Sizing Control Valves

Engineering Encyclopedia
Saudi Aramco DeskTop Standards
SIZING CONTROL VALVES
Note: The source of the technical material in this volume is the Professional
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Engineering Encyclopedia Sizing & Selecting Control Valves - Part 1
Sizing Control Valves
Section Page
INFORMATION ............................................................................................................... 9
MANUALLY SIZING CONTROL VALVES FOR LIQUID APPLICATIONS ...................... 9
The Importance of Sizing ............................................................................................ 9
Undersizing Problems............................................................................................ 9
Oversizing Problems.............................................................................................. 9
Fluid States ............................................................................................................... 10
Fluid States and Sizing Equations ....................................................................... 10
Scope of Presented Equations ............................................................................ 11
Guidelines for Capacity vs. Percent of Rated Travel................................................. 11
Sizing for Maximum, Normal, and Minimum Flow Conditions .............................. 11
Tendency to Oversize Valves .............................................................................. 11
Valve Manufacturer's Guidelines ......................................................................... 12
Saudi Aramco Standards ..................................................................................... 12
Converting Degrees Rotation to Percent Travel .................................................. 12
The Basic Liquid Flow Equation ................................................................................ 13
Predicting Flow Through a Restriction ................................................................. 13
Solving for Required Valve Cv ............................................................................. 13
ISA Standards ........................................................................................................... 14
Recognized Valve Sizing Standards .................................................................... 14
ISA Forms of the Basic Sizing Equation .............................................................. 14
Terms in the ISA Equation ................................................................................... 15
Choked Flow ............................................................................................................. 16
Limits of the Basic Liquid Sizing Equation ........................................................... 16
Pressure and Velocity Profiles ............................................................................. 17
Pressure Recovery .............................................................................................. 18
Fluid Vapor Pressure ........................................................................................... 19
Mechanics of Choked Flow.................................................................................. 20
Cavitation............................................................................................................. 21
Flashing ............................................................................................................... 22
Implications of Choked Flow for Sizing ................................................................ 22
Calculating the Allowable Pressure Drop .................................................................. 22
Valve Recovery Coefficient.................................................................................. 22
Solving for ∆P Allowable ...................................................................................... 24
Implementing Choked Flow Equations................................................................. 27
Saudi Aramco DeskTop Standards i

Piping Geometry ....................................................................................................... 28

Significance of Pipe Fittings in Valve Sizing ........................................................ 28
ISA Corrections for Swaged Lines ....................................................................... 28
Piping Factors and Choked Flow ......................................................................... 32
Limitations of Calculated FLP .............................................................................. 34
Alternate Methods for Calculating Swage Effects ................................................ 35
Viscosity Corrections................................................................................................. 36
Flow Regimes ...................................................................................................... 36
Impact of Flow Regime on Valve Sizing............................................................... 37
Reynolds Numbers .............................................................................................. 37
ISA Equations for Non-Turbulent Flow................................................................. 38
Other Viscosity Correction Methods .................................................................... 40
Summary of Valve Sizing Equations ......................................................................... 42
ISA Method .......................................................................................................... 42
Equations Used by Fisher Controls and Others................................................... 43
COMPUTER SIZING CONTROL VALVES FOR LIQUID APPLICATIONS ................... 45
Introduction to the Fisher Sizing Program ................................................................. 45
Benefits of Computer Sizing Methods.................................................................. 45
Overview of the Fisher Sizing Program (FSP 1.4) ............................................... 45
Overview of Program Operation................................................................................ 46
Booting the Program ............................................................................................ 46
Project Information............................................................................................... 46
Main Menu ........................................................................................................... 47
Selecting Units ..................................................................................................... 47
Selecting a Valve Sizing Method ......................................................................... 48
Selecting Variables and Conditions ..................................................................... 49
Valve Sizing Calculation Screen .......................................................................... 50
Selecting Calculation Options .............................................................................. 51
Other Important Operations ................................................................................. 54
COMPUTER SIZING CONTROL VALVES FOR GAS AND STEAM
APPLICATIONS ............................................................................................................ 55
Introduction ............................................................................................................... 55
Differences in Compressible and Incompressible Fluid Flow............................... 55
Use of Computer Software................................................................................... 55
The ISA Sizing Equations for Compressible Fluids ................................................... 55
Saudi Aramco DeskTop Standards ii

Popular Standard ................................................................................................. 55

Saudi Aramco Standards ..................................................................................... 55
Alternate Forms of the ISA Equation ................................................................... 56
Nomenclature ...................................................................................................... 57
Numerical Constants............................................................................................ 58
Basic Equation..................................................................................................... 58
Choked Flow........................................................................................................ 59
Expansion Factor: Y............................................................................................. 62
Adapting the Equation for Use with Gasses other than Air .................................. 66
Real Gas Behavior............................................................................................... 67
Piping Effects....................................................................................................... 69
Final Equation Form............................................................................................. 70
Summary of ISA Equation Terms ........................................................................ 71
Computer Sizing Control Valves for Gasses Using the ISA Equations ..................... 72
Introduction .......................................................................................................... 72
Valve Sizing Methods Available ........................................................................... 72
Selecting the Desired Calculation Type ............................................................... 73
Overview of Sizing Procedures............................................................................ 73
Selecting Options................................................................................................. 74
The Fisher Universal Gas Sizing Equation................................................................ 76
Introduction .......................................................................................................... 76
Fisher and ISA Equation Comparison.................................................................. 76
Equation Basics ................................................................................................... 77
Equation Limits .................................................................................................... 78
Pressure Recovery and Critical Flow ................................................................... 79
Blending the Two Equations ................................................................................ 80
The C1 Factor...................................................................................................... 82
Mechanics of the Sine Term ................................................................................ 84
Alternate Forms of the Universal Sizing Equation................................................ 85
Solving for Cg ...................................................................................................... 87
Comparison of Fisher and ISA Gas Sizing Equations.......................................... 88
Computer Sizing Control Valves for Gasses Using the Fisher Controls Equations ... 90
Valve Sizing Methods Available ........................................................................... 90
Selecting a Calculation Type ............................................................................... 91
Overview of Sizing Procedures............................................................................ 91
F3 Options ........................................................................................................... 92
Saudi Aramco DeskTop Standards iii

ENTERING VALVE SIZING DATA ON THE SAUDI ARAMCO ISS .............................. 95

Body and Flange Size ............................................................................................... 95
Control Valve Physical Size Information .............................................................. 95
Capacity Ratings ....................................................................................................... 95
Capacity at Minimum, Normal, and Maximum Flow Conditions ........................... 95
Valve Travel at Minimum, Normal, and Maximum Flow Conditions ..................... 96
WORK AIDS.................................................................................................................. 98
WORK AID 1: PROCEDURES THAT ARE USED TO MANUALLY SIZE
CONTROL VALVES FOR LIQUID APPLICATIONS ..................................................... 98
Work Aid 1A: Procedures that are Used to Calculate the Required Control Valve
Cv .............................................................................................................................. 98
Work Aid 1B: Procedures that are Used to Calculate the Allowable Pressure
Drop (∆Pallow) ........................................................................................................ 100
Work Aid 1C: Procedures that are Used to Calculate the Effect of Piping
Factors on Cv .......................................................................................................... 102
Work Aid 1D: Procedures that are Used to Calculate the Effect of Laminar Flow
on Cv ....................................................................................................................... 103
WORK AID 2: PROCEDURES THAT ARE USED TO COMPUTER SIZE
CONTROL VALVES FOR LIQUID APPLICATIONS ................................................... 104
Work Aid 2A: Procedures that are Used to Computer Size Control Valves for
Water Applications .................................................................................................. 104
Work Aid 2B: Procedures that are Used to Computer Size Control Valves for
Choked Flow ........................................................................................................... 106
Work Aid 2C:Procedures that are Used to Computer Size Control Valves for
Fluids in the Sizing Database.................................................................................. 107
Work Aid 2D: Procedures that are Used to Computer Size Control Valves with
Piping Factor Correction.......................................................................................... 109
Work Aid 2E: Procedures Used to Computer Size Control Valves with Viscosity
Correction................................................................................................................ 111
Work Aid 2F: Procedures that are Used to Computer Size Control Valves with
Viscosity and Piping Factor Correction.................................................................... 114
Work Aid 2G: Procedures that are Used to Computer Size Control Valves for
Minimum, Normal, and Maximum Flow Conditions ................................................. 116
Minimum, Normal, and Maximum Flow Conditions (Cont'd).................................... 118
CONTROL VALVES FOR GAS AND STEAM APPLICATIONS .................................. 120
Saudi Aramco DeskTop Standards iv

Work Aid 3A: Procedures that are Used to Computer Size Control Valves for
Ideal Gasses with the ISA Method .......................................................................... 120
Work Aid 3B: Procedures that are Used to Computer Size Control Valves for
Real Gasses with the ISA Method........................................................................... 120
Work Aid 3C: Procedures that are Used to Computer Size Control Valves for
Vapors with the ISA Method.................................................................................... 121
Work Aid 3D: Procedures that are Used to Computer Size Control Valves for
Steam with the ISA Method..................................................................................... 122
Work Aid 3E: Procedures that are Used to Computer Size Control Valves for
Ideal Gasses with the Fisher Method ...................................................................... 123
Work Aid 3F: Procedures that are Used to Computer Size Control Valves for
Real Gasses with the Fisher Method ...................................................................... 125
Vapors with the Fisher Method................................................................................ 126
Work Aid 3H: Procedures that are Used to Computer Size Control Valves for
Steam with the Fisher Method................................................................................. 127
Work Aid 3I: Procedures that are Used to Calculate the Effect of Compressibility
on Valve Size .......................................................................................................... 128
Work Aid 3J: Procedures that are Used to Computer Size Control Valves for All
Flow Conditions....................................................................................................... 130
WORK AID 4: PROCEDURES THAT ARE USED TO ENTER VALVE SIZING
DATA ON THE SAUDI ARAMCO ISS......................................................................... 133
GLOSSARY ................................................................................................................ 134
Saudi Aramco DeskTop Standards v

LIST OF FIGURES
Figure 1. Fluid States as a Function of Pressure and Heat Content ............................. 10
Figure 2. Pressure and Flow Relationships................................................................... 17
Figure 3. Pressure and Velocity Profiles Around a Restriction ...................................... 18
Figure 4. Comparison of High and Low Recovery Valves ............................................. 19
Figure 5. Fluid Vaporization when Pvc < Pv .................................................................. 19
Figure 6. Pressure and Flow Relationships................................................................... 20
Figure 7. Pressure Profiles for Flashing and Cavitating Flows ...................................... 21
Figure 8. Generalized Relationship of Pvc to Pv for High and Low Recovery
Valves at Different Pressure Drops ............................................................ 23
Figure 9. Critical Pressure Ratios for Liquids other than Water..................................... 25
Figure 10. Critical Pressure Ratios for Water ................................................................ 26
Figure 11. Flow Limiting Influences of Reducers and Expanders.................................. 30
Figure 12. Piping Factor Effect Vs. Travel for Different Valve Styles ............................ 32
Figure 13. Flow Profiles of Laminar and Turbulent Flow Regimes ................................ 36
Figure 14. Valve Reynolds Number Vs. the Reynolds Number Factor FR .................... 40
Figure 15. Main Menu of the Fisher Sizing Program ..................................................... 46
Figure 16. Screen that Appears when the Units Option Under Config is Selected........ 48
Figure 17. Drop-Down Menu that Lists Valve Sizing Methods ...................................... 48
Figure 18. Options for Variables to Solve for................................................................. 50
Figure 19. Calculation Screen for ISA Liquid Sizing ...................................................... 50
Figure 20. Calculation Options ...................................................................................... 52
Figure 21. Pull-Down Menu that Lists Units Options for Q ............................................ 53
Figure 22. Pull-Down Menu that Lists Fluids in the Sizing Database ............................ 53
Figure 23. Table of Values that is Displayed when the F9 Key is Pressed.................... 54
Figure 24. Gas Flow and Pressure Relationships ......................................................... 59
Figure 25. Choked Flow as a Function of xT ................................................................. 60
Figure 26. Effects of k on FKxT and qmax .................................................................... 61
Figure 27. Pressure and Flow Relationships as x Increases from 0.02 to xT ................ 62
Saudi Aramco DeskTop Standards vi

Figure 28. Reduced Pressure PVC Leads to Reduced Fluid Density and
Reduced Flow ............................................................................................ 63
Figure 29. Effect of Sonic Velocity on Flow ................................................................... 63
Figure 30. Effect of Vena Contracta Enlargement......................................................... 64
Figure 31. Relationships Among x, FkxT, and Y ........................................................... 65
Figure 32. Generalized Compressibility Chart ............................................................... 68
Figure 33. Valve Sizing Method Options ....................................................................... 72
Figure 34. Available Calculation Types ......................................................................... 73
Figure 35. Valve Sizing Screen for the ISA Gas Valve Sizing Method .......................... 73
Figure 36. Calculation Options for the ISA Gas Valve Sizing Method ........................... 74
Figure 37. Line-by-Line Units Options for Flow ............................................................. 76
Figure 38. Actual Flow Versus Predicted Flow .............................................................. 79
Figure 39. Critical Flow for Low and High Recovery Valves.......................................... 79
Figure 40. Predicting Low Flow and Critical Flow.......................................................... 81
Figure 41. Tested Values of Flow Compared to a Sine Curve ...................................... 82
Figure 42. C2 Factor Versus k ...................................................................................... 86
Figure 43. Valve Sizing Methods................................................................................... 90
Figure 44. Selection of a Calculation Type.................................................................... 91
Figure 45. Valve Sizing Screen for the Fisher Real Gas Sizing Method........................ 91
Figure 46. Calculation Options for the Fisher Ideal Gas Sizing Method ........................ 92
Figure 47. Calculation Options for the Fisher Real Gas Sizing Method......................... 93
Figure 48. Calculation Options for the Fisher Vapor Sizing Method .............................. 93
Figure 49. Calculation Options for the Fisher Steam Sizing Method ............................. 94
Figure 50. Pull-Down Menu Options for Temperature ................................................... 94
Figure 51. The Saudi Aramco ISS................................................................................. 97
Saudi Aramco DeskTop Standards vii

LIST OF TABLES
Table 1. Typical Vendor Recommendations for Percent Travel Versus Flow................ 12

Table 2. Guidelines for Percent Travel at Various Flow Conditions Per Section
5.2 of SAES-J-700...................................................................................... 12
Table 3. Units Constants for the ISA Liquid Sizing Equations. ...................................... 15
Table 4. R Values that are Used in the Piping Factor Correction Method ..................... 35
Table 5. Viscosity Conversion ....................................................................................... 39
Table 6. Numerical Constants for the ISA Gas Sizing Equations .................................. 58
Table 7. Comparison of Cv, Cg, and C1 Values............................................................ 84
Table 8. Comparison of ISA and Fisher Sizing Terms................................................... 89
Saudi Aramco DeskTop Standards viii

INFORMATION
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". Valve sizing procedures are based on
accepted mathematical equations that are used to model flow
through ideal restrictions such as orifice plates and flow nozzles.
While control valves do not always resemble ideal restrictions,
the mathematical models generally give useful results if the
specifier inputs accurate data. However, if the service conditions
and fluid properties that are used as inputs to the sizing process
are not accurate, the specifier may be led to the selection of 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 production quotas. Limited capacity
may result in process failure because of the inability to supply
needed fluids in sufficient quantity. Inadequate capacity can
also result in safety hazards; for example, an undersized control
valve that is used in a relief application may allow upstream
pressure to reach unsafe levels.
Oversizing Problems
Excessive Seat Wear is a common result of oversizing control

valves. a valve with excess capacity may spend most of its life
throttling near the seat. Sustained throttling with the plug near
the seat causes high velocity flow that impinges on and around
the seating 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, the relief system may have insufficient
capacity to control the excess input to the relief system.
Saudi Aramco DeskTop Standards 9

Stable Control is another problem that is associated with

oversized valves. Process gain is typically quite high when the
valve closure member operates near the seat. The high gain
can cause large changes in the process variable, which results
in instability. In addition, any friction or deadband in the valve
has a pronounced effect on performance 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 the flow rate or to calculate the required control
valve Cv. The chart below (Figure 1) illustrates how a fluid state
can change as a function of pressure and enthalpy (heat
content).
Figure 1. Fluid 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) when the 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, ideal gasses, 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 flow condition only, it is equally important to
calculate Cv requirements at normal and minimum flow
conditions.
Sizing for maximum flow ensures adequate capacity.
Sizing for normal flow conditions allows the specifier to ensure
that the valve will normally throttle in a range of travel (or
percentage of maximum valve Cv) that provides good control
and sufficient reserve capacity.
Sizing for minimum flow conditions allows the specifier to ensure
that the valve is capable of providing stable control at the low-
flow condition. Most valves are designed to provide good control
down to about 10 percent of rated travel. Throttling below 10
percent travel can cause system instability because of the high
valve gain at low lifts, and it can cause high velocity flow that
results in accelerated seat wear.
Tendency to Oversize Valves
In many engineering environments, several individuals or

groups may have direct or indirect input 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 control valve problem is the
oversized valve, and they should strive to use actual service
conditions when sizing control valves.

Valve Manufacturer's
Guidelines
Most valve manufacturers use a rule of thumb that establishes

acceptable percentages of travel for the minimum, normal, and
maximum flow conditions. The flow versus travel
recommendations that are shown in Table 1 are common.
Table 1. Typical Vendor Recommendations for Percent Travel Versus Flow

Flow Condition Percent of Rated Travel
Minimum 10
Normal 20-80
Maximum 90
Saudi Aramco Standards
Section 6.2.2 of SAES-J-700 contains guidelines for the

percentage of valve travel that produces the normal and
maximum flow rates. The recommended percentages vary with
the inherent valve characteristics as shown in Table 2.
Table 2. Guidelines for Percent Travel at Various Flow Conditions Per Section 5.2
of SAES-J-700
Flow Characteristic Percent Travel at Normal Percent Travel at Maximum
Flow Flow
Equal Percentage 85 93
Linear 75 90
Modified Parabolic 80 90
Converting Degrees Rotation

to Percent Travel
The guidelines for travel versus flow are expressed in percent

travel and apply directly to sliding-stem valves; however, travel
for rotary-shaft valves is expressed in degrees rotation. In order
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 maximum acceptable travel
for a given condition is 93 percent, the equivalent rotation is
approximately 84 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 and equations that are used to describe flow
through orifice plates and flow nozzles. The most common and
basic form of the liquid flow equation is as follows:
∆P
Q = Cv (1)
G
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., the
test fluid is water with a specific gravity of 1.0, and
the pressure drop across 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 the pressure drop between upstream pressure and
the pressure at the limiting flow area of the restriction, which is
called the vena contracta; however, Equation 1 provides the
basis for developing the complete equation.
Solving for Required Valve Cv
Rearranging the equation to solve for the control valve Cv

results in the base equation that is used for sizing valves for
non-compressible fluids (liquids).
G
Cv =Q (2)
∆P

ISA Standards
Recognized Valve Sizing
Standards
ISA - One organization that publishes standards that are widely

accepted for control valve sizing is the Instrument Society of
America (ISA). The ISA standard that includes the valve sizing
equations is ANSI/ISA-S75.01-1985.
Section 6.1 of SAES-J-700 requires the use of the ISA equations for
valve sizing, but it allows manufacturers to deviate from the ISA
formulas provided that the reason is detailed in the technical
quotation.
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:
p1 − p2
q = N1 Cv (3)
Gf
To Calculate Control Valve Cv - Tocalculate the control valve Cv

that is required to pass a specified flow rate, the equation is as
follows:
q Gf
Cv = (4)
N1 p1 − p2
Where:
q = The volumetric flow rate.
N1 = A numerical constant for units of measurement
(Table 3).
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 (15.6 degrees C).

p1 = The upstream absolute pressure, psia.

p2 = The downstream absolute pressure, psia.
Units Constants - Thefollowing table includes the values of some
of the constants that are used in the various forms of the ISA
sizing equation:
Table 3. Units Constants for the ISA Liquid Sizing Equations.

Constant Units that are Used in Equations
N w q p, ∆P d, D g1 n
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 --- centistokes
N6 2.73 kg/h --- kPa --- kg/m3
27.3 kg/h --- bar --- kg/m3
63.3 lb/h --- psia --- lb/ft3
The constant N1 is included in Equations 3 and 4. The constants

N2 through N6 are used in supplemental equations that will be
discussed later in this Module.
Terms in the ISA Equation
ISA Equation Compared to the Generic Equation - TheISA liquid flow

sizing equation (Equation 6) differs in minor ways from the
generic form of the equation (Equation 5), as shown below:
G
Generic: C v = Q (5)
∆P
q Gf
ISA: C v = (6)
N1 p1 − p2
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, the specifier may apply the equation by
using either metric or English measurement units.
Conversions are possible with the generic equation as well.
ISA vs. Generic Equation Similarities - Despiteminor differences in
nomenclature, the two equation forms are algebraically
identical, and as a result, they will give identical results. The
only exception is the use of the N1 term (units constant) in the
ISA equation; however, a units conversion factor can be applied
to any sizing equation.
Common Use of Equation Forms - When reviewing sizing catalogs,
technical articles, and other documentation, specifiers will
commonly encounter both the ISA nomenclature and minor
departures from the ISA nomenclature that some valve
manufacturers employ.
Choked Flow
Limits of the Basic Liquid
Sizing Equation
Predicted Flow - Thebasic liquid sizing equations that have been

discussed to this point predict an increase in flow for every
increase in the square root of the pressure drop as shown in
Figure 2 below. In reality, the relationship between pressure
drop and flow rate only holds true for a limited range of
conditions.
Choked Flow - In every application, it is possible to reach a point
at which increasing the pressure drop by reducing P2 does not
result in a proportional increase in flow. at some pressure drop
limit, a condition of maximum flow is realized in spite of
increases in the pressure drop across the valve. The condition
of maximum flow is known as choked flow and is represented
with Qmax or Qchoked.

Predicting Qmax and ∆Pchoked - Equations have been developed

that can be used to predict the value of Qmax (Qchoked) with
relative certainty. The equations that are used to 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 than the actual ∆P across the valve, the
specifier knows that choked flow exists. When choked flow does
exist, the maximum pressure drop that can be used for sizing
purposes is the computed value of ∆Pchoked or ∆Pallow.
Figure 2. Pressure and Flow Relationships.
Pressure and Velocity Profiles
a plot that shows mean fluid pressure and mean velocity profiles
at and around a control valve helps to explain the mechanics of
choked flow. Refer to Figure 3.
Vena Contracta - Recallthat as a fluid passes through a restriction
such as a control valve, the flowstream continues to neck down
to a minimum cross-sectional area. The point of minimum cross-
sectional area is known as the vena contracta. The vena
contracta may be located at the control valve port, or it may be
located downstream of the valve, depending on service
conditions and valve style.

Pressure and Velocity at the Vena Contracta - at

the vena contracta,
fluid velocity increases to a maximum. In accordance with
Bernoulli's equation, the increase in velocity is accompanied by
a decrease in pressure. The low pressure at the vena contracta
is referred to as Pvc.
Figure 3. Pressure and Velocity Profiles Around a Restriction
Pressure Recovery
Pressure Recovery Defined - The difference between Pvc and P2 is

referred to as pressure recovery. P2 is a fixed value that is
dictated by the process, while the pressure at the vena
contracta (Pvc) is a function of valve style and geometry.
High Recovery vs. Low Recovery Control Valves - Low recovery
(globe style) control valves produce a relatively small pressure
dip at the vena contracta. High recovery valves (ball and
butterfly valves) produce a greater pressure dip at the vena
contracta. Refer to Figure 4 below. Whether a valve is a high
recovery or low recovery type has a significant bearing on the
pressure drop at which choked flow occurs.

Figure 4. Comparison of High and Low Recovery Valves
Fluid Vapor Pressure
Defined - All
subcritical, single-species fluids have a vapor
pressure (Pv). Vapor pressure is the pressure at which a fluid at
a stated temperature will begin to change state from the liquid to
the vapor phase. The liquid-to-vapor change of state can be
thought of as causing a liquid to boil by reducing the fluid
pressure, as opposed to increasing the fluid temperature.
Pvc vs Pv - As the pressure at the vena contracta is reduced to
the vapor pressure of the fluid (Figure 5), the fluid will begin to
vaporize. The fluid now consists of a mixture of a liquid and
vapor. The fluid is no longer incompressible (a liquid); therefore,
the basic liquid flow equation is no longer valid.
Figure 5. Fluid Vaporization when Pvc < Pv

Mechanics of Choked Flow
Increasing Pressure Drop and Fluid Density - Oncethe Pvc has fallen
below the Pv, further increases in the pressure drop result in
additional vapor bubble formation and a further reduction in the
density of the fluid mixture. The decrease in fluid density offsets
any increase in the velocity of the mixture; as a result, no
additional mass flow is realized(Figure 6). Vapor formation and
the subsequent reduction in fluid density help to explain the
phenomenon of choked flow.
Figure 6. Pressure and Flow Relationships

Associated Phenomenon - Whenever the fluid pressure at the vena
contracta falls below the fluid vapor pressure, one of two other
phenomena will occur in conjunction with choked flow. The fluid
will either be cavitating or flashing, depending, as shown in
Figure 7, on the value of P2.

Figure 7. Pressure Profiles for Flashing and Cavitating Flows
Cavitation
Cavitation Defined - Ifdownstream pressure (P2) recovers to a

pressure that is greater than the local vapor pressure (Pv) of the
fluid, the vapor cavities collapse and the fluid mixture reverts to
a liquid. The entire liquid-vapor-liquid phase change is known as
cavitation.
Cavitation Damage results from the collapse of millions of tiny
vapor cavities on boundary surfaces. Depending on cavitation
intensity, proximity to critical surfaces, and time of exposure, the
micro-jets and the shock waves that are associated with the
collapse of vapor cavities can produce extreme damage to
valves and other components. Cavitation damage has a
characteristic appearance that is rough and cinderlike.
Anti-Cavitation Trim is available for many valves to reduce or
eliminate cavitation damage. 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 pressure of the fluid, the vapor remains in the
fluid stream, and the mixture is said to be flashing.
Flashing Damage results from liquid droplets impinging on metal
surfaces at high velocity. Flashing damage has a smooth and
polished appearance.
Selection of Valves for Flashing Fluids follows
the same general
strategy as valve selection for other erosive applications,
including the selection of harder body materials, 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 of choked flow is not identified and
accounted for, the basic flow equation can grossly over predict
the flow capacity of the control valve. In addition, choked flow is
always accompanied by 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 of choked flow is determined by
calculating the maximum flow-producing pressure drop (∆Pallow
or ∆Pchoked).
Valve Recovery Coefficient
Pressure Recovery Coefficient Defined - Thevalve pressure

recovery coefficient (or simply, recovery coefficient) plays a
major role in calculating the ∆Pallow or the ∆Pchoked. The
recovery coefficient accounts for the influence of the valve's
internal geometry on its capacity at the choked flow condition.
The equations that are included in ISA Standard S75.01 use the
term FL to express the recovery coefficient. Some
manufacturers also use the coefficient Km. Manufacturers
determine the value of FL and/or Km for each valve style by test,
and they publish the coefficients along with other sizing
information.

Equation for Determining the Valve Recovery Coefficient - The

valve
recovery coefficient relates the valve pressure drop to the drop
at the vena contracta as follows:
P1 − P2
ISA: FL = (7)
P1 − Pvc
P −P
Fisher: Km = 1 2 (8)
P1 − Pvc
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 low recovery globe style valves than for high
recovery ball and butterfly valves. Refer to Figure 8 and note
that high recovery valves tend to choke at lower pressure drops
than low recovery valves do because high-recovery valves
produce a greater pressure dip at the vena contracta. Low
recovery valves produce a smaller drop at the vena contracta;
therefore, more pressure drop can be taken across the valve
before Pvc approaches Pv.
Figure 8. Generalized 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 one pressure recovery coefficient for each
style and size of globe valve. The recovery coefficient applies to
all percentages of travel. Typical recovery coefficients for sliding
stem 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 significantly with the percent of
valve travel; therefore, the recovery coefficient for a specific
angle of opening must be used in the sizing equations. Typical
values are Km = 0.4 to 0.6 and FL = 0.6 to 0.8.
Solving for ∆P Allowable
Rearranging the Equation - The usefulness of the equations to

calculate the recovery coefficient (Equations 7 and 8) becomes
more apparent when the equations are rearranged to solve for
the flow limiting pressure drop, as shown in Equations 9 and 10.
P1 − P2
ISA: FL = arranges to ∆Pchoked = FL2 (P1-Pvc)
P1 − Pvc
(9)
P −P
Fisher Controls: Km = 1 2 arranges to ∆Pallow = Km
P1 − Pvc
(P1-Pvc) (10)
From the above, it becomes clear that the value of the recovery
coefficient can be used to 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 flow condition can be estimated as a
nonlinear function of the fluid vapor pressure multiplied by the
value of the critical pressure ratio. This hypothesis is included in
the Appendix of the ISA Standard S75.01 - 1985. The critical
pressure ratio is identified in the 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 the prevailing conditions, it has been established
that data for a variety of fluids can be generalized, 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 the First 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 plot that is shown in Figure 9 is used. The ratio
of the fluid vapor pressure to the fluid critical pressure is shown
on the X axis. at the point where the vapor pressure to critical
pressure ratio intersects the curve, the critical pressure ratio (rc)
is read from the Y axis.
Figure 9. Critical Pressure Ratios for Liquids other than Water

Calculating the Value of rc for Water - a
special rc curve allows the
straightforward determination of rc for water (Figure 10). 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.

Figure 10. Critical Pressure Ratios for Water

Locating Values - The vapor pressure and critical pressure of
the fluid may be supplied to the valve specifier in a description
of the process, or they may be found in any one of a number of
references that give properties of fluids.
Equation for rc - anequation has also been developed that allows
the specifier to calculate 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 be calculated, the equations to
calculate the flow-limiting pressure drop can be completed. 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 functionally identical 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 following equations:
p1 − FFp v qmax Gf
qmax = N1FL Cv and C v = (20)
Gf N1 FL p1 − FF pv
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 been determined if choked flow
exists, the specifier may first calculate the ∆Pchoked by using
Equation 16. Then, the lesser of either the actual ∆P or the
∆Pchoked is used in the basic sizing equations.
q Gf p1 − p2
Cv = and q = N1 Cv (21)
N1 p1 − p2 Gf
Fisher Controls Sizing Equation - The standard procedure for use

of the Fisher equation is to 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 sizing equations.
G ∆P
Cv =Q and Q = Cv (23)
∆P G
Iterative Nature of Sizing Calculations - The
procedures that are
used to calculate Cv through 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 the required Cv. Observe the actual Km
(FL) of the selected valve size at the travel that was just
determined.
4. If the actual Km (FL) is different than the estimated Km (FL),

use the actual value 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 actual Km (FL).
Piping Geometry
Significance of Pipe Fittings in
Valve Sizing
ISA Standards for Testing Valve Cv - Valvemanufacturers

determine control valve Cv ratings according to ISA test
standards. These standards specify the use of test piping that is
the same diameter as the nominal valve size. In many
applications, the valve size 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 the combination of a reducer and an expander
is a reduction in the apparent pressure drop and a
corresponding reduction in flow rate. The reduction in flow
capacity that results from 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 to account for the flow-limiting effect of
swages. for maximum accuracy, FP values must be determined
by test.
Use of FP Factor - The
piping geometry factor FP is included in the
ISA equations as follows:

p1 − p2
q = N1 FP Cv (24)
Gf
q Gf
Cv =
N1 FP p1 − p2 (25)
ISA Standards for Calculating FP - The
ISA standard states that
when tested values of FP are not available, FP may be
estimated as follows:
− 1
 ΣK C 2  2
FP =  v + 1 (26)
 N2 d 4 
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 for inches; N2 = 0.00214 for mm);
see Table 3.
d = The inside diameter of the valve inlet, specified in
inches or mm according to the value of N2.
Calculating K - K is the algebraic sum of all the loss coefficients
that influence flow through 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 and KB2)
Refer to Equations 26 and 27, and to Figure 11.
ΣK = K1 + K 2 + KB1 − KB2 (27)

Figure 11. Flow Limiting Influences of Reducers and Expanders

Resistance Coefficients K1 and K2 account for the pressure that is
lost to turbulence and friction in the inlet and outlet fittings
respectively. K1 and K2 values may be found in standard 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 the following equations:
2 2
 d2   d2 
K1 = 0. 5  1− 2  K2 = 1. 0  1− 2 
 D1   D2 
and
or when D1 = D2
2
 d2 
K1 + K 2 = 1. 5  1− 2 
 D1 
(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) is the key flow-limiting influence. As
D increases relative to d, the flow limiting effects increase.
Note that the combined equation (to solve for K1 + K2) can be
used only when inlet and outlet piping are the same size. Note
also that all the K terms are dimensionless.
Bernoulli Coefficients KB 1 and KB 2 are used to compensate for
changes in pressure that result from differences in flow stream
area and fluid velocity. Each term is calculated by means of the
following equations:
4 4
 d  d 
KB1 = 1−   and KB2 = 1−   (29)
 D1   D2 
Refer to Equations 27 and 29, and note that for equal size inlet
and outlet piping, KB1 and 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 Cv and the valve inlet diameter d.
− 1
 ΣK C 2  2
FP =  v + 1 (30)
 N2 d 4 
When isolated from the remainder of the equation, the Cv and d

terms can be seen as an indicator of relative valve efficiency,
(i.e., a large Cv and a small valve inlet diameter (d) indicates a
high efficiency valve such as a ball or butterfly valve).
Cv
Relative Valve Efficiency = (31)
d2
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 determine whether or not to
account for swage effects. One rule of thumb is expressed by
the following:
Cv
If ≥ 20, account for piping factors
d2 (32)
Cv
If ≤ 20, ignore piping factors
d2 (FP = 1.0) (33)

Equation Analysis - Given the mathematical relationship of the Cv

and d terms, it follows that FP will have the largest impact on
high efficiency (high recovery) valves such as rotary valves.
Refer to Figure 12 and note that FP will have the greatest effect
on flow when high efficiency valves are operated near their full
rated capacity. Generally speaking, swage effects diminish
rapidly as valve position is reduced to about 50% of rated travel.
for sliding-stem valves, the impact of swages on control valve
sizing is generally in the range of 2-5 percent. This margin of
error is within the accuracy limits of the sizing equation;
therefore, swage effects are commonly ignored for low recovery,
sliding-stem valves.
Figure 12. Piping 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 ISA Standard S75.01-1985
describes the use of an additional coefficient FLP. FLP is a
coefficient that is the product of the recovery coefficient that has
been corrected for piping factors (FL)P and the piping geometry
factor FP as shown in the following equations:
q Gf
Cv = (34)
N1 FP (FL )P p1 − p2
and, combining terms:

FLP = FP (FL )P (35)

therefore:
q Gf
Cv = (36)
N1 FLP p1 − p2
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 be determined by test. The standard also states
that if tested values are not available, reasonable accuracy can
be achieved with the use of Equation 37.
− 1
 K F 2C 2  2
F LP = FL  i L 4 v + 1 (37)
 N2 d 
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 in Equation 38.
 F LP  2
∆Pchoked = 
 FP 
(
 P1 − FF Pv ) (38)
Note that the sizing equation (Equation 39) is modified to

account for FLP only if flow is choked.
q Gf
Cv = (39)
N1 FLP p1 − p2

Limitations of Calculated FLP
Imprecise 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 only an
approximation of swage effects, and it generally over-predicts
the impact of reducers and expanders. The lack of precision is
caused by several factors, including the following:
• Difficulty in obtaining precise values for the K terms.
• The equations are based on liquid flow across abrupt
transitions (as opposed to the smooth transitions of most
expanders and reducers).
• The combined effects of swages and specific valve geometry
are not accounted for.
Iterative Nature of FP, FLP, and Cv Calculations - When calculating
control valve Cv requirements, 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 to
Equations 40 and 41.
When ∆Pactual < ∆Pchoked:
1
q Gf  ΣK C 2  2
but FP = 
Cv = v + 1
(40)
N1 FP p1 − p 2  N2 d4 
When ∆Pactual > ∆Pchoked:

1
 K F 2C 2
v + 1
q Gf 2
but F LP = FL 
Cv = i L
N1 FLP p1 − p2  N2 d4 
(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 the selected valve, solve for Cv again.
4. Using actual values for FL (Km) and the calculated values

for Cv and FP or FLP, 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) is determined by test for each
valve type and line-to-valve size ratio. Many manufacturers
publish rotary valve FL, Km, and Cv values that have been
corrected for swage effects.
Calculating Swage Effects with Sizing Software - Most valve sizing
software includes options for calculating FP and FLP factors.
The computer can quickly perform the iterations of the
calculation that are necessary to arrive at useful (though
approximate) results.
When no specific vendor data is available for valves that are
mounted between pipe reducers, the approximate correction
factors as indicated in Table 4 have been used in the past. The
correction factors (R) for D/d ratios (pipe diameter to valve size)
of 1.5 and 2.0 for a variety of valve styles may still be used as
an approximate check. The R factors are applied as follows:
Calculated C v
Required C v = (42)
R
Table 4. R Values that are Used in the Piping Factor Correction Method
Valve Type D/d = 1.5 D/d = 2.0
R R
Globe Valves (Flow to Close) 0.96 0.94
Globe Valves (Flow to Open) 0.96 0.94
Angle Valves (Flow to Close) 0.85 0.77
Angle Valves (Flow to Open) 0.95 0.91
Ball Valves 0.84 0.80
Butterfly Valves 90 Degrees Open 0.77 0.67
Butterfly Valves 60 Degrees Open 0.91 0.85

R-Value Considerations - Because R factors are derived without

consideration for valve Cv or the percent of rated travel, the
correction will not be as accurate as a correction that is
calculated with the ISA method. (Recall the significance of
Cv/d2). In spite of this 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 that the flowing fluid is turbulent, as
opposed to laminar.
Laminar Flow - In laminar flow, the fluid flows in smooth, ordered
layers. Refer to Figure 13 below. Fluid velocity is highest in the
layers in the center of the pipe, while drag forces cause a
reduction in the fluid velocity nearer the pipe wall. Laminar flow
is also referred to as viscous flow. Although effects other than
fluid viscosity may cause laminar flow, most laminar flow occurs
with high viscosity fluids.
Turbulent Flow - In turbulent flow, the uniform layers disappear
and the flowstream is made up of turbulent eddies that occur
randomly in the fluid stream as shown in Figure 13. The flow
profile is more blunt, and the velocity at the center of the pipe
and the velocity near the pipe wall are nearly equal.
Transitional Flow - Between laminar and turbulent flow, a
condition of transitional flow exists. The transitional flow regime
has characteristics of both laminar and turbulent flow.
Figure 13. Flow 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 the relationship between energy losses in
the valve (pressure drop) and flow rate. for turbulent flow, the
standard sizing equation describes a relationship in which the
flow rate 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 to pressure 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 be required to produce a flow rate that is
equal to the flow rate of a fluid flowing in the turbulent regime.
Depending on the magnitude of the viscous effects, the flow rate
of a fluid in the transitional regime will fall somewhere between
the flow rate of a fluid in the laminar regime and a fluid in the
turbulent flow regime.
Reynolds Numbers
Inertial and Viscous Influences - The physical quantities that

determine the flow regime can be represented as a ratio of
inertial to viscous forces. This ratio is a dimensionless
parameter that is known as the Reynolds number, R. To
illustrate the concept, the Reynolds number for a straight piece
of piping is represented with the following:
VDρ
R= (45)
µ
Inertial influences are:

V - fluid velocity
D - pipe inside diameter
ρ - fluid density
The viscous influence is:

µ - fluid absolute viscosity

Influences on Reynolds Numbers - Note that a decrease in fluid
velocity, pipe diameter, or fluid density will result in a lower
Reynolds number and a tendency toward laminar flow. Also,
note that increasing fluid viscosity will result in a lower Reynolds
number and a tendency toward laminar flow.
ISA Equations for Non-

Turbulent Flow
Reynolds Number Factor FR - The ISA Standard uses a Reynolds

number factor FR to account for the effects of viscous flow. The
factor FR is included in the basic sizing equation as follows:
p1 − p2
q = N1 FR Cv (46)
Gf
q Gf
Cv = (47)
N1 FR p1 − p2
The FR factor expresses the ratio of the nonturbulent flow rate

to the turbulent flow rate that is predicted by the basic sizing
equation. Note also that Equations 46 and 47 do not include the
piping correction factor FP. The effect of valve fittings and
swages on nonturbulent flow is currently not well understood;
therefore, when the ISA equations are used, the specifier may
correct for piping factors or viscous effects, but not for both.
Reynolds Number Vs. Flow Regime - a chart that relates the valve
Reynolds number to the value of FR helps to illustrate the effect
that laminar flow can have on the calculated flow rate or the
control valve Cv. The plot that is shown in Figure 14 illustrates
that when the valve Reynolds is 10 000 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 number falls below
10, 000, the flow-limiting effects of laminar flow increase, and
the value of FR decreases.
Section 6.5 of SAES-J-700 requires an evaluation of viscous effects
whenever the Reynolds number is below 10 000.
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:

1
N4 Fd q F 2 C 2  4
Re v =  L v 
1 1  N d4 + 1 (48)
υFL 2 Cv 2 2
Note that the equation is iterative because Rev, Cv, and FL are
all unknown at the beginning of the process. Estimates must be
made for all values, and, then, several iterations are performed
to arrive at useful results.
Note also the use of the term Fd. Fd is a valve style modifier.
Currently, the ISA Standard recognizes only two values of Fd. a
value of 0.7 is used for double ported globe 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 in terms other than centistokes, it is
necessary to convert the viscosity to centistokes with the use of
the methods that are shown in the table below:
Table 5. Viscosity Conversion
Viscosity Expressed as: Convert to Centistokes by:
m2/s Multiply m2/s by 106

centipoise divide centipoise by Gf
2. The calculated valve Reynolds number (Rev) is used to

enter a plot (see Figure 14) that relates Rev to a value of
FR. The value of FR is used as shown in Equations 46 and
47.

Figure 14. Valve Reynolds Number Vs. the Reynolds Number Factor FR
Other Viscosity Correction

Methods
Viscosity Correction Nomograph - To avoid time-consuming

calculations, valve manufacturers provide simplified approaches
to obtain low Reynolds number (viscous liquid) correction
factors. Fisher Controls provides a simple nomograph that
allows the specifier to compensate for viscous effects when
performing flow, pressure drop, and Cv calculations. The
nomograph uses known inputs of valve Cv, flow rate, and fluid
viscosity to arrive at a Reynolds number NR. The value of NR is
then used to identify a correction factor Fv. Fv is used to correct
the initial Cv calculation to arrive at a corrected value of Cvr (Cv
required ). for purposes of selecting an appropriately sized
control 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 include options that automatically check for the
effects of viscous (laminar) flow. The specifier enters the fluid
viscosity along with other service conditions, and the software
performs all of the necessary calculations.

Summary of Valve Sizing Equations

ISA Method
Basic Flow Equation - for nonchoking, turbulent fluids, Cv is

calculated with:
q Gf
Cv = (50)
N1 p1 − p2
Choked Flow Sizing Equation - To determine if choked flow exists,

the specifier calculates the ∆Pchoked, compares ∆Pchoked to the
actual ∆P, and uses the lesser of the two 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 the use of the following equation:
q Gf
Cv = max (52)
N1 F L p1 − FF pv
Alternatively, the basic flow equation (Equation 50) may be used

for choked flow sizing if the ∆Pchoked is used as the sizing
pressure drop.
Piping Correction for Non-Choked Flow Applications - In applications
where the flow is not choked, the flow limiting effect of piping
reducers and expanders is calculated with the use of the piping
correction factor FP as follows:
− 1
q Gf  ΣK C 2  2
Cv = where FP =  v + 1
N1 FP p1 − p2  N2 d4 
(53)
Piping Correction for Choked Flow Applications - To compensate for

piping factors under conditions of choked flow, a single
coefficient FLP is used to compensate for both choked flow and
piping factors as follows:

qmax Gf
Cv = where
N1 FLP p1 − p2
− 1
 K F 2C 2  2
F LP = FL  i L v + 1 (54)
 N2 d4 
Viscosity Corrections FR - The effect of nonturbulent (laminar) flow

is included in the sizing equation with the Reynolds number
factor, FR, as shown in Equation 55.
q Gf
Cv = (55)
N1 FR p1 − p2
The value of FR is determined by first calculating the valve

Reynolds number with the use of Equation 56 and, then,
locating a value of FR from the chart that was shown previously
in Figure 14.
1
N4 Fd q FL 2 Cv 2  4
Re v =  + 1 (56)
1 1  N d 
υFL 2 Cv 2 2 4
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 (refer to Equation 57) is similar in form to
the ISA equation.
∆P
Q = Cv (57)
G
Checking for Choked Flow - The potential for choked flow is
investigated by calculating the ∆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 sizing pressure 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 found from tables or calculated with a simple
equation.
Piping Corrections - The effect of reducers and expanders on
valve capacity is determined by testing each type and size of
valve with different line-to-body size ratios. Corrected Cv's are
then published for rotary valves. Corrected values of Km are
also published. The effect of reducers and expanders on globe
valve capacity and recovery characteristics is negligible;
therefore, no corrections are published or are necessary.
Viscosity Corrections - During a manual sizing procedure,
viscosity corrections are easily made with the use of a
nomograph that relates valve Cv, flow rate, and viscosity to a
correction factor Fv. The Cv required (CVR) is calculated by
taking the product of the correction 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 many advantages 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 to perform sizing calculations according to the
ISA sizing equations and the equations that are used by Fisher
Controls and by other manufacturers. The ability to perform
calculations with the use of either method will be helpful in
demonstrating various sizing approaches.
Generic Sizing Engine - The Fisher Sizing Program uses accepted
equations, does not rely on proprietary valve specifications, and
calculates results that are useful during the selection of any
valve - regardless of manufacturer - provided that valve
recovery coefficients are expressed in terms of FL or Km. The
flexibility of the software becomes most apparent in special
sizing applications.

Other Capabilities - The program allows the specifier to select a

system of units, to build a database of common fluids and fluid
properties, and to print both standard and custom reports and
specification sheets; however, only those features that directly
relate to valve sizing will be discussed in this Module.
participants with ongoing responsibility for valve sizing will
benefit from exploring other options that are included 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 the executive (exec) file "FSP" and, then,
pressing the ENTER key.
Project Information
After launching the program, a main menu and identification

screen appears as shown in Figure 15. This screen allows for
specifier identification, project identification, equipment tag
number, and other information.
Valve Ssact Rotact Stroking Report Specsheet File Other Config Exit
Apr 18, 1994 FISHER SIZING PROGRAM Rev 1.41
Engineer : Quote :
Customer : Order :
Reference : Item :
Date : Tag :
Fluid :
Equipment :
Comments :
:
:
( Press [ ESC ] or [ F10 ] to enter application information above )
Valve Sizing : Fisher Real Gas File :
Actuator : -- Dir : C : \ FSP141 \
Striking Time : -- Printer : PRN
Spec Sheet : --
Notepad : --
Valve sizing calculations .

F1 - HELP F2 - Valve F3 - Actuator ALT - F5 - Clear all ALT - menu letter F10 - Form
Figure 15. Main Menu of the Fisher Sizing Program

Main Menu
a menu at the top of this screen lists several different sizing

activities and functions. The specifier selects a specific sizing
activity by moving the cursor to the desired selection and
pressing 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 the results 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 set atmospheric 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 menu and, then, selecting the
Units option. See Figure 16. Each entry may be changed
individually by highlighting it and pressing ENTER. Also, notice
the option at the bottom of the screen to make all units either
English (by pressing the F2 key) or metric (by pressing the F3
key). Pressing the F10 key exits this screen.

Rev 1.41 CHANGE UNITS

Unit Category Current Unit
PRESSURE psig
GAS FLOW lb / h
VAPOR FLOW lb / h
LIQUID FLOW gpm (US)
TEMPERATURE deg F
MASS (GAS) SG
DENSITY lb / ft3
AREA in 2
LENGTH in
FORCE lbf
VELOCITY ft / s
SPRING RATE lbf / in
VISCOSITY cSt
TORQUE lbf. in
Use to select unit category. Press ENTER to change unit .

F1 - HELP F2 - All English F3 - All Metric F4 - Default Config Set F10 - Exit
Figure 16. Screen 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 sizing gasses, liquids, and vapors. Each
option uses different equations within the computer program.
The three available methods for liquid sizing are shown in
Figure 17 and are described below.
Fisher Real Gas FISHER SIZING PROGRAM Rev 1.41
Fisher Ideal Gas
Fisher Vopor Quote :
Fisher Steam Order :
Fisher Liquid Item :
Fisher Water Tag :
Fisher Pulp
Two - Phase Gas /Liq
Two - Phase Vap /Liq
ISA / EN Gas
ISA / EN Vapor or [ F10 ] to enter application information above >
ISA / EN Liquid

Spec Sheet : --
Notepad : --
Valve sizing calculations .

Figure 17. Drop-Down Menu that Lists Valve Sizing Methods

ISA Liquid - When the ISA Liquid method is selected, the

software uses the ISA sizing equations.
Fisher Liquid - When the Fisher Liquid method is selected, the
software uses the same fundamental equations that are used in
the ISA method, except that the terms Km and rc are used
instead of FL and FF, respectively. In the Fisher Liquid method,
there is no option for calculating FP because piping effects are
included in the valve Cv's that are published 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 other information that is entered
by the specifier. The Fisher Water method saves time because
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 specifier selects the variable to solve for. Refer to
Figure 18. 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 sizing calculations will be performed for the
minimum, normal, or maximum flow conditions, 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 of inputs. Copying parameters from one condition to
another is performed by pressing the cursor keys until the
cursor is on the target condition, pressing ALT C, and selecting
the condition from which data will be copied.

Rev 1.41 ISA / EN Liquid Valve Sizing
Quick - key Calculation MIN NRM MAX OTH

ALTB VAalve Sizing & LpA
ALTV Velocity
ALTQ LpA vs Q
ALTS Cv Simple
Press ALT - C to copy another condition to the highlighted condition.

Press SPACE to clear calculation status, [F5] to clear column.
F1 - HELP F3 - Options F4 - Condition Labels AF5 - Clear All F8 - Units F9 - Table F10 - Exit
Figure 18. Options 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 actual sizing screen (shown in Figure 19).
This screen is divided into several sections.
Rev 1.41 NRM ISA / EN Liquid ValveSizing
Liquid Properties & State Valve Specifications
Liquid F1 --
Pc --psia
Pv --psia
SG
Service Conditions
P1
dP --psig
Q --psig Calculated Results
T ( optional) --gpm (US)
--deg F Cv --
Intermediate Results dP Choked -- psid
Ar --
Ff
Notes :
Liquid name (optional). Press [F4] for a list of liquids.

F1 - HELPF2 - CalcF3 - OptionF4 - ChoiceF5 - Clear F9 - TableF10 - Exit
Figure 19. Calculation Screen for ISA Liquid Sizing
Liquid Properties and State - This section is where the specifier
enters the fluid and fluid properties such as the fluid critical
pressure (Pc), vapor pressure (Pv), and specific gravity (SG).
Service Conditions - In this section, the specifier enter pressure,
flow, and temperature information.

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 as the value of FL. When pipe and
valve size are required for calculating FP or FR, they are also
entered in this section.
Calculated Results - After all data have been entered, the specifier
presses the function key F2 to calculate the required valve Cv.
The results of the sizing calculations appear in the Calculated
Results section. In addition to valve Cv, other important
information such as the ∆Pchoked is also shown.
Selecting Calculation Options
The F3 Options Key - at any time, the specifier may choose from
several different sizing options (see Figure 20) by pressing the
function key F3. Options are toggled by highlighting the
appropriate line and pressing ENTER. The option that is visible
when the option menu is stored (by pressing the ESCAPE key)
is the option that will be used in 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, Solve for 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 only calculate the Pv for fluids for which data
have been included in the permanent database; for other
fluids, the specifier must enter the Pv.)
• Line 7: Warnings ON - Option: Warnings OFF


Liquid F1 --
Pc --psia
Pv --psia
SG --
OPTIONAL SELECTION
Service Conditions
Solve for Cg. Cs or Cv
P1
dP LpA (SPL) OFF
Q Omit Fp ults
T ( optional) Viscous Correction OFF
Pipe : Size / Sched --
Intermediate Results Input Pv -- psid
Warnings ON --
Ff
Notes :
Liquid name (optional). Press [ F4 ] for a list of liquids.

Use to select. Press ENTER to change -[ ESC ] to exit F10 - Exit
Figure 20. Calculation Options
As various options are selected, the fields for inputs and for
calculated results will change; for example, if the Viscous
Correction option is set to ON, the program will require the
specifier to input fluid viscosity and valve inlet diameter. In
addition, the calculated 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 for any input parameter by placing the
cursor on that parameter and pressing F8. Pressing F8
produces a sub-menu that lists all possible choices. Refer to
Figure 21. a choice is made by positioning the cursor on the
desired unit and pressing the ENTER key. The option that is
visible when the option menu is stored (by pressing the ENTER
key) is the option that is used in the program.


Liquid F1 --
Pc --psia
Pv --psia
SG --
Service Conditions
P1 --psig
dP --psid
Q -- alculated Results
T ( optional) -- gpm (US) v --
Intermediate Results l/m PChoked -- psid
lb / h r --
Ff kg / h
m3 / h
barrel / d otes :
Liquid flow through valve.

F1 - HELPF2 - CalcF3 - OptionF5 - ClearF8 - Unit F9 - Table F10 - Exit
Figure 21. Pull-Down Menu that Lists Units Options for Q

Pull-Down Menus - F4 Key - Pull-down menu options for several of
the input fields can be 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 as shown in
Figure 22. Fluids that are preceded with a tilde character (~) are
included in a fixed database. The fixed database also includes
sufficient data to allow automatic calculation of the fluid vapor
pressure at the service conditions. The fixed database cannot
be edited; however, the software does allow the specifier to
construct a separate database of fluids and fluid properties that
can be edited.
Liquid F1 --
Pc gpm (US)
Pv WATER VAPOR
SG N-OCTANE
NITRIC OXIDE
Service Conditi ~ACETYLENE
~AMMONIA
P1 ~ARGON
dP ~BENZENE
Q ~ISOBUTANE Calculated Results
T ( optional) ~N-BUTANE
~ISOBUTYLENE Cv --
Intermediate Re ~CARBON DIOXIDE dPChoked -- psid
~CARBON MONOXIDE Ar --
Ff
~CHLORINE
~ETHANE
~ETHYLENE Notes :
~FLUORINE
~FREON11
Cursorkeyscr [ ESC ]exitschoice menu.
F1 - HELPF2 - CalcF3 - OptionF4 - ChoiceF5 - Clear F9 - Table F10 - Exit
Figure 22. Pull-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 to the calculation
screen. Pressing the escape key also allows the specifier to
step backwards 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 presses the 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 performed when F1 was
pressed. Pressing F1 again brings up an index of topics for
which on-line help is available. a topic is selected by moving the
cursor and, then, pressing the ENTER key.
Table of Values - F9 - Pressing F9 displays a table of input
parameters and calculated results for all flow conditions as
shown in Figure 23 below.
MIN NRM MAX OTH
Liquid N-BUTANE N-BUTANE N-BUTANE
P1(psig) 150.000 150.000 150.000
dP(psid) 130.000 100.000 80.000
Pv(psia) 0.949 0.949 0.949
SG 1.000 1.000 1.000
T(deg F) 100.000 100.000 100.000
Q(gpm (US) ) 500.000 800.000 950.000
F1 0.800 0.800 0.800
Ff 0.948 0.948 0.948
Cv 48.835 80.000 106.213
dPChoked(psid) 104.829 104.829 104.829
Ar 0.794 0.611 0.489
Notes : CHOKED
Please press any key to continue.
Figure 23. Table 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 density of 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 equations that 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 of the 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 accepted both by valve manufacturers and
by valve users. The ISA equations are used in virtually all
industries, and they are endorsed in most world areas.
Saudi Aramco Standards
Section 6.1 of SAES-J-700 states that valve sizing procedures

shall be based on the equations that are included in the ISA
standard that is referenced above. Section 6.1 of SAES-J-700
also allows manufacturers to deviate from the ISA formulas
provided that the reason is detailed in the technical quotation.

Alternate Forms of the ISA

Equation
The specifier may select from many forms of the ISA equation.
The choice of equation form depends 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 with specific weight (g) or molecular weight (M)
are used. These equations are sometimes referred to as the
'vapor' forms of the equation.
xM
w = N6 Fp Cv Y xp1 γ 1 or w = N8 Fp Cv p1 Y (59)
T1 Z
Volumetric Flow - To solve for volumetric flow (q), either specific

gravity (Gg) or molecular weight (M) can be used to account for
fluid density.
x x
q = N7 Fp Cv p1 Y or q = N9 Fp Cv p1 Y (60)
G g T1 Z MT1 Z
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 specified in terms of
specific weight () or in terms of molecular weight (M), Cv is
calculated with the use of one of the following equations:
w w T1 Z
Cv = or C v = (61)
N6 Fp Y xp1 γ 1 N8 Fp p1 Y xM
When the flow rate is specified in terms of volumetric flow (q)

and fluid density is specified in terms of specific gravity (Gg) or
molecular weight (M), Cv is calculated with the use of one of the

q Gg T1 Z q MT1 Z
Cv = or C v = (62)
N7 Fp p1 Y x N9 Fp p 1 Y x
Units Systems - The various N terms in the equations allow the

specifier to use the desired engineering units such as psi or bar
for pressure, and scfm or kg/m3 for flow rate.
Nomenclature
The terms that are used in Equations 59 through 62 are

described below.
Cv control valve flow coefficient
Fp piping geometry factor; dimensionless
Gg 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 units
Nx constants for units of measure; see table below
pX p1 = static fluid pressure upstream of the valve; p2 =
static fluid pressure downstream of the valve; see
the table below for units
T1 absolute temperature of fluid at valve inlet; degrees K or
R
w mass flow rate; kg/h or lb/h - see the table below for units
x pressure drop ratio ∆ p p1 ; dimensionless
Y expansion factor; dimensionless
Z 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.

Table 6. Numerical Constants for the ISA Gas Sizing Equations
Constant Units
N w q* p1, p2, ∆P g T1 d, D
N5 0.00241 --- --- --- --- --- mm
1000 --- --- --- --- --- 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 --- 3
m /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 --- 3
m /hr kPa - - - K - --
2250 --- 3
m /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 15.6 degrees C
Basic Equation
To help develop an understanding of the ISA sizing equations,

the complete equation for volumetric flow (Equation 63) will be
stripped to its most basic form, and each term will be explained
as it is added to the basic equation.
x
q = N7 Fp Cv p1 Y (63)
G gT1 Z
Flow Rate: a Function of Pressure Drop Ratio - Recall that for liquid
flow, q is a function of the square root of the pressure drop, as
shown below.
∆P
q = Cv (64)
G
Similarly, gas flow is a function of pressure conditions and Cv.
Over a limited set of conditions, tests show that the basic
relationship between gas flow, Cv, and pressure conditions is as
follows:
q = Cv p1 x (65)
Where:

∆P
x= (66)
p1
Equation 65 predicts a flow rate that is a linear function of x as

shown in Figure 24.
Figure 24. Gas Flow and Pressure Relationships
Choked Flow
Overview of Choked Flow - The equation that was just shown

predicts an increase in flow for every increase in the value of x;
however, when the value of the square root of x becomes
greater than about 0.02, the observed increases in flow rate
become less than the equation predicts. Refer to Figure 25.
Ultimately, there is a point of choked flow. at the choked flow
condition, increases in x (by reducing downstream pressure) do
not produce any increase in flow rate. Choking occurs when the
jet stream at the vena contracta achieves sonic velocity. The
choked flow rate is associated with a flow limiting value of x,
which is known as xT.
Pressure Drop Ratio Factor xT - The flow limiting value of x (refer to
Figure 25) is called the pressure drop ratio factor, or xT (T
stands for terminal). The value of xT is related to valve style and
geometry; therefore, valve manufacturers determine xT values
by test, and they publish them in sizing catalogs and other
documents. The values of xT are different for every different
valve style and size. xT values also change as a function of the
percentage of valve travel.

Figure 25. Choked Flow as a Function of xT

xT and the Ratio of Specific Heats Factor - Manufacturers test valves
for xT values at standard conditions and with standard fluids.
The test fluid is air. To make the value of xT meaningful with
fluids other than air, the sizing equations account for properties
of flowing fluids that are different than the properties of air. One
of the significant fluid properties of any compressible fluid is its
specific heat ratio, which is expressed as k. k represents the
ratio of a fluid's specific heat at a constant pressure to its
specific heat at a constant volume. When a valve is used with a
fluid other than air, the value of xT value should be corrected for
the specific heat of the flowing gas. The correction factor is
called the ratio of specific heats factor and it is referred to as Fk.
Fk is simply the specific heat ratio for the flowing gas (k) divided
by the specific heat ratio (k) of air, which is 1.4. Refer to
Equation 67.
k
Fk = (67)
1. 4
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 of xT becomes FkxT. The value of xT that
is used in any sizing equation should be limited to the value of
FKxT.
Locating k Values - k values are included in many standard
references such as the Gas Processor's Handbook, and they
are also included in the fluid databases of many sizing
programs. Specifiers should note that k values vary with service
temperature, and that these values can change dramatically
(generally increase) at high temperatures.
Use of FKxT - To prevent overpredicting flow or undersizing
valves, the value of x that is used in any of the sizing equations
must not exceed the value of FKxT. Refer to Equation 68.
q = Cv p1 x becomes q = Cv p1 FK xT (68)
Effect of Fk on XT - Refer to Figure 26 and note that larger values

of k result in higher values of FKxT, and vice versa. The values
of qmax are similarly affected. Note that the effects that are
shown are exaggerated to help illustrate the concept.
Figure 26. Effects of k on FKxT and qmax

Us of FK in Valve Sizing - Many hydrocarbon gasses and vapors
have k values that range from 1.2 to 1.5 at moderate
temperatures. k values in this range typically have a very small
impact on valve sizing; therefore, many specifiers ignore the
specific heat correction 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 equation was presented as:
∆p
q = Cv p1 x , where x = (69)
p1
It has been shown that the x can be used to predict flow when x
< 0.02, that choked flow can be predicted when x is limited to
xT, and that xT can be further modified to account for the
thermodynamic properties of the fluid. Refer to Equation 70.
q = Cv p1 FK xT (70)
The equations above do not express the non-linear relationship

between x and q in the region where x>0.02 and x<Fk xT.
Refer to Figure 27.
q Versus x when x > 0.02 and x < FKxT - The expansion factor, Y, is
included in the ISA equations to account for the relationship of q
to x when x > 0.02 and x < FKxT. The expansion factor (Y) helps
to account for the following:
• Changes in fluid density that result from increased fluid
velocity and reduced fluid pressure at the vena contracta.
• The effect of vena contracta enlargement.
These conditions are discussed in the following sections.
Figure 27. Pressure 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 and fluid pressure decreases. See
Figure 27 and Figure 28. The reduction in local fluid pressure
causes the fluid to expand, which results in a reduction in fluid
density. Because fluid density decreases with each incremental
increase in x, incremental increases in x no longer produce
proportional increases in flow rate.
Figure 28. Reduced Pressure PVC Leads to Reduced Fluid Density and Reduced
Flow
Vena Contracta Enlargement - When the fluid velocity becomes
sonic, a shock wave is created that limits velocity to a maximum
(terminal) value. Flow rate becomes a function of sonic
(terminal) velocity and the effective flow area at the vena
contracta. Refer to Figure 27 and Figure 29.
Figure 29. Effect of Sonic Velocity on Flow

After the fluid attains sonic velocity, a decrease in P2 may

produce a limited increase in flow rate, depending on the valve
style. The increase in flow rate occurs because an increase in x
reduces backpressure and causes the vena contracta to move
upstream to the valve throat as shown in Figure 30. The flow
area at the valve throat is typically larger than the flow area of
an unconstrained vena contracta that is located in the piping
downstream of the control valve; therefore, some increase in
flow rate may occur.
Figure 30. Effect of Vena Contracta Enlargement

Inclusion of Y in Sizing Equations - The ISA equation accounts for
the conditions listed above by means of the expansion factor Y.
The Y term is used in the sizing equation as follows:
q = Cv p1 Y x (71)
Calculating Y - Y can be taken as a linear function of x. The

equation to calculate Y is as follows:
x
Y =1 −
3FK x T (72)
Relationships of x, xT, Fk, and Y - The relationships between the

values of x, xT, and Y are best shown graphically as in
Figure 31. Note that the value of Y will always fall in a range
between 0.67 and 1.0.

Figure 31. Relationships Among x, FkxT, and Y

Basis for Y - for compressible fluids, the expansion factor can be
defined as the ratio of the flow coefficient for a gas to the flow
coefficient for a liquid. When the value of Y is 1.0, there is no
difference in the liquid and gas flow coefficients. Values of Y
that are less than 1.0 indicate a flow limiting effect due to
density changes that result from fluid expansion.
In other words, as x approaches zero (very low pressure drop
ratios), flow resembles that of an incompressible fluid (a liquid);
accordingly, fluid expansion has a small effect on flow, and Y
approaches 1.0. As x approaches xT, the fluid becomes less
dense. 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-limiting effect 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 to calculate Y are dimensionless;
therefore, Y is also dimensionless.
Equation Development - at this point of discussion, the flow
equation takes the form:
q = Cv p1 Y x (73)
This equation:
• predicts flow at low pressure drop ratios ( p1 x )
• predicts critical flow (with the use of xT)
• predicts the effect of density changes that result from fluid
expansion due to low 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 based on the flow of air at standard conditions.
It can be generalized for any gas at any temperature with a
simple modification to account for fluid specific gravity and
temperature as shown in Equation 74.
x
q = Cv p1 Y (74)
Gg T1
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 the reference fluid (air) are at standard
conditions of 60 degrees F and 14.7 psia.
T1 = The absolute temperature of the fluid at the valve inlet
in degrees Rankine or in Kelvin.
The manner in which fluid density is included in the gas sizing
equations is different than the method that is used for liquid
sizing. Recall that for liquid sizing, fluid density is included in the
equation as the actual SG of the liquid at the valve inlet; that is,
the SG of the liquid must be corrected for temperature before
the sizing equations are used.
for gas sizing, the fluid density that is used in the sizing
equations is the fluid density at standard conditions (i.e., 14.7
psia and 60 degrees F). The sizing equation corrects the 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 follow the ideal gas law.

Note also that the correction is not necessary when the mass
flow forms of the equation are used, and density is expressed in
terms of specific weight () at the valve inlet (e.g., lbs/ft3, kg/m3,
etc.).
Real Gas Behavior
Real Versus Ideal Gasses - Many gasses and vapors do not

behave according to ideal gas law of pV = RT, and those
gasses that do not exhibit ideal gas behavior are referred to as
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.:
RT
V≠ (76)
p
Non-linear changes in the relationships between p, V, and T are

a result of a phenomenon known as compressibility. Valve
specifiers are interested in compensating for the effects of fluid
compressibility because of the direct relationship of fluid specific
volume to fluid density and because of the impact of fluid
density on flow 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 specific weight is a
computed value. The correction for fluid compressibility is not
necessary when 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, the effects 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 the behavior of a non-ideal gas as follows:
x
q = Cv p1 Y (78)
Gg T1 Z
Note that a compressibility factor of 1.0 indicates ideal gas

behavior (i.e., there are no compressibility effects), whereas a
lower value of Z (e.g., Z= 0.8) would indicate a tendency toward
incompressible (liquid) flow. Also, note that lower values of Z will
result in an increase in flow (q).

Application of Z Factor - The correction for fluid compressibility is

not necessary when the flowing gas displays ideal gas behavior
or when fluid density is expressed in terms of specific weight.
Calculating Z - Z can be determined in many ways. One popular
approach is to calculate the reduced pressure (pr) and the
reduced temperature (Tr) and, then, to locate the value of Z
from a generalized compressibility chart (refer to Figure 32). As
shown in Equation 79, the reduced pressure (pr) is the ratio of
inlet pressure to the fluid critical pressure, and the reduced
temperature (Tr) is the ratio of inlet temperature to the fluid
critical temperature. All values are expressed in absolute units.
p T1
pr = 1 and Tr = (79)
pc Tc
To determine the value of Z, the value of pr is located on the X

axis. at the point where pr intersects the appropriate Tr plot, the
value of Z is read at the Y axis of the chart.
Figure 32. Generalized Compressibility Chart

Maximum Impact of Z - Refer to Figure 32 and note that

compressibility effects become most significant when the inlet
pressure approaches the fluid critical pressure (i.e., as pr
approaches 1.0), and/or as the inlet temperature approaches or
falls below the fluid critical temperature.
Piping Effects
Piping Factor FP - When expanders and reducers are used, the

piping factor FP is included in the equation as shown below:
x
q = Fp C v p1 Y (80)
Gg T1 Z
The following equation is used to calculate Fp. The equation is

the same equation that is used for liquids:
− 1
 ΣK C 2  2
Fp =  v + 1 (81)
 N2 d4 
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 it
is calculated with the following:
−1
xT  x T Ki Cv2 
x TP = 2  + 1 (82)
F p  N5 d4 
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 xT significantly; therefore, it is often ignored,
except in the case of large, highly efficient valves. Experienced
specifiers often ignore the effect of inlet reducers on xT except
when the ratio of Cv to d (ratio of valve capacity to valve size)
becomes very large (as it does with ball and butterfly valves),
and the valve inlet is much smaller than the pipe size. In these
situations, the value of x that is used in the sizing equations
should be limited to the value of xTP.

Calculating XTP - The equation that is used to calculate control

valve Cv through the use of the xTP factor (see Equation 83) is
highly iterative. Note that the equation to calculate Cv requires
the terms Fp and xTP; however, the equations that are used to
calculate Fp and xTP both include the Cv term. Therefore, an
estimated value of Cv must 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 calculated
values Fp and xTP are then used to solve for Cv. Several
iterations of the equations must 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
successive iterations of the calculations result in very small
differences in the calculated Cv, the specifier knows that
accuracy has been achieved
q Gg T1 Z
Cv = (83)
N7 Fp p1 Y x TP
but
− 1 −1
 ΣK C 2  2 x x K C 2 
Fp =  v + 1 T
and x TP = 2 
T i v + 1
 N2 d4  F p  N5 d4 
(84)
Although manual sizing involves the use of many calculations,

the necessary calculations are performed easily and quickly with
personal computers and appropriate software.
Final Equation Form
Numerical Constants - The final term in the ISA equation is the

term N7, or the units constant. The specifier selects a units
constant that allows use of either the metric or the English units
system.
x
q = N7 Fp Cv p1 Y (85)
G g T1 Z
Solving for Cv - for

purposes of valve sizing, Equation 85 is
arranged to solve for Cv as follows:
q Gg T1 Z
Cv = (86)
N7 Fp p1 Y x

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 valve inside diameters to be expressed in
mm (N2=0.00214) or in inches (N2=890); refer to Table 3.
N5 units constant that is used in the equation to calculate XTP;

N5 allows pipe and valve inside diameters to be expressed in
mm (N2=0.00214) or in inches (N2=890); refer to Table 6.
N7 units constant to determine units for pressure, flow, and

temperature measurements; refer to Table 6.
Fp piping geometry factor, dimensionless
Cv control valve flow coefficient
p1 inlet pressure, absolute
x
Y expansion factor. Y = 1− where Fk = ratio of specific
3Fk x T
heats factor
Gg gas specific gravity (ratio of the density of the flowing gas to the density of air,
with both at standard conditions)
T1 inlet temperature, absolute
Z compressibility factor, dimensionless
x pressure drop ratio ( ∆P / p1 ); limited to xT for choked flow, FKxT to account for
specific 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 valves for compressible fluids are
similar to the procedures that are used with the liquid sizing
method. The major differences are the required inputs, the
entries in the Intermediate Results section, 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 sizing options as shown in Figure 33.
The ISA options are as follows:
ISA Gas - Selectingthe ISA Gas method causes the software to
use the equations in which fluid density is expressed in terms of
SG or M.
ISA Vapor - Selecting the ISA Vapor method causes the software
to use the equations in which 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.
Fisher Real Gas FISHER SIZING PROGRAM Rev 1.41
Fisher Ideal Gas
Fisher Water
Fisher Pulp Tag :

ISA / EN Gas
ISA / EN Vapor
ISA / EN Liquid or [ F10 ] to