specific weight at inlet conditions

P1 Upstream absolute static pressure # Kinematic viscosity, centistokes

1. Standard conditions are defined as 60_F (15.5_C) and 14.7 psia (101.3kPa).

4. Determine qmax (the maximum flow rate at given up-stream conditions) or "Pmax (the allowable sizing pres-sure drop).

The maximum or limiting flow rate (qmax), commonlycalled choked flow, is manifested by no additional in-crease in flow rate with increasing pressure differentialwith fixed upstream conditions. In liquids, choking occursas a result of vaporization of the liquid when the staticpressure within the valve drops below the vapor pres-sure of the liquid.

The IEC standard requires the calculation of an allow-able sizing pressure drop ("Pmax), to account for thepossibility of choked flow conditions within the valve.The calculated "Pmax value is compared with the actualpressure drop specified in the service conditions, andthe lesser of these two values is used in the sizing equa-tion. If it is desired to use "Pmax to account for the possi-bility of choked flow conditions, it can be calculated us-

ing the procedure for Determining "qmax, the MaximumFlow Rate, or "Pmax, the Allowable Sizing Pressure Dropon page 4. If it can be recognized that choked flow con-ditions will not develop within the valve, "Pmax need notbe calculated.

5. Determine FR, the Reynolds number factor.

FR is a correction factor to account for nonturbulent flow-ing conditions within the control valve to be sized. Suchconditions might occur due to high viscosity fluid, verylow pressure differential, low flow rate, or some com-bination of these. If nonturbulent flow is suspected, de-termine the FR factor according to the procedure for De-termining FR on page 6. For most valve sizingapplications, however, nonturbulent flow will not occur. Ifit is known that nonturbulent flow conditions will not de-velop within the valve, FR has a value of 1.0 and simplydrops out of the equation.

ANSI/ISA/IEC Valve SizingSizing Valves for Liquids



Catalog 12

Table 2. Equation Constants (1)

Numerical Constant with Subscript N w q p(2) $ # T d,D

N1

0.08650.8651.00

- - -- - -- - -

m3/hm3/hgpm

kPabarpsia

- - -- - -- - -

- - -- - -- - -

- - -- - -- - -

- - -- - -- - -

N20.00214

890- - -- - -

- - -- - -

- - -- - -

- - -- - -

- - -- - -

- - -- - -

mminch

N47600017300

- - -- - -

m3/hgpm

- - -- - -

- - -- - -

centistokescentistokes

- - -- - -

mminch

N50.00241

1000- - -- - -

- - -- - -

- - -- - -

- - -- - -

- - -- - -

- - -- - -

mminch

N6

2.7327.363.3

kg/hkg/hlb/h

- - -- - -- - -

kPabarpsia

kg/m3

kg/m3

lb/ft3

- - -- - -- - -

- - -- - -- - -

- - -- - -- - -

Normal ConditionsTN = 0_C

3.94394

- - -- - -

m3/hm3/h

kPabar

- - -- - -

- - -- - -

deg Kdeg K

- - -- - -

N7(3) Standard Conditions

Ts = 15.5_C4.17417

- - -- - -

m3/hm3/h

kPabar

- - -- - -

- - -- - -

deg Kdeg K

- - -- - -

Standard ConditionsTs = 60_F

1360 - - - scfh psia - - - - - -- - - deg R - - -

N8

0.94894.819.3

kg/hkg/hlb/h

- - -- - -- - -

kPabarpsia

- - -- - -- - -

- - -- - -- - -

deg Kdeg Kdeg R

- - -- - -- - -

Normal ConditionsTN = 0_C

21.22120

- - -- - -

m3/hm3/h

kPabar

- - -- - -

- - -- - -

deg Kdeg K

- - -- - -

N9(3) Standard Conditions

Ts = 15.5_C22.42240

- - -- - -

m3/hm3/h

kPabar

- - -- - -

- - -- - -

deg Kdeg K

- - -- - -

Standard ConditionsTS = 60_F

7320 - - - scfh psia - - - - - - deg R - - -

1. Many of the equations used in these sizing procedures contain a numerical constant, N, along with a numerical subscript. These numerical constants provide a means for usingdifferent units in the equations. Values for the various constants and the applicable units are given in the above table. For example, if the flow rate is given in U.S. gpm and thepressures are psia, N1 has a value of 1.00. If the flow rate is m3/hr and the pressures are kPa, the N1 constant becomes 0.0865.2. All pressures are absolute.3. Pressure base is 101.3 kPa (1.013 bar) (14.7 psia).

6. Solve for required Cv, using the appropriate equation:

D For volumetric flow rate units—

Cv =q

N1FpP1−P2

Gf

D For mass flow rate units—

Cv = wN6Fp (P1 − P2)g

In addition to Cv, two other flow coefficients, Kv and Av,are used, particularly outside of North America. The fol-lowing relationships exist:

Kv = (0.864)(Cv)

Av = (2.40 X 10-5)(Cv)

7. Select the valve size using the appropriate flow coeffi-cient table and the calculated Cv value.

Determining Fp, the Piping GeometryFactorDetermine an Fp factor if any fittings such as reducers,elbows, or tees will be directly attached to the inlet andoutlet connections of the control valve that is to be sized.When possible, it is recommended that Fp factors bedetermined experimentally by using the specified valvein actual tests.

Calculate the Fp factor using the following equation.

Fp = 1 + SKN2Cv

d22−1∕2


Determining FP


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Catalog 12

where,

N2 = Numerical constant found in table 2d = Assumed nominal valve size

Cv = Valve sizing coefficient at 100-percent travel forthe assumed valve size

In the above equation, %K is the algebraic sum of thevelocity head loss coefficients of all of the fittings that areattached to the control valve. To calculate %K, use thefollowing formula:

SK = K1 + K2 + KB1 − KB2

where,

K1 = Resistance coefficient of upstream fittingsK2 = Resistance coefficient of downstream fittingsKB1 = Inlet Bernoulli coefficientKB2 = Outlet Bernoulli coefficient

The Bernoulli coefficients, KB1 and KB2, are used onlywhen the diameter of the piping approaching the valve isdifferent from the diameter of the piping leaving thevalve:

KB1 or KB2 = 1--dD4

where,

d = Nominal valve sizeD = Internal diameter of piping

If the inlet and outlet piping are of equal size, then theBernoulli coefficients are also equal, KB1 = KB2, andtherefore they are dropped from the equation to calculate%K.

The most commonly used fitting in control valve installa-tions is the short-length concentric reducer. The equa-tions necessary to calculate %K for this fitting are as fol-lows:

D For an inlet reducer—

K1 = 0.51 − d2

D22

D For an outlet reducer—

K2 = 1.01 − d2

D22

D For a valve installed between identical reducers—

K1 + K2 = 1.51 − d2

D22

Once you have %K, calculate FP according to the equa-tion at the beginning of this section. A sample problemthat finds for FP is on page 9.

Determining qmax (the MaximumFlow Rate) or "Pmax (the AllowableSizing Pressure Drop)Determine either qmax or "Pmax if possible for chokedflow to develop within the control valve that is to besized. The values can be determined by using the follow-ing procedures.

Determining qmax (the Maximum Flow Rate)

qmax = N1FLCvP1 − FF Pv

Gf

Values for FF, the liquid critical pressure ratio factor, canbe obtained from the following equation:

FF = 0.96 − 0.28Pv

Pc

Values for FL, the recovery factor for valves installedwithout fittings attached, can be found in the flow coeffi-cient tables. If the given valve is to be installed with fit-tings such as reducer attached to it, FL in the equationmust be replace by the quotient FLP/Fp, where:

FLP = K1

N2Cv

d22

+ 1FL

2−1∕2

and

K1 = K1 + KB1

where,

K1 = Resistance coefficient of upstream fittingsKB1 = Inlet Bernoulli coefficient

(See the procedure for Determining Fp, the Piping Ge-ometry Factor, for definitions of the other constants andcoefficients used in the above equations.)

ANSI/ISA/IEC Valve SizingDetermining qmax


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Catalog 12

Figure 1. Liquid Critical Pressure Ratio Factor for Water

Figure 2. Liquid Critical Pressure Ratio Factor for All Fluids

A2738-1


Determining qmax or "Pmax


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Catalog 12

Determining "Pmax (the AllowableSizing Pressure Drop)

"Pmax (the allowable sizing pressure drop) can be deter-mined from the following relationships:

For valves installed without fittings—

DPmax(L) = FL2 P1 − FF Pv

For valves installed with fittings attached—

DPmax(LP) = FLP

Fp2

P1 − FF Pv

where,

P1 = Upstream absolute static pressureP2 = Downstream absolute static pressurePv = Absolute vapor pressure at inlet temperature

Values of FF, the liquid critical pressure ratio factor, canbe obtained from figure 1 for water, or figure 2 for all oth-er liquids.

Values of FL, the recovery factor for valves installedwithout fittings attached, can be found in the flow coeffi-cient tables. An explanation of how to calculate values ofFLP, the recovery factor for valves installed with fittingsattached, is presented in the procedure for determiningqmax (the Maximum Flow Rate).

Once the "Pmax value has been obtained from the ap-propriate equation, it should be compared with the actualservice pressure differential (i.e., "P = P1 - P2). If"Pmax is less than "P, this is an indication that chokedflow conditions will exist under the service conditionsspecified. If choked flow conditions do exist (i.e., "Pmax< P1 - P2), then step 6 of the procedure for Sizing Valvesfor Liquids must be modified by replacing the actual ser-vice pressure differential (i.e., P1 - P2) in the appropriatevalve sizing equation with the calculated "Pmax value.

Note

Once it is known that choked flow condi-tions will develop within the specified valvedesign ("Pmax is calculated to be less than"P), a further distinction can be made to de-termine whether the choked flow is causedby cavitation or flashing. The choked flowconditions are caused by flashing if the out-let pressure of the given valve is less thanthe vapor pressure of the flowing liquid. Thechoked flow conditions are caused by cavi-tation if the outlet pressure of the valve isgreater than the vapor pressure of the flow-ing liquid.

Determining FR, the ReynoldsNumber Factor(3)

Nonturbulent flow conditions can occur in applicationswhere there is high fluid viscosity, very low pressure dif-ferential, or some combination of these conditions. Inthose instances where nonturbulent flow exists, FR, theReynolds number factor, must be introduced. DetermineFR using the following procedure.

A. Calculate Rev, the Reynolds number, using the equa-tion:

Rev =N4 Fd q

n FL1∕2 Cv

1∕2FL

2 Cv2

N2 D4+ 11∕4

where,

N2, N4 = Numerical constants determined from table 2

D = Internal diameter of the piping

& = Kinematic viscosity of the fluid

Cv = Cvt, the pseudo sizing coefficient

Cvt =q

N1

P1−P2Gf

Fd = Valve style modifier that is dependent on

the valve style used. Valves that use two par-allel flow paths, such as double-ported globe-style valves, butterfly valves, or 8500 Seriesvalves, use an Fd of 0.7. For any other valvestyle, use an Fd of 1.0.

B. Once Rev is known, use one of the following threeapproaches to obtain the desired information.

ANSI/ISA/IEC Valve SizingDetermining FR

Figure 3. Reynolds Number Factor, FR

Determining Required FlowCoefficient for Selecting Valve SizeThe following treatment is based on valves without at-tached fittings; therefore, Fp = 1.0.

1. Calculate a pseudo valve flow coefficient Cvt, assum-ing turbulent flow, using:

Cvt =q

N1

P1−P2Gf

2. Calculate Rev, substituting Cvt from step 1 for Cv. ForFL, select a representative value for the valve style de-sired.

3. Find FR as follows:

a. If Rev is less than 56, the flow is laminar, and FR canbe found by using either the curve in figure 3 labeled“FOR SELECTING VALVE SIZE” or by using the equa-tion:

FR = 0.019Rev0.67

b. If Rev is greater than 40,000, the flow can be takenas turbulent, and FR = 1.0.

c. If Rev lies between 56 and 40,000, the flow is transi-tional, and FR can be found by using either the curve infigure 3 or the column headed “Valve Size Selection” intable 3.

Table 3. Reynolds Number Factor, FR,for Transitional Flow

Valve Reynolds Number, Rev(1)

FR(1) Valve

SizeSelection

FlowRate

Prediction

PressureDrop

Prediction0.2840.320.360.400.44

56667994

110

106117132149167

3038485974

0.480.520.560.600.64

130154188230278

188215253298351

90113142179224

0.680.720.760.800.84

340471620980

1560

416556720

11001690

280400540870

14300.880.920.961.00

24704600

10,20040,000

26604800

10,40040,000

23004400

10,00040,000

1. Linear interpolation between listed values is satisfactory.


Determining FR


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Catalog 12

4. Obtain the required Cv from:

Cv =Cvt

FR

5. After determining Cv, check the FL value for the se-lected valve size and style. If this value is significantlydifferent from the value selected in step 2, use the newvalue, and repeat steps 1 through 4.

Predicting Flow Rate

1. Calculate qt, assuming turbulent flow, using:

qt = N1CvP1 − P2

Gf

2. Calculate Rev, substituting qt for q from step 1.


a. If Rev is less than 106, the flow is laminar, and FRcan be found by using the curve in figure 3 labeled “FORPREDICTING FLOW RATE” or by using the equation:

FR = 0.0027 Rev


c. If Rev lies between 106 and 40,000, the flow is transi-tional, and FR can be found by using either the curve infigure 3 or the column headed “Valve Size Selection” intable 3.

4. Obtain the predicted flow rate from:

q = FR qt

Predicting Pressure Drop

1. Calculate Rev.


a. If Rev is less than 30, the flow is laminar, and FR canbe found by using the curve in figure 3 labeled “FORPREDICTING PRESSURE DROP” or by using theequation:

FR = 0.052Rev0.5


c. If Rev lies between 30 and 40,000, the flow is transi-tional, and FR can be found by using the curve in figure 3or the column headed “Pressure Drop Prediction” intable 3.

3. Calculate the predicted pressure drop from:

Dp = Gf qN1 FR Cv

2

Liquid Sizing Sample Problems

Liquid Sizing Sample Problem No. 1Assume an installation that, at initial plant start-up, willnot be operating at maximum design capability. Thelines are sized for the ultimate system capacity, but thereis a desire to install a control valve now which is sizedonly for currently anticipated requirements. The line sizeis 8 inches, and a Class 300 Design ES valve with anequal percentage cage has been specified. Standardconcentric reducers will be used to install the valve intothe line. Determine the appropriate valve size.

1. Specify the necessary variables required to size thevalve:

D Desired valve design—Class 300 Design ES valvewith equal percentage cage and an assumed valve size of 3inches.

D Process fluid—liquid propane

D Service conditions—

q = 800 gpmP1 = 300 psig = 314.7 psiaP2 = 275 psig = 289.7 psia"P = 25 psiT1 = 70_FGf = 0.50Pv = 124.3 psiaPv = 616.3 psia

2. Determine an N1 value of 1.0 from table 2.

3. Determine Fp, the piping geometry factor.

Because it is proposed to install a 3-inch valve in an8-inch line, it will be necessary to determine the pipinggeometry factor, Fp, which corrects for losses caused byfittings attached to the valve.

Fp = 1 + SKN2Cv

d22−1∕2



where,

N2 = 890, from table 2d = 3 in., from step 1

Cv = 121, from the flow coefficient table for a Class 300,3 in. Design ES valve with equal percentage cage

To compute %K for a valve installed between identicalconcentric reducers:

Sk = K1 + K2

= 1.51 − d2

D22

= 1.51 −(3)2

(8)22

= 1.11

where,

D = 8 in., the internal diameter of the piping so,

Fp = 1 + 1.11890

121322−1∕2

= 0.90

4. Determine "Pmax (the Allowable Sizing PressureDrop).

Based on the small required pressure drop, the flow willnot be choked (i.e., "Pmax > "P).


Under the specified service conditions, no correctionfactor will be required for Rev (i.e., FR = 1.0).

6. Solve for Cv using the appropriate equation.

Cv =q

N1 FpP1−P2

Gf

= 8001.00.90 25

0.5

= 125.7

7. Select the valve size using the flow coefficient tableand the calculated Cv value.

The required Cv of 125.7 exceeds the capacity of theassumed valve, which has a Cv of 121. Although for thisexample it may be obvious that the next larger size (4inches) would be the correct valve size, this may notalways be true, and a repeat of the above procedureshould be carried out.

Assuming a 4-inch valve, Cv = 203. This value was de-termined from the flow coefficient table for a Class 300,4-inch Design ES valve with an equal percentage cage.

Recalculate the required Cv using an assumed Cv valueof 203 in the Fp calculation.

where,

Sk = K1 + K2

= 1.51 − d2

D22

= 1.51 − 16642

= 0.84

and

Fp = 1.0 + SKN2Cv

d22−1∕2

= 1.0 + 0.84890

203422−1∕2

= 0.93

and

Cv =q

Nq FpP1−P2

Gf

= 8001.00.93 25

0.5

= 121.7

This solution indicates only that the 4-inch valve is largeenough to satisfy the service conditions given. Theremay be cases, however, where a more accurate predic-tion of the Cv is required. In such cases, the required Cvshould be redetermined using a new Fp value based onthe Cv value obtained above. In this example, Cv is121.7, which leads to the following result:




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Catalog 12

Fp = 1.0 + SKN2Cv

d22−1∕2

= 1.0 + 0.84890

121.7422−1∕2

= 0.97

The required Cv then becomes:

Cv =q

N1 FpP1−P2

Gf

= 8001.00.97 25

0.5

= 116.2

Because this newly determined Cv is very close to theCv used initially for this recalculation (i.e., 116.2 versus121.7), the valve sizing procedure is complete, and theconclusion is that a 4-inch valve opened to about 75-per-cent of total travel should be adequate for the requiredspecifications.

Liquid Sizing Sample Problem No. 2

Determine the appropriate valve size for the followingapplication. A Design ED valve with a linear cage hasbeen specified. Assume piping size will be the same asthe valve size.

1. Specify the variables required to size the valve:

D Desired valve design—a Class 300 Design ED valvewith linear cage

D Process fluid—water


q = 2200 gpmP1 = 375 psig = 389.7 psiaP2 = 100 psig = 114.7 psia"P = P1 - P2 = 275 psiT1 = 270_FGf = 0.93Pv = 41.9 psia

2. Determine an N1 value of 1.0 from table 2.


Because valve size equals line size, Fp = 1.0

4. Determine "Pmax, the allowable sizing pressure drop.

DPmax = FL2P1 − FF Pv

where,

P1 = 389.7 psia, given in step 1P2 = 114.7 psia, given in step 1Pv = 41.9 psia, given in step 1FF = 0.90, determined from figure 1

Assume FL = 0.84 (from the flow coefficient table, 0.84appears to be a representative FL factor for Design EDvalves with a linear cage.) Therefore,

DPmax = (0.84)2 [389.7 − (0.90)(41.9)]

= 248.4 psi

"Pmax < "P (i.e., 248.4 < 275.0) indicates that chokedflow conditions will exist. Because, from the initial speci-fications, it is known that the outlet pressure (P2 = 114.7psia) is greater than the vapor pressure of the flowingwater (Pv = 41.9 psia), the conditions of choked flow, inthis case, are caused by cavitation. Therefore, somefurther consideration of valve style and trim selectionmight be necessary.


For water at the pressure drop given, no Rev correctionwill be required (i.e., FR = 1.0).

6. Solve for required Cv using "Pmax.

Cv =q

N1 Fp FRDPmax

Gf

= 2200248.40.93

= 134.6


A 3-inch Class 300 Design ED valve with a linear cagehas a Cv of 133 at 80-percent travel and should be satis-factory from a sizing standpoint. However, FL was as-sumed to be 0.84, whereas for the 3-inch Design EDvalve at maximum travel, FL is 0.82. Reworking the prob-lem using the actual value of FL yields "Pmax = 236.7psi. These result in required Cv values of 137.6 (usingthe assumed FL of 0.84) and 137.9 (using the actual FLvalue of 0.82), which would require the valve to be85-percent open.



Liquid Sizing Sample Problem No. 3

Assume there is a desire to use a Design V100 valve ina proposed system controlling the flow of a highly vis-cous Newtonian lubricating oil. The system design is notyet complete, and the line size has not been established.Therefore, assume that the valve will be line size. Deter-mine valve size.

1. Specify the variables required to size the valve:

D Desired valve—Design V100 valve

D Process fluid—lubricating oil


q = 300 m3/hP1 = 7.0 bar gauge = 8.01 bar absoluteP2 = 5.0 bar gauge = 6.01 bar absolute"P = 2.0 barPv = negligibleT1 = 15.6_C = 289_KGf = 0.908& = 8000 centistokes

2. Determine N1 from table 2.

For the specified units of m3/h and bar, N1 = 0.865


Assuming valve size equals line size, Fp = 1.0.

4. Determine "Pmax, the allowable sizing pressure drop.

Based on the required pressure drop, the flow will not bechoked.


a. Calculate the pseudo sizing coefficient, Cvt:

Cvt =q

N1

P1−P2Gf

= 300

0.865 2.00.908

= 234

b. Calculate Rev, the Reynolds number:

Rev =N4 Fd q

n FL1∕2 Cv

1∕2FL Cv2

N2 D4 + 11∕4

where,

N2 = 0.00214, from table 2N4 = 7600, from table 2

Cv = 234, the value determined for the pseudo sizingcoefficient, Cvc.

D = 80 mm. The pseudo sizing coefficient of 234 indi-cates that an 80 mm (3-inch) Design V100 valve,which has a Cv of 372 at 90 degrees of ball rota-tion, is required (see the flow coefficient table).Assuming that line size will equal body size, the 80mm (3-inch Design V100 will be used with 80 mmpiping

q = 300 m3/h& = 8000 centistokes from step 1

Fd = 1.0 because the Design V100 valve has a singleflow passage

From the flow coefficient table, the FL value for an 80mm (3-inch) Design V100 valve is 0.68. Therefore,

Rev =(7600)(1.0)(300)

(8000) (0.68)(234) 0.682234

2

0.00214804 + 11∕4

= 241

c. Read FR off the curve, For Selecting Valve Size, infigure 3 using an Rev of 241, FR = 0.62.

6. Solve for required Cv using the appropriate equation.

Cv =q

N1 Fp FR

P1 − P2Gf

= 300

0.865(1.0)(0.62) 2.00.908

= 377


The assumed valve (80 mm or 3-inch), which has a Cv of372 at 90 degrees of ball rotation, is obviously too smallfor this application. For this example, it is also obviousthat the next larger size (100 mm or 4-inch), which has arated Cv of 575 and an FL of 0.61, would be largeenough.

To obtain a more precise valve sizing measurement, theproblem can be reworked using the calculated Cv valueof 377. For the required 100 mm (4-inch) Design V100valve, a Cv of 377 occurs at a valve travel of about 80degrees, and this corresponds to an FL value of 0.71.Reworking the problem using this corresponding value of





Catalog 12


March 2001Page 2-12

Catalog 12

FL = 0.71 yields FR = 0.61 and Cv = 383. Because thetabulated Cv value, 377, is very close to the recalculatedCv value, 383, the valve sizing procedure is complete,and the determined 100 mm (4-inch) valve opened to 80degrees valve travel should be adequate for the requiredspecifications.

Sizing Valves for CompressibleFluidsFollowing is a six-step procedure for the sizing of controlvalves for compressible flow using the ISA standardizedprocedure. Each of these steps is important and must beconsidered during any valve sizing procedure. Steps 3and 4 concern the determination of certain sizing factorsthat may or may not required in the sizing equation de-pending on the service conditions of the sizing problem.If it is necessary for one or both of these sizing factors tobe included in the sizing equation for a particular sizingproblem, refer to the appropriate factor determinationsection(s), which is referenced and located in the follow-ing text.

1. Specify the necessary variables required to size thevalve as follows:

D Desired valve design (e.g., Design ED with linearcage); refer to the appropriate valve flow coefficient table inthis catalog

D Process fluid (e.g., air, natural gas, steam, etc.) and

D Appropriate service conditions—

q, or w, P1, P2 or "P, T1, Gg, M, k, Z, and $1

The ability to recognize which terms are appropriate for aspecific sizing procedure can only be acquired throughexperience with different valve sizing problems. If any ofthe above terms appear to be new or unfamiliar, refer totable 1 for a complete definition.

2. Determine the equation constant, N.N is a numericalconstant contained in each of the flow equations to pro-vide a means for using different systems of units. valuesfor these various constants and their applicable units aregiven in table 2.

Use either N7 or N9 if sizing the valve for a flow rate involumetric units (i.e., scfh or m3/h). Which of the twoconstants to use depends upon the specified serviceconditions. N7 can be used only if the specific gravity,Gg , of the flowing gas has been specified along with theother required service conditions. N9 can be used only ifthe molecular weight, M, of the gas has been specified.

Use either N6 or N8 if sizing the valve for a flow rate inmass units (i.e., lb/h or kg/h). Which of the two constantsto use depends upon the specified service conditions. N6can be used only if the specific weight, $1 of the flowinggas has been specified along with the other requiredservice conditions. N8 can be used only if the molecularweight, M, of the gas has been specified.

3. Determine Fp , the piping geometry factor. Fp is acorrection factor that accounts for any pressure lossesdue to piping fittings such as reducers, elbows, or teesthat might be attached directly to the inlet and outlet con-nections of the control valves to be sized. If such fittingsare attached to the valve, the Fp factor must be consid-ered in the sizing procedure. If, however, no fittings areattached to the valve, Fp has a value of 1.0 and simplydrops out of the sizing equation.

Also, for rotary valves valves with reducers, Fp factorsare included in the appropriate flow coefficient table. Forother valve designs and fitting styles, determine the Fpfactors by using the procedure for Determining Fp thePiping Geometry Factor, which is located in the sectionfor Sizing Valves for Liquids.

4. Determine Y, the expansion factor, as follows:

Y = 1 − x3 Fk xT

where,

Fk = k/1.4 the ratio of specific heats factork = Ratio of specific heatsx = P/P1, the pressure drop ratio

xT = The pressure drop ratio factor for valves installedwithout attached fittings. More definitively, xT isthe pressure drop ratio required to produce criti-cal, or maximum, flow through the valve whenFk = 1.0.

If the control valve to be installed has fittings such asreducers or elbows attached to it, then their effect is ac-counted for in the expansion factor equation by replacingthe xT term with a new factor xTP. A procedure for deter-mining the xTP factor is described in the section for De-termining xTP, the Pressure Drop Ratio Factor.

Note

Conditions of critical pressure drop arerealized when the value of x become equalto or exceed the appropriate value of theproduct of either Fk xT or Fk xTP at whichpoint:

y = 1 − x3 Fk xT

= 1 − 1∕3 = 0.667


Sizing Valves for Compressible Fluids

Although in actual service, pressure drop ratios can, andoften will, exceed the indicated critical values, it shouldbe kept in mind that this is the point where critical flowconditions develop. Thus, for a constant P1, decreasingP2 (i.e., increasing "P) will not result in an increase inthe flow rate through the valve. Values of x, therefore,greater than the product of either FkxT or FkxTP mustnever be substituted in the expression for Y. This meansthat Y can never be less than 0.667. This same limit onvalues of x also applies to the flow equations that areintroduced in the next section.

5. Solve for the required Cv using the appropriate equa-tion:

For volumetric flow rate units—

D If the specific gravity, Gg, of the gas has been speci-fied:

Cv =q

N7FpP1Yx

GgT1Z

D If the molecular weight, M, of the gas has been speci-fied:

Cv =q

N9FpP1Yx

M T1 Z

For mass flow rate units—

D If the specific weight, $1, of the gas has been specified:

Cv = wN6 Fp Y x P1 g1

D If the molecular weight, M, of the gas has been speci-fied:

Cv = w

N8 Fp P1Yx MT1 Z

In addition to Cv, two other flow coefficients, Kv and Av,are used, particularly outside of North America. The fol-lowing relationships exist:

Kv = (0.865)(Cv)

Av = (2.40X10−5)(Cv)


Note

Once the valve sizing procedure is com-pleted, consideration can be made for aero-dynamic noise prediction. To determine thegas flow sizing coefficient (Cg) for use in theFisher aerodynamic noise prediction tech-nique, use the following equation:

Cg = 40Cv xT

Determining xTP, the Pressure DropRatio FactorIf the control valve is to be installed with attached fittingssuch as reducers or elbows, then their effect is ac-counted for in the expansion factor equation by replacingthe xT term with a new factor, xTP.

xTP =xT

Fp21 +

xT Ki

N5Cv

d22−1

where,

N5 = Numerical constant found in table 2d = Assumed nominal valve size

Cv = Valve sizing coefficient from flow coefficient tableat 100 percent travel for the assumed valve size

Fp = Piping geometry factorxT = Pressure drop ratio for valves installed without

fittings attached. xT values are included in the flowcoefficient tables.

In the above equation, Ki, is the inlet head loss coeffi-cient, which is defined as:

Ki = K1 + KB1

where,

K1 = Resistance coefficient of upstream fittings (see theprocedure for Determining Fp, the Piping GeometryFactor, which is contained in the section for SizingValves for Liquids).

KB1 = Inlet Bernoulli coefficient (see the procedure forDetermining Fp the Piping Geometry Factor, whichis contained in the section for Sizing Valves forLiquids).


Determining XTP


December 1999Page 2-13

Catalog 12


July 2000Page 2-14

Catalog 12

Compressible Fluid Sizing SampleProblems

Compressible Fluid Sizing Sample ProblemNo. 1

Determine the size and percent opening for a DesignV250 valve operating with the following service condi-tions. Assume that the valve and line size are equal.


D Desired valve design—Design V250 valve

D Process fluid—Natural gas


P1 = 200 psig = 214.7 psiaP2 = 50 psig = 64.7 psia"P = 150 psi

x = "P/P1 = 150/214.7 = 0.70T1 = 60_F = 520_RM = 17.38

Gg = 0.60k = 1.31q = 6.0 x 106 scfh

2. Determine the appropriate equation constant, N, fromtable 2.

Because both Gg and M have been given in the serviceconditions, it is possible to use an equation containingeither N7 or N9 . In either case, the end result will be thesame. Assume that the equation containing Gg has beenarbitrarily selected for this problem. Therefore, N7 =1360.

3. Determine Fp , the piping geometry factor. Since valveand line size are assumed equal, Fp = 1.0.

4. Determine Y, the expansion factor.

Fk =k

1.40

= 1.311.40

= 0.94

It is assumed that an 8-inch Design V250 Valve will beadequate for the specified service conditions. From theflow coefficient table, xT for an 8-inch Design V250 valveat 100-percent travel is 0.137.

x = 0.70 (This was calculated in step 1.)

Since conditions of critical pressure drop are realizedwhen the calculated value of x becomes equal to or ex-ceeds the appropriate value of FkxT, these values shouldbe compared.

FkxT = (0.94)(0.137)

= 0.129

Because the pressure drop ratio, x = 0.70 exceeds thecalculated critical value, FkxT = 0.129, choked flow con-ditions are indicated. Therefore, Y = 0.667and XLIM toFkxT = 0.129.


Cv =q

N7 Fp P1 Y xGg T1 Z

The compressibility factor, Z, can be assumed to be 1.0for the gas pressure and temperature given and Fp = 1because valve size and line size are equal.

So,

Cv = 6.0 x 106

(1360)(1.0)(214.7)(0.667) 0.129(0.6)(520)(1.0)

= 1515


The above result indicates that the valve is adequatelysized (i.e., rated Cv = 2190). To determine the percentvalve opening, note that the required Cv occurs atapproximately 83 degrees for the 8-inch Design V250valve. Note also that, at 83 degrees opening, the xT val-ue is 0.525, which is substantially different from the ratedvalue of 0.137 used initially in the problem. The nextstep is to rework the problem using the xT value for 83degrees travel.

The FkxT product must now be recalculated.

x = FkxT

= (0.94)(0.252)

= 0.237

The required Cv now becomes:

Cv =q

N7 Fp P1 Y xGg T1 Z


Compressible Fluid Sizing Sample Problems

= 6.0 x 106

(1360)(1.0)(214.7)(0.667) 0.237(0.6)(520)(1.0)

= 1118

The reason that the required Cv has dropped so dramati-cally is attributable solely to the difference in the xT val-ues at rated and 83 degrees travel. A Cv of 1118 occursbetween 75 and 80 degrees travel.

The appropriate flow coefficient table indicates that xT ishigher at 75 degrees travel than at 80 degrees travel.Therefore, if the problem were to be reworked using ahigher xT value, this should result in a further decline inthe calculated required Cv.

Reworking the problem using the xT value correspondingto 78 degrees travel (i.e., xT = 0.328) leaves:

x = Fk xT

= (0.94)(0.328)

= 0.308

and,

Cv =q

N7 Fp P1 Y xGg T1 Z

= 6.0 x 106

(1360)(1.0)(214.7)(0.667) 0.308(0.6)(520)(1.0)

= 980

The above Cv of 980 is quite close to the 75 degree trav-el Cv. The problem could be reworked further to obtain amore precise predicted opening; however, at this point itcan be stated that, for the service conditions given, an8-inch Design V250 valve installed in an 8-inch line willbe approximately 75 degrees open.

Compressible Fluid Sizing Sample ProblemNo. 2

Assume steam is to be supplied to a process designedto operate at 250 psig. The supply source is a headermaintained at 500 psig and 500_F. A 6-inch line from thesteam main to the process is being planned. Also, makethe assumption that if the required valve size is less than6 inches, it will be installed using concentric reducers.Determine the appropriate Design ED valve with a linearcage.


a. Desired valve design—Class 300 Design ED valvewith a linear cage. Assume valve size is 4 inches.

b. Process fluid—superheated steam

c. Service conditions—

w = 125,000 lb/hP1 = 500 psig = 514.7 psiaP2 = 250 psig = 264.7 psia"P = 250 psi

x = "P/P1 = 250/514.7 = 0.49T1 = 500_F$1 = 1.0434 lb/ft3 (from steam properties handbook)k = 1.28 (from steam properties handbook)

2. Determine the appropriate equation constant, N, fromtable 2.

Because the specified flow rate is in mass units, (lb/h),and the specific weight of the steam is also specified, theonly sizing equation that can be used in that which con-tains the N6 constant. Therefore,

N6 = 63.3


Fp = 1 + SKN2Cv

d22−1∕2

where,

N2 = 890, determined from table 2d = 4 in.Cv = 236, which is the value listed in the flow coefficient

table for a 4-inch Design ED valve at 100-percenttotal travel.

and,

Sk = K1 + K2

= 1.51 − d2

D22

= 1.51 − 42

622

= 0.463

Finally:

Fp = 1 + 0.463890(1.0)(236)

(4)22−1∕2

ANSI/ISA/IEC Valve SizingCompressible Fluid Sizing Sample Problems



Catalog 12



Catalog 12

= 0.95

4. Determine Y, the expansion factor.

Y = 1 − x3 Fk xTP

where,

Fk =k

1.40

= 1.281.40

= 0.91

x = 0.49(This was calculated in step 1.)

Because the 4-inch valve is to be installed in a 6-inchline, the xT term must be replaced by xTP,

xTP =xT

Fp21 +

xT Ki

N5Cv

d22−1

where,

N5 = 1000, from table 2d = 4 in.

Fp = 0.95, determined in step 3xT = 0.688, a value determined from the appropriate

listing in the flow coefficient tableCv = 236, from step 3

and

Ki = K1 + KB1

= 0.51 − d2

D22

+1 − dD4

= 0.51 − 42

622

+1 − 464

= 0.96

where D = 6 in.

so:

xTP = 0.690.9521 +

(0.69)(0.96)1000

236422−1

= 0.67

Finally:

Y = 1 − x3 Fk xTP

= 1 − 0.49(3)(0.91)(0.67)

= 0.73


Cv = wN6 Fp Y x P1 g1

Cv =125, 000

(63.3)(0.95)(0.73) (0.49)(514.7)(1.0434)

= 176


Refer to the flow coefficient tables for Design ED valveswith linear cage. Because the assumed 4-inch valve hasa Cv of 236 at 100-percent travel and the next smallersize (3 inches) has a Cv of only 148, it can be surmisedthat the assumed size is correct. In the event that thecalculated required Cv had been small enough to havebeen handled by the next smaller size or if it had beenlarger than the rated Cv for the assume size, it wouldhave been necessary to rework the problem again usingvalues for the new assumed size.


Compressible Fluid Sizing Sample Problems

Version 1.4 of the Fisher Sizing Program offers the abili-ty to estimate the vapor pressure of fluids at the givenservice temperature. These estimations are based on acorrelation of actual Pv data for the specified fluid to thefollowing form of the Wagner equation:

In Pvpr =a' + b'1.5 + c' 3 + d' 6

TrTr-min ± Tr ± Tr-max

(1)

where,Pvpr = reduced vapor pressure = Pv/PcTr = reduced temperature = T/TcPv = saturated vapor pressurePc = thermodynamic critical pressure' = 1 - TrTr-min = reduced minimum temperature -- Tmin/TcTr-max = reduced maximum temperature = Tmax/TcTmin = minimum valid calculation temperatureTmax = maximum valid calculation temperature

This equation was selected because of it’s overall supe-riority to more widely used but simpler equations. Thisequation replicates the actual shape of the vapor pres-sure curve well and yields accurate results over a fairlybroad temperature range. For the fluids contained in theFSP v1.4 internal (non-editable) library, typical resultsfall within the lessor of ¦1% or ¦1 psi of the referencevalues for the individual fluids. Worst case results areusually within the lessor of ¦3% or ¦5 psi. While theAntoine equation is widely used for vapor pressure cor-relations, it is, in general, more limited in range overwhich accurate results can be obtained. Furthermore it isstrictly limited to use within the prescribed temperaturerange.

The coefficients a, b, c, and d have been determined forall of the fluids contained in the internal fluids library(non-editable) by curve fitting to published data. Provi-sions to input these values for user defined fluids areprovided in the external library (editable). While thesecoefficients can be found for some fluids in the generalliterature, they are not widely available. For select casesconsidered to be commercially strategic, support is avail-able to determine these coefficients for customer fluids.To obtain this support, please complete the data form onthe reverse side of this sheet and send to ApplicationsEngineering. Please note that a minimum of ten datapoints are recommended to define a good baselinecurve.

As is evident on inspection of equation (1), the value ofthe thermodynamic critical pressure is used in calculat-ing the value of the vapor pressure. The Pv coefficientssupplied in the internal library are based on the value ofthe critical pressure contained in the library. Therefore, inorder to preserve the integrity of the Pv calculation, thevalue of Pc cannot be changed within a calculation caseif the vapor pressure is being calculated. If it is desired touse an alternate value of Pc in lieu of the value suppliedby the fluid library, it will be necessary to disable the“calculate Pv” option and manually input both the Pc andPv values.

The temperatures Tmin and Tmax establish the limits ofthe temperature range over which the calculation is con-sidered valid (this version of the program will not con-tend with extrapolations beyond these limits). Typicallythe upper temperature limit coincides with the thermody-namic critical pressure, although there are instanceswhere this is not the case and Tmax < Tc. In no case isTmin less than the triple point temperature.

FSP Vapor Pressure Calculation (v1.4)

Printed in U.S.A. on recycled paper.!Fisher Controls International, Inc., 1999;All Rights Reserved

April 1999Page 2-17

Catalog 12


April 1999Page 2-18

Catalog 12

The following information is required in order to deter-mine the vapor pressure coefficients, a, b, c, and d, foruse in the external fluids library. Please supply all re-quired information and FAX or mail to your sales office.

Fluid Name:

Chemical Formula:

Physical Constants:

Critical Temperature, Tc =

Critical Pressure, Pc =

Triple Point Temperature, Ttp =

Molecular Weight, MW =

Specific Heat Ratio, ko =

Data Source*: j Lab Data

j Technical Ref.

j Other

*Optional information not required for coefficient determination

Customer

Representative

Office

May this information be share with other Fisher

Sizing Program users? jYes jNo

Vapor Pressure Data(1)

Data Point T, (units) Pv, (units)

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

1. A minimum of ten data points are recommended.

Custom Pv Coefficient Request

Fisher Sizing Program

IntroductionThe behavior of flowing pulp stock is different from wateror viscous Newtonian flows. It is necessary to accountfor this behavior when determining the required valvesize. Methods have been developed to aid in determin-ing correct valve size for these types of applications. Thepurpose of this PS sheet is to provide an overview of thecurrent recommended sizing method and discuss specif-ic implementations of the technology in the Fisher SizingProgram, Rev. 1.4.

Basic MethodThe pulp stock sizing calculation uses the following mod-ified form of the basic liquid sizing equation:

Q = CvKp D P (1)

where:"P = sizing pressure drop, psidCv = valve flow coefficientKp = pulp stock correction factorQ = volumetric flow rate, gpm

The crux of this calculation is the pulp stock correctionfactor, Kp. This factor is the ratio of the pulp stock flowrate to water flow rate under the same flowing condi-tions. It therefore modifies the relationship between Q,Cv, and "P to account for the effects of the pulp stockrelative to that for water. The value of this parameter intheory depends on many factors such as pulp stocktype, consistency, freeness, fiber length, valve type andpressure drop. However, in practice it appears that the

dominant effects are due to three primary factors: pulptype, consistency and pressure differential. Values of Kpfor three different pulp stock types are shown in Figures1-3. These methods are based on the technology pre-sented in reference (1).

Once the value of the pulp stock correction factor isknown, determining the required flow coefficient or flowrate is equivalent to basic liquid sizing. For example,consider the following:

Q = 1000 gpm of 8% consistency kraft pulp stock"P = 16 psidP1 = 150 psia

Kp ¶ 0.83 (from Figure 2), therefore,

Cv = QKp D P

= 1000(0.83) 16 = 301

Effect of fluid vaporization and choked flow of pulp stockon the effective pulp stock correction factor is not knownas of this writing. The effects of pulp stock on soundpressure level and cavitation are discussed below.

The uncertainty of this calculation is currently unknown,but should be considered to be greater than for normalliquid sizing. As noted above, only the major effects ofstock type and consistency and pressure drop are ac-counted for. Tests conducted by Fisher Controls atWestern Michigan University on low consistency stockaffirm the general behavior reported in (1), although insome cases the degree of correction was not as signifi-cant. This suggests that the overall variance of this rela-tively simple method may be moderate (e.g., estimatedto be in excess of ¦10%).

FSP Pulp Stock Sizing Calculations (v1.4)


April 1999Page 2-19

Catalog 12


April 1999Page 2-20

Catalog 12

Fisher Sizing ProgramImplementationThe pulp stock correction factor is automatically calcu-lated and utilized in sizing when Pulp Stock Sizing isselected. This value is determined on the basis of thepulp stock type, consistency and pressure drop. Theequations used to calculate this value were used to gen-erate the curves in Figures 1-3. This value is displayedin the Intermediate Results area of the screen and can-not be manually overridden. Checks for valid consisten-cy range and minimum pressure drop are conducted.The calculation is aborted and an appropriate warningmessage is displayed if either of these conditions is notsatisfied.

The sizing calculations are carried out in a mannerequivalent to basic liquid sizing. The sizing "P is deter-mined in the conventional manner, i.e., it is the lessor ofDPactual or DPallowable. [Note that for best accuracy theallowable pressure differential computations should bebased on the Km (FL

2) associated with the valve at theactual opening.] The fluid vapor pressure and criticalpressure drop ratio (Pv, rc) are based on the propertiesof fresh water. The fluid vapor pressure may be input,but the critical pressure used in calculating rc is that offresh water. Whereas the effect of choked flow on Kp isunknown, the sizing program defaults to the conserva-tive alternative and bases Kp on "Psizing as determinedabove.

Pressure differential ("P) calculations are not currentlyoffered because of the dependency of the Kp factor on"P. If this value is desired it will be necessary to esti-

mate it manually. It may be included in future revisions ofthe program if this is perceived to be a critical calcula-tion.

The basic sizing calculations are referenced to water,and therefore to not require a value of the specific gravityfor the pulp stock. However, other calculations supportedby the program, such as sound pressure level and veloc-ity calculations do require this value. To satisfy theneeds of these calculations, an estimate of the specificgravity is also produced and displayed in the Intermedi-ate Results area of the basic calculation screen. Thisestimate is a function only of stock consistency (at50 _F) and is shown graphically in Figure 4.

If the stock consistency is less than two percent (2%),there is no difference from conventional hydrodynamicnoise prediction methods. The noise level is calculatedin the same manner as for normal liquid sizing. If theconsistency is greater than two percent, then the calcu-lated noise level is adjusted by a constant value:

Predicted LpA = Calculated LpA − 5dBA (2)

The cavitation behavior of low consistency pulp stock(e.g., < 4%) is treated as equivalent to that of water.Generally, pulp stock of a consistency greater than fourpercent is not known to be problematic. Therefore, thesizing program indicates that Ar > Kc, but that no cavita-tion problems are likely to occur.

References:1. Andrews, E. and M. Husu, “Sizing and Cavitation Damage Reductionfor Stock and White Water Control Valves”, 1991 Process Control Con-ference, TAPPI Proceedings, pp. 65-73.


Figure 1. Pulp Stock Correction Factors for Kraft Pulp

Figure 2. Pulp Stock Correction Factors for Mechanical Pulp



April 1999Page 2-21

Catalog 12


April 1999Page 2-22

Catalog 12

Figure 3. Pulp Stock Correction Factors for Recycled Pulp

Figure 4. Specific Gravity for All Pulp Types


Conversions for Units of MeasureTable 1. LengthTable 2. AreaTable 3. VolumeTable 4. MassTable 5. DensityTable 6. VelocityTable 7. Heat Flow Rate

Table 8. ForceTable 9. PowerTable 10. TorqueTable 11. Pressure and Liquid HeadTable 12. Volumetric Rate of FlowTable 13. TemperatureTable 14. Abbreviated Conversions of Degrees

Fahrenheit to Degrees Celsius

Table 1. Length

MultiplyNumber of

ToObtain

bymillimeter

mmmeter

minch

infeetft

yardyd

millimetersmetersinches

feetyards

1100025.40304.8914.4

0.0010001

0.025400.30480.9144

0.0393739.37

112.0036.00

0.0032813.281

0.083331

3.00

0.0010941.094

0.027780.3333

1Note: 1 meter = 10 decimeters = 100 centimeters = 1000 millimeters = 0.001 kilometers = 1 x 106 microns

Table 2. Area

MultiplyNumber of

ToObtainby

square meterm2

squaremillimeter

mm2

square inchin2

square feetft2

square yardyd2

square meterssquare millimeters

square inchessquare feet

square yards

10.0000010.00064520.092900.8361

1,000,0001

645.192,900836,100

15500.001550

1144.01296

10.760.000010760.006944

19.000

1.1960.0000011960.0007716

0.11111

Table 3. Volume

MultiplyNumber of

ToObtainby

cubic meterm3

cubiccentimeter

cm3

literl

cubic inchin3

cubic footft3

Imperialgallon

Imp gal

U.S. gallonU.S. gal

m3

cm3

literin3

ft3

Imp galU.S. gal

10.000001000

0.0010000.00001639

0.028320.0045460.003785

1,000,0001

100016.39

28,32045463785

10000.001000

10.0163928.324.5463.785

61,0200.0610261.02

11728277.4231.0

35.310.00003531

0.035310.0005787

10.16050.1337

220.00.0002200

0.22000.003605

6.2291

0.8327

264.20.0002642

0.26420.004329

7.4801.201

1

Technical Information


April 1999Page 2-23

Catalog 12


April 1999Page 2-24

Catalog 12

Table 4. Mass

MultiplyNumber of

ToObtain

byOunce

ozPound

lbShort ton

sh tonLong ton

L tonKilogram

KgMetric ton

tonne

OuncesPounds

Short tonsLong tonsKilogramsMetric tons

116.00

32,00035,84035.27

35,270

0.062501

200022402.2052205

0.000031250.0005000

11.120

0.0011021.102

0.000027900.0004464

0.89291

0.00098420.9842

0.028350.4536907.21016

11000

0.000028350.0004536

0.90721.016

0.0010001

Table 5. Density

MultiplyNumber of

ToObtainby gram per

milliliter g/ml

kilogram percubic meter

kg/m3

pound percubic foot

lb/ft3

pound per cubicinch lb/in3

g/mlkg/m3

lb/ft3lb/in3

10.0010000.0160227.68

10001

16.0227,680

62.430.06243

11728

0.036130.000036130.0005787

1

Table 6. Velocity

MultiplyNumber of

ToObtainby

feet persecondft/sec

feet per minuteft/min

miles per hourmi/hr

meter per secondm/sec

meter per minutem/min

kilometer perhourkm/hr

ft/secft/minmi/hrm/secm/minkm/hr

10.016671.4673.280

0.054680.9113

60.001

88.00196.93.28154.68

0.68180.01136

12.237

0.037280.6214

0.30480.0050800.4470

10.016670.2778

18.290.304826.8260.00

116.67

1.0970.018291.6093.600

0.060001

Table 7. Heat Flow Rate

MultiplyNumber of

ToObtain

byWatts

W

calorie persecondcal/sec

kilocalorieper hourkcal/hr

British thermalunit per hour

Btu/hr

Wcal/seckcal/hrBtu/hr

14.1841.162

0.2831

0.23901

0.27780.07000

0.86043.600

10.2522

3.41214.283.966

1

Table 8. Force

MultiplyNumber of

ToObtainby

kilonewtonKN

kilogram forcekgf

pound forcelbf

poundalpdl

kilonewtonskilogram forcepound force

poundal

10.0098070.0044480.0001383

102.01

0.45360.01410

224.82.205

10.03108

723370.9332.17

1

Technical Information Continued

Table 9. Power

MultiplyNumber of

ToObtain

by WattW

kilogram forcemeter per second

kgf m/sec

metrichorsepower

foot pound forceper second

ft lbf/sec

horsepowerhp

Wkgfm/secmetric hpft lb/sec

horsepower

19.807735.51.356745.7

0.10201

75.000.138376.04

.0013600.01333

10.001843

1.014

0.73767.233542.5

1550.0

0.0013410.013150.9863

0.0018181

Table 10. Torque

MultiplyNumber of

ToObtain

by Newton MeterNm

kilogram forcemeterkgf m

foot poundft lb

inch poundin lb

Nmkgf mft lbin lb

19.8071.3560.1130

0.10201

0.13830.01152

0.73767.233

10.08333

8.85186.8012.00

1

Table 11. Pressure and Liquid Head

MultiplyNumber of

ToObtain

by bar(1)

kilogramforce persquare

centimeterkgf/cm2(2)

pound persquare inch

psi orlbf/in2

InternationalStandard

Atmosphereatm

foot ofwater(4 _C)ft H2O

inch ofwater(4 _C)in H2O

meter ofwater(4 _C)m H2O

centimeter ofMercury(0 _C)cm Hg

inch ofMercury

(0 _C)in Hg

millimeter ofMercury(0 _C)

torr or mm Hg

barkgf/cm2

psiatm

ft H2Oin H2Om H2Ocm Hgin Hgtorr

10.98070.068951.013

0.029890.0024910.098060.013330.03386

0.001333

1.0201

0.07031.033

0.03050.0025400.10000.013600.03453

0.001359

14.5014.22

114.69

0.43350.03611.422

0.19340.4911

0.01934

0.98690.96780.06805

10.02950

0.0024580.096780.013160.03342

0.001316

33.4532.812.30733.90

10.83333.281

0.44601.133

0.04460

401.5393.727.68406.8

121

39.375.35213.60

0.5352

10.2010.00

0.703110.33

0.30480.2540

10.13600.34530.0136

75.0173.565.17176.002.242

0.18687.356

12.540

0.1000

29.5328.962.03629.92

0.88260.07355

2.8960.3937

10.03937

750.1735.551.71760.022.421.86873.5610.0025.40

11. The unit of pressure in the International System of Units (SI) is the pascal (Pa), which is 1 Newton per square meter (N/m2). 1 bar = 105 Pa2. Technical (metric) atmosphere (at)

Table 12. Volumetric Rate of Flow

MultiplyNumber of

ToObtain

byliter persecond

l/sec

liter perminutel/min

cubic meterper hour

m3/hr

cubic footper hour

ft3/hr

cubic footper minute

ft3/min

Imp gallonper minute

Imp gal/min

US gallonper minuteUS gal/min

US barrelper day

(42 US gal)US barrel/d

l/secl/minm3/hrft3/hr

ft3/minImp gal/minUS gal/minUS barrel/d

10.016670.2778

0.0078650.47190.075770.06309

0.001840

601

16.670.471928.324.5463.7850.1104

3.6000.06000

10.028321.699

0.27270.2271

0.006624

127.12.11935.31

160.009.6338.021

0.2339

2.1190.035320.58860.01667

10.16060.1337

0.003899

13.200.22003.666

0.10386.229

10.83270.02428

15.850.26424.403

0.12477.4811.201

10.02917

543.49.057150.94.275256.541.1734.29

1

Technical Information (Continued)


April 1999Page 2-25

Catalog 12


April 1999Page 2-26

Catalog 12

Table 13. Temperaturedegrees

Celsius(1)

_C

KelvinK

degreesFahrenheit

_F

degreesRankine_R

_C_C + 273.159/5_C + 32

9/5_C + 491.67

K-273.15K

9/5K-459.679/5K

5/9(_F-32)5/9(_F + 459.67)

_F_F + 459.67

5/9(_R-491.67)5/9_R

_R-459.67_R

1. Formerly called Centigrade.

Table 14. Abbreviated Conversions of DegreesFahrenheit to Degrees Celsius

_F _C _F _C _F _C–50–45–40–35–30

–25–20–15–10–5

05101520

2530323540

4550556065

7075808590

95100110120130

140150160170180

190200210212

–45.6–42.8–40

–37.2–34.4

–31.7–28.9–26.1–23.3–20.6

–17.8–15

–12.2–9.4–6.7

–3.9–1.1

01.74.4

7.210

12.815.618.3

21.123.926.729.432.2

3537.8434954

6066717782

889399100

220230240250260

270280290300310

320330340350360

370380390400410

420430440450460

470480490500510

520530540550560

570580590600610

620630640650660

104110116121127

132138143149154

160166171177182

188193199204210

216221227232238

243249254260266

271277282288293

299304310316321

327332338343349

670680690700710

720730740750760

770780790800810

820830840850860

870880890900910

920930940950960

97098099010001050

11001150120012501300

1350140014501500

354360366371377

382388393399404

410416421427432

438443449454460

466471477482488

493499504510516

521527532538566

593621649677704

732760788816

Useful Equivalents

1 US Gallon of Water = 8.33 pounds @ 60_F1 Cubic Foot of Water = 62.36 pounds @ 60_F1 Cubic Meter of Water = 1000 Kilograms @ 4_C1 Cubic Foot of Air = .076 pounds

(Std. Press. and Temp.)1 Pound of Air = 13.1 Cubic Feet

(Std. Press. and Temp.)1 Kilogram of Air = .77 Cubic Meters

(Normal Press. and Temp.)1 Cubic Meter of Air = 1.293 Kilograms

(Normal Press. and Temp.)

Gas Molecular Weight29

= Sp. Gravity of that gas

Molecular Wt. of Air = 29

1/Density = Specific Volume

Mass Rate

Where:Standard Conditions (scfh) are 14.7 psia and 60_FNormal Conditions (norm) are 760 mm Hg and 0_CSG1 Water = 1 at 60_F. SG2 Water = 1 at 4_CM = Molecular Weight(1 = Density lb/ft3 (std); (2 = Density kg/m3 (norm)G1 = sp. gr. Air = 1 at (std); G2 = sp. gr. Air. = 1 at

(norm)

Gases

scfh =lb∕hr x 379

M

scfh =lb∕hrÃ1

scfh =lb∕hr x 13.1

G1

m3∕hr (norm) =kg∕hr x 22.40

M

m3∕hr (norm) =kg∕hrÃ2

m3∕hr (norm) =kg∕hr x 0.773

G2

Liquids

US gal∕min =lb∕hr

500xSG1m3∕hr =

.001 kg∕hrSG2

Technical Information Continued

The test classifications listed below are for factory accep-tance tests under the conditions shown. Because of thecomplex interaction of many physical properties, extrapo-lation of very low leakage rates to other than test conditionscan be extremely misleading. Consult the appropriateproduct bulletin for individual valve body leak classifica-tions.

ANSI/FCI 70-2 Maximum Leakage(1) Test Medium Pressure and Temperature

Class II 0.5% valve capacity at full travel Air Service nP or 50 psid (3.4 bar differential),whichever is lower, at 50 to 125_F (10 to 52_C)

Class III 0.1% valve capacity at full travel Air Service nP or 50 psid (3.4 bar differential),whichever is lower, at 50 to 125_F (10 to 52_C)

Class IV 0.01% valve capacity at full travel Air Service nP or 50 psid (3.4 bar differential),whichever is lower, at 50 to 125_F (10 to 52_C)

Class V 5 x 10--4 mL/min/psid/in. port dia.(5 x 10--12 m3/sec/bar differential/mm port dia) Water Service nP at 50 to 125_F (10 to 52_C)

Nominal PortDiameter Bubbles per

MinutemL perMinuteInch mm Minute Minute

Class VI

11-1/2

22-1/2

3

2538516476

12346

0.150.300.450.600.90

Air Service nP or 50 psid (3.4 bar differential),whichever is lower, at 50 to 125_F (10 to 52_C)

468

102152203

112745

1.704.006.75

Leakage Specifications


April 1999Page 2-27

Catalog 12


April 1999Page 2-28

Catalog 12

A1256

Use this curve for water. Enter on the abscissa at thewater vapor pressure at the valve inlet. Proceed vertical-ly to intersect the curve. Move horizontally to the left toread the critical pressure ratio, rc, on the ordinate.

Figure 1. Critical Pressure Ratios for Water

A1257

Use this curve for liquids other than water. Determinethe vapor pressure/critical pressure ratio by dividing theliquid vapor pressure at the valve inlet by the criticalpressure of the liquid. Enter on the abscissa at the ratiojust calculated and proceed vertically to intersect the

curve. Move horizontally to the left and read the criticalpressure ratio, rc, on the ordinate.

Figure 2. Critical Pressure Ratios for Liquids Other than Water

Critical Pressure of Various Fluids, Psia*

Ammonia 1636. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Argon 705.6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Butane 550.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Carbon Dioxide 1071.6. . . . . . . . . . . . . . . . . . . . . . . . . . . .Carbon Monoxide 507.5. . . . . . . . . . . . . . . . . . . . . . . . . . .Chlorine 1118.7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Dowtherm A 465. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Ethane 708. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Ethylene 735. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Fluorine 808.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Helium 33.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Hydrogen 188.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Hydrogen Chloride 1198. . . . . . . . . . . . . . . . . . . . . . . . . . .Isobutane 529.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Isobutylene 580. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Methane 673.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Nitrogen 492.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Nitrous Oxide 1047.6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Oxygen 736.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Phosgene 823.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Propane 617.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Propylene 670.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Refrigerant 11 635. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Refrigerant 12 596.9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Refrigerant 22 716. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Water 3206.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

*For values not listed, consult an appropriate reference book.

Valve Sizing forCavitating and Flashing Liquids(Continued)

IntroductionSpecial consideration is required when sizing valveshandling mixtures of liquid and gas or liquid and vapor.The equation for required valve Cv for liquid-gas or liq-uid-vapor mixtures is:

Cvr = (Cvl + Cvg) (1 + Fm) (1)

The value of the correction factor, Fm, is given in figure 1as a function of the gas volume ratio, Vr. The gas vol-ume ratio for liquid-gas mixtures may be obtained by theequation:

Vr =Vg

VL + Vg=

Qg284 QlP1

T1+ Qg (2)

or for liquid-vapor mixtures:

Vr =Vg

Vg Vl1−x

x (3)

If the pressure drop ratio ("P/P1) exceeds the ratio re-quired to give 100% critical gas flow as determined fromfigure 2, the liquid sizing drop should be limited to thedrop required to give 100% critical gas flow.

Because of the possibility of choked flow occurring, theliquid sizing drop may also have to be limited by theequation:

DP(allow) = Km(P1 − rc Pv) *

NomenclatureCv = Standard liquid sizing coefficientCvr = Cv required for mixture flowCvl = Cv for liquid phaseCg = Cg for gas phaseCvg = Cv required for gas phase = Cg/C1C1 = Cg/Cv ratio for valveFm = Cv correction factorKm = Valve recovery coefficient"P = Valve pressure drop, psiP1 = Valve inlet pressure, psiaPv = Liquid vapor pressure, psiaQg= Gas flow, scfhQl = Liquid flow, scfhQs = Steam or vapor flow, lb/hrrc = Critical pressure ratioT1 = Inlet Temperature, _Rankine (_R = _F + 460_)Vg = Gas flow, ft3/sec

Vl = Liquid flow, ft3/secVr = Gas volume ratioVg = Specific volume of gas phase, ft3/lbVl = Specific volume of liquid phase, ft3/lbx = Quality, lb vapor/lb mixture

Figure 1. Cv Correction Factor, Fm

Figure 2. Pressure Drop Ratio Resulting in Critical Gas Flow

Valve Sizing forLiquid-Gas Mixtures


April 1999Page 2-29

Catalog 12

*See equation 1 of “Valve Sizing for Cavitating and Flashing Liquids” in this section.


April 1999Page 2-30

Catalog 12

Sizing ExamplesLiquid-Gas Mixture

Given:

Liquid flow (Ql) = 3000 gpmGas flow (Qg) = 625,000 scfhInlet temperature (T1) = 100_F = 560_RInlet pressure (P1) = 414.7 psia (400 psig)Pressure drop ("P) = 40 psiLiquid specific gravity (Gl) = 1.5Vapor pressure of liquid (Pv) = 30 psiaCritical pressure of liquid = 200 psiaGas specific gravity (Gg) = 1.4C1 of valve under consideration = 24.7Km of valve under consideration = 0.40

Solution:

1. The pressure drop ratio of the application ("P/P1 =40/414.7 -- 0.096) does not exceed that required for100% critical flow (0.40 from figure 2). Check the maxi-mum allowable liquid pressure drop:

DP(allow) = Km(P1 − rc Pv)

The critical pressure ratio (rc) is 0.84 from figure 2 of“Valve Sizing for Cavitating and Flashing Liquids” at Va-por Pressure/Critical Pressure = 30/200 = 0.15.

DP(allow) = 0.40 [414.7 − (0.84)(30)]

= 156 psi

Since the pressure drop ratio is less than that requiredfor 100% critical gas flow and the pressure drop is lessthan the maximum allowable liquid pressure drop, usethe given pressure drop of 40 psi in the remaining steps.

2. Using the Universal Valve Sizing Slide Rule or sizingnomographs, the calculated required liquid sizing coeffi-cient for the liquid phase (Cvl) is 581 and the calculated

required gas sizing coefficient for the gas phase (Cg) is2710.

3. Calculate the Cv required for gas phase:Cvg = Cg∕C1

= 271024.7

= 110

4. Calculate the gas volume ratio:

Vr =Qg

284Q1P1T1

+ Qg

(2)

= 625, 000(284)(3000)(414.7)

560 + 625, 000

= 0.498

Then from figure 1 at Vr = 0.498:

Fm = 0.475

5. Calculate the Cv required for the mixture:Cvr = (Cvl + Cvg)(1 + Fm)

= (581 + 110)(1 + 0.475)

= 1020

(1)

Liquid-Vapor Mixture

Given:

Mixture flow (Q) = 200,000 lb/hr of wet steamQuality (x) = 0.05Inlet pressure (P1) = 84.7 psia (70 psig)Pressure drop ("P) = 50 psiC1 of valve under consideration = 21.0Km of valve under consideration = 0.50

Valve Sizing forLiquid-Gas Mixtures(Continued)

Solution:

1. Calculate the flow of vapor (Qs) and of liquid (Ql):Qs = (x) (Mixture Flow)

= (0.05) (200,000)= 10,000 lb/hr of steam

Ql = Mixture Flow -- Qs= 200,000 -- 10,000= 190,000 lb/hr of water= 417 gpm

2. Using the sizing slide rule or the steam, vapor, andgas flow equation shown with the Universal Sizing No-mograph, find the calculated required gas sizing coeffi-cient (Cg) for the vapor phase. Steam inlet density(0.193 lb/ft3) can be calculated from steam table data.

Cg = 2330

3. Calculate Cv required for the vapor phase:

Cvg = Cg∕C1

= 230021.0

= 111

4. Before determining the Cv required for the liquidphase, calculate the maximum allowable liquid pressuredrop:

DP(allow) = Km (P1 − rcPv)

Since this is a mixture of a liquid and its vapor, vaporpressure (Pv) equals inlet pressure (P1). Find the criticalpressure ratio (rc) from figure 1 of “Valve Sizing for Cavi-tating and Flashing Liquids” in this section.

DP(allow) = 0.50[84.7 − (.92)(84.7)]

= 3.39 psi

Use this pressure drop and the specific gravity of thewater (from steam tables) with the sizing slide rule orliquid nomograph to determine the required liquid sizingcoefficient of the liquid phase (Cvl):

Cvl = 216

5. Calculate the gas volume ratio. specific volumes (vgand vl) can be found in steam tables:

Vr =Vg

Vg Vl1−x

x (3)

= 5.1855.185 + 0.01761−0.05

0.05

= 0.939

The from figure 1 at Vr = 0.939:

Fm = 0.97

6. Calculate the Cv required for the mixture:Cvr = (Cvl + Cvg)(1 + Fm)

= (216 + 111) (1 + 0.97)

= 644

(1)

Valve Sizing forLiquid-Gas Mixtures

Continued


April 1999Page 2-31

Catalog 12


April 1999Page 2-32

Catalog 12

VAPOR PRESSURETEMPERATURE STEAM WATER

Absolute,Psia

Vacuum,In. Hg.

TEMPERATUREDEGREES F

STEAMDENSITY

LBS/CU.FT.

WATERSPECIFICGRAVITY

0.200.250.300.350.40

29.5129.4129.3129.2129.11

53.1459.3064.4768.9372.86

.000655

.000810

.000962.00111.00126

1.001.001.001.001.00

0.450.500.600.700.80

29.0028.9028.7028.4928.29

76.3879.5885.2190.0894.38

.00141

.00156

.00185

.00214

.00243

1.001.001.001.001.00

0.901.01.21.41.6

28.0927.8827.4827.0726.66

98.24101.74107.92113.26117.99

.00271

.00300

.00356

.00412

.00467

.99

.99

.99

.99

.99

1.82.02.22.42.6

26.2625.8525.4425.0324.63

122.23126.08129.62132.89135.94

.00521

.00576

.00630

.00683

.00737

.99

.99

.99

.99

.99

2.83.03.54.04.5

24.2223.8122.7921.7820.76

138.79141.48147.57152.97157.83

.00790

.00842

.00974.0110.0123

.98

.98

.98

.98

.98

5.05.56.06.57.0

19.7418.7217.7016.6915.67

162.24166.30170.06173.56176.85

.0136

.0149

.0161

.0174

.0186

.98

.98

.98

.97

.97

7.58.08.59.09.5

14.6513.6312.6111.6010.58

179.94182.86185.64188.28190.80

.0199

.0211

.0224

.0236

.0248

.97

.97

.97

.97

.97

10.011.012.013.014.0

9.567.525.493.451.42

193.21197.75201.96205.88209.56

.0260

.0285

.0309

.0333

.0357

.97

.97

.96

.96

.96


Absolute,Psia

Gauge,Psig


STEAMDENSITY

LBS/CU.FT.


14.69615.016.017.018.019.0

0.00.31.32.33.34.3

212.00213.03216.32219.44222.41225.24

.0373

.0380

.0404

.0428

.0451

.0474

.96

.96

.96

.96

.96

.95

20.021.022.023.024.0

5.36.37.38.39.3

227.96230.57233.07235.49237.82

.0498

.0521

.0544

.0567

.0590

.95

.95

.95

.95

.95

25.026.027.028.029.0

10.311.312.313.314.3

240.07242.25244.36246.41248.40

.0613

.0636

.0659

.0682

.0705

.95

.95

.95

.94

.94

30.031.032.033.034.0

15.316.317.318.319.3

250.33252.22254.05255.84257.38

.0727

.0750

.0773

.0795

.0818

.94

.94

.94

.94

.94

35.036.037.038.039.0

20.321.322.323.324.3

259.28260.95262.57264.16265.72

.0840

.0863

.0885

.0908

.0930

.94

.94

.94

.94

.94


Absolute,Psia

Gauge,Psig


STEAMDENSITY

LBS/CU.FT.


40.041.042.043.044.0

25.326.327.328.329.3

267.25268.74270.21271.64273.05

.0953

.0975

.0997.102.104

.94

.93

.93

.93

.93

45.046.047.048.049.0

30.331.332.333.334.3

274.44275.80277.13278.45279.74

.106

.109

.111

.113

.115

.93

.93

.93

.93

.93

50.051.052.053.054.0

35.336.337.338.339.3

281.01282.26283.49284.70285.90

.117

.120

.122

.124

.126

.93

.93

.93

.93

.93

55.056.057.058.059.0

40.341.342.343.344.3

287.07288.23289.37290.50291.61

.128

.131

.133

.135

.137

.93

.93

.93

.92

.92

60.061.062.063.064.0

45.346.347.348.349.3

292.71293.79294.85295.90296.94

.139

.142

.144

.146

.148

.92

.92

.92

.92

.92

65.066.067.068.069.0

50.351.352.353.354.3

297.97298.99299.99300.98301.96

.150

.152

.155

.157

.159

.92

.92

.92

.92

.92

70.071.072.073.074.0

55.356.357.358.359.3

302.92303.88304.83305.76306.68

.161

.163

.165

.168

.170

.92

.92

.92

.92

.92

75.076.077.078.079.0

60.361.362.363.364.3

307.60308.50309.40310.29311.16

.172

.174

.176

.178

.181

.92

.91

.91

.91

.91

80.081.082.083.084.0

65.366.367.368.369.3

312.03312.89313.74314.59315.42

.183

.185

.187

.189

.191

.91

.91

.91

.91

.91

85.086.087.088.089.0

70.371.372.373.374.3

316.25317.07317.88318.68319.48

.193

.196

.198

.200

.202

.91

.91

.91

.91

.91

90.091.092.093.094.0

75.376.377.378.379.3

320.27321.06321.83322.60323.36

.204

.206

.209

.211

.213

.91

.91

.91

.91

.91

95.096.097.098.099.0

80.381.382.383.384.3

324.12324.87325.61326.35327.08

.215

.217

.219

.221

.224

.91

.91

.91

.91

.90

100.0101.0102.0103.0104.0

85.386.387.388.389.3

327.81328.53329.25329.96330.66

.226

.228

.230

.232

.234

.90

.90

.90

.90

.90

105.0106.0107.0108.0109.0

90.391.392.393.394.3

331.36332.05332.74333.42334.10

.236

.238

.241

.243

.245

.90

.90

.90

.90

.90

Saturated SteamPressure and Temperature


Absolute,Psia

Gauge,Psig


STEAMDENSITY

LBS/CU.FT.


110.0111.0112.0113.0114.0

95.396.397.398.399.3

334.77335.44336.11336.77337.42

.247

.249

.251

.253

.255

.90

.90

.90

.90

.90

115.0116.0117.0118.0119.0

100.3101.3102.3103.3104.3

338.07338.72339.36339.99340.62

.258

.260

.262

.264

.266

.90

.90

.90

.90

.90

120.0121.0122.0123.0124.0

105.3106.3107.3108.3109.3

341.25341.88342.50343.11343.72

.268

.270

.272

.275

.277

.90

.90

.90

.90

.90

125.0126.0127.0128.0129.0

110.3111.3112.3113.3114.3

344.33344.94345.54346.13346.73

.279

.281

.283

.285

.287

.90

.89

.89

.89

.89

130.0131.0132.0133.0134.0

115.3116.3117.3118.3119.3

347.32347.90348.48349.06349.64

.289

.292

.294

.296

.298

.89

.89

.89

.89

.89

135.0136.0137.0138.0139.0

120.3121.3122.3123.3124.3

350.21350.78351.35351.91352.47

.300

.302

.304

.306

.308

.89

.89

.89

.89

.89

140.0141.0142.0143.0144.0

125.3126.3127.3128.3129.3

353.02353.57354.12354.67355.21

.311

.313

.315

.317

.319

.89

.89

.89

.89

.89

145.0146.0147.0148.0149.0

130.3131.3132.3133.3134.3

355.76356.29356.83357.36357.89

.321

.323

.325

.327

.330

.89

.89

.89

.89

.89

150.0152.0154.0156.0158.0

135.3137.3139.3141.3143.3

358.42359.46360.49361.52362.53

.332

.336

.340

.344

.349

.89

.89

.89

.88

.88

160.0162.0164.0166.0168.0

145.3147.3149.3151.3153.3

363.53364.53365.51366.48367.45

.353

.357

.361

.365

.370

.88

.88

.88

.88

.88

170.0172.0174.0176.0178.0

155.3157.3159.3161.3163.3

368.41369.35370.29371.22372.14

.374

.378

.382

.387

.391

.88

.88

.88

.88

.88

180.0182.0184.0186.0188.0

165.3167.3169.3171.3173.3

373.06373.96374.86375.75376.64

.395

.399

.403

.407

.412

.88

.88

.88

.88

.88

190.0192.0194.0196.0198.0

175.3177.3179.3181.3183.3

377.51378.38379.24380.10380.95

.416

.420

.424

.429

.433

.88

.87

.87

.87

.87

200.0205.0210.0215.0220.0

185.3190.3195.3200.3205.3

381.79383.86385.90387.89389.86

.437

.448

.458

.469

.479

.87

.87

.87

.87

.87

225.0230.0235.0240.0245.0

210.3215.3220.3225.3230.3

391.79393.68395.54397.37399.18

.490

.500

.511

.522

.532

.87

.87

.86

.86

.86


Absolute,Psia

Gauge,Psig


STEAMDENSITY

LBS/CU.FT.


250.0255.0260.0265.0270.0

235.3240.3245.3250.3255.3

400.95402.70404.42406.11407.78

.542

.553

.563

.574

.585

.86

.86

.86

.86

.86

275.0280.0285.0290.0295.0

260.3265.3270.3275.3280.3

409.43411.05412.65414.23415.79

.595

.606

.616

.627

.637

.85

.85

.85

.85

.85

300.0320.0340.0360.0380.0

285.3305.3325.3345.3365.3

417.33423.29428.97434.40439.60

.648

.690

.733

.775

.818

.85

.85

.84

.84

.83

400.0420.0440.0460.0480.0

385.3405.3425.3445.3465.3

444.59449.39454.02458.50462.82

.861

.904

.947

.9911.03

.83

.83

.82

.82

.81

500.0520.0540.0560.0580.0

485.3505.3525.3545.3565.3

467.01471.07475.01478.85482.58

1.081.121.171.211.25

.81

.81

.81

.80

.80

600.0620.0640.0660.0680.0

585.3605.3625.3645.3665.3

486.21489.75493.21496.58499.88

1.301.341.391.431.48

.80

.79

.79

.79

.79

700.0720.0740.0760.0780.0

685.3705.3725.3745.3765.3

503.10506.25509.34512.36515.33

1.531.571.621.661.71

.78

.78

.77

.77

.77

800.0820.0840.0860.0880.0

785.3805.3825.3845.3865.3

518.23521.08523.88526.63529.33

1.761.811.851.901.95

.77

.77

.76

.76

.76

900.0920.0940.0960.0980.0

885.3905.3925.3945.3965.3

531.98534.59537.16539.68542.17

2.002.052.102.142.19

.76

.75

.75

.75

.75

1000.01050.01100.01150.01200.0

985.31035.31085.31135.31185.3

544.61550.57556.31561.86567.22

2.242.372.502.632.76

.74

.74

.73

.73

.72

1250.01300.01350.01400.01450.0

1235.31285.31335.31385.31435.3

572.42577.46582.35587.10591.73

2.903.043.183.323.47

.71

.71

.70

.69

.69

1500.01600.01700.01800.01900.0

1485.31585.31685.31785.31885.3

596.23604.90613.15621.03628.58

3.623.924.254.594.95

.68

.67

.66

.65

.64

2000.02100.02200.02300.02400.0

1985.32085.32185.32285.32385.3

635.82642.77649.46655.91662.12

5.325.736.156.617.11

.62

.61

.60

.59

.57

2500.02600.02700.02800.02900.0

2485.32585.32685.32785.32885.3

668.13673.94679.55684.99690.26

7.658.248.909.6610.6

.56

.54

.53

.51

.49

3000.03100.03200.03206.2

2985.33085.33185.33191.5

695.36700.31705.11705.40

11.713.317.219.9

.46

.43

.36

.32

Saturated SteamPressure and Temperature

Continued


April 1999Page 2-33

Catalog 12


April 1999Page 2-34

Catalog 12

The degree of superheat is the difference between the actual temperatureand the saturation steam temperature.

Saturated and Superheated SteamDensity/TemperatureCurve

Sonic VelocitySonic velocity for a fluid that obeys the perfect gas law can be found by using the flowing equation:

c = kgRT

Mach NumbersInlet and outlet Mach numbers for a control valve can be calculated from:

M1 =5.97

k + 1 2

k + 11∕k−1 1

1900Cg

A1 sin3417

C1

DPP1

deg.

M2 =

1

k − 12

+ M1

1 − DP∕P1

2A1

A22

M 21+ 2

k − 11∕2

− 1k − 1

1∕2

Calculate Mean VelocityActual velocity at valve inlet or outlet can be determined by multiplying the sonic velocity times the Mach number.

V = cM

Simplified Steam Flow Velocity EquationThe following equation can be used to determine the velocity of steam at either the inlet or outlet of a valve.

V = Qv

25 A

Note

To solve the equation, use steam tables to find the steam specific volume (v) for the pressure and tem-perature at the flow stream location where it is desired to determine velocity. Use the flow stream cross-sectional area at the same location.

Definition of TermsA = Cross sectional area of the flow stream, square

inches---- see tables 2, 3, 4, 5, and 6c = Speed of sound in the fluid, feet per second

Cg = Gas Sizing CoefficientCv = Liquid Sizing CoefficientC1 = Cg/Cv"P = Pressure drop

g = Gravitational constant, 32.2 feet per secondsquared

k = Specific heat ratioSpecific heat at constant pressure

Specific heat at constant volumesee table 1 for common values

M = Mean Mach numberP = Pressure, psiaQ = Vapor flow rate, pounds per hourR =

Individual gas constant,

T = Temperature, Rankine—_R = _F + 460_v = Vapor specific volume, cubic feet per poundV = Mean velocity, feet per second

sub 1 = Upstream or inlet conditionssub 2 = Downstream or outlet conditions

Velocity Equations


April 1999Page 2-35

Catalog 12

1545molecular weight



Catalog 12

Table 1. Specific Heat Ratio (k)

Gas Specific Heat Ratio(k)

AcetyleneAir

ArgonButane

Carbon Monoxide

1.381.401.671.171.40

Carbon DioxideEthaneHelium

HydrogenMethane

1.291.251.661.401.26

0.6 Natural GasNitrogenOxygenPropane

Propylene

1.321.401.401.211.15

Steam(1) 1.331. Use property tables if available for greater accuracy.

Table 2. Flow Area for e-body, Design EU, and EW Valve Bodies(1, 2) (Square Inches),Not Appropriate for Design FB, EH, and HP Valve Bodies

ANSI CLASS RATING

VALVE SIZE, 150 and 300 600 900(3)VALVE SIZE,INCH Flow Area, Valve Diameter (dv) Flow Area, Valve Diameter (dv) Flow Area, Valve Diameter (dv)Flow Area,

Inch2 mm InchFlow Area,

Inch2 mm InchFlow Area,

Inch2 mm Inch

11-1/2

2

0.791.83.1

25.438.150.8

1.001.502.00

0.791.83.1

25.438.150.8

1.001.502.00

- - -- - -- - -

- - -- - -- - -

- - -- - -- - -

2-1/23468

4.97.1132850

63.576.2102152203

2.503.004.006.008.00

4.97.1132849

63.576.2102152200

2.503.004.006.007.87

- - -- - -- - -- - -44

- - -- - -- - -- - -190

- - -- - -- - -- - -7.50

1012162024

79113171262380

254305375464559

10.0012.0014.7518.2522.00

75108171262380

248298375464559

9.7511.7514.7518.2522.00

- - -97154- - -- - -

- - -283356- - -- - -

- - -11.1214.00- - -- - -

1. Use class rating of valve body shell. For example, a Design E 6” size, butt weld valve schedule 80 is available in classes 600, 1500 and 2500 shells. Likewise, a Design EW 8 x 6’’size butt weld valve body, schedule 80, is available in either shell class 600 or 900.2. All of the 12-inch and larger Design EU valves and the 16x12-inch and larger Design EW valves are only Class 600. The lighter flanges (Class 150 to 300) are made from Class 600flanged castings, with Class 600 flow areas. However, Class 150 and 300 12-inch Design EU valves manufactured in Cernay have Class 300 flow areas.3. Design E ANSI Class 900, 3’’ through 6’’ flanged valve body uses a class 1500 shell.

Velocity Equations

Table 3. Flow Area for Pipe (Square Inches)BodySize

ScheduleSize,Inch 10 20 30 40 80 120 160 XS XXS

1/23/41

1-1/22

- - -- - -- - -- - -- - -

- - -- - -- - -- - -- - -

- - -- - -- - -- - -- - -

0.300.530.862.03.4

0.230.430.721.83.0

- - -- - -- - -- - -- - -

0.170.300.521.42.2

0.230.430.721.83.0

0.050.150.280.951.8

2-1/23468

- - -- - -- - -- - -- - -

- - -- - -- - -- - -52

- - -- - -- - -- - -51

4.87.4132950

4.26.6112646

- - -- - -102441

3.55.49.32136

4.26.6112646

2.54.27.81937

1012162024

- - -- - -189299434

83118186291425

81115183284411

79112177278402

72102161253378

6591144227326

5781129203291

75108177284415

- - -- - -- - -- - -- - -

Table 4. Design FB Outlet Flow Area, Inch2

ANSI CLASS RATINGS

OUTLET 150 300 600 900OUTLETSIZE,

INCHESFlowArea

Valve Diameter (dv) FlowArea



Valve Diameter (dv)INCHES Area,

Inch2 mm InchArea,Inch2 mm Inch

Area,Inch2 mm Inch

Area,Inch2 mm Inch

10121618

75108177224

248298381429

9.7511.7515.0016.88

72102161204

243289363409

9.5611.3714.3116.12

6591145183

230273344387

9.0610.7513.5615.25

5781129164

216257325367

8.510.1312.8114.44

20243036

278402638921

478575724870

18.8122.6228.5034.25

253365594855

456548699838

17.9421.5627.5033.00

227326521755

432518654787

17.0020.3825.7531.00

203293- - -- - -

408490- - -- - -

16.0619.31- - -- - -

Table 5. Design EH Flow Area, Inch2

ANSI CLASS RATINGS

VALVE SIZE, 1500 2500VALVE SIZE,INCHES

Flow Area Inch2Valve Diameter (dv)


Flow Area, Inch2mm Inch


1, 1-1/2 x 1, or2 x 1 0.60 22.2 0.87 0.44 19.0 0.75

2 or 3 x 2 2.8 47.6 1.87 1.8 38.1 1.50

3 or 4 x 3 5.9 69.9 2.75 4.0 57.2 2.25

4 or 6 x 4 10 92.1 3.62 6.5 73.0 2.87

6 or 8 x 6 23 137 5.37 15 111 4.37

8 or 10 x 8 38 178 7.00 26 146 5.75

12 or 14 x 12 85 264 10.37 58 219 8.62

Velocity Equations



Catalog 12



Catalog 12

Table 6. Design HP Flow Area, Inch2

CLASS RATINGS

VALVE SIZE, 900 & 1500 2500VALVE SIZE,INCHES





1 0.61 22.2 0.87 0.44 19.0 0.75

2 2.8 47.6 1.87 1.77 38.1 1.50

3(1) 6.5 69.9 2.75 - - - - - - - - -

3(2) or 4 x 3(1,2) 5.9 73.1 2.75 - - - - - - - - -

4 or 6 x 4 10.3 92.1 3.62 - - - - - - - - -

6 or 8 x 6 22.7 136.5 5.37 - - - - - - - - -1. Manufactured in U.S.A.2. Manufactured in Europe and Japan.

Table 7. Diffuser Tube Cross-Sectional AreaDiffuser

Tube Size,Inch

O.D., Inch Area, Inch2

22-1/2

33-1/2

4

2.3752.8753.5004.0004.500

4.436.499.6212.6015.9

568

10

5.5636.6258.625

11

24.334.558.490.8

121416

131416

128.0154201

182024

182024

254314452

Table 8. Flow Area for Pipe, Inch2

BODYSIZE

SCHEDULESIZE,INCH 10 20 30 40 80 120 160 STD XS XXS

1/23/41

1-1/23

- - -- - -- - -- - -- - -

- - -- - -- - -- - -- - -

- - -- - -- - -- - -- - -

0.300.530.862.03.4

0.230.430.721.83.0

- - -- - -- - -- - -- - -

0.170.300.521.42.2

0.300.530.862.03.4

0.230.430.721.83.0

0.050.150.280.951.8

2-1/23468

- - -- - -- - -- - -- - -

- - -- - -- - -- - -52

- - -- - -- - -- - -51

4.87.4132950

4.26.6112646

- - -- - -102441

3.55.49.32136

4.87.4132950

4.26.6112646

2.54.27.81937

1012162024

- - -- - -189299434

83118186291425

81115183284411

79112177278402

72102161253378

6591144227326

5781129203291

79113183290425

75108177284415

- - -- - -- - -- - -- - -

3036

678983

661962

649948

- - -935

- - -- - -

- - -- - -

- - -- - -

672976

661962

- - -- - -

Velocity Equations

Documents

Fisher CV Sizing Info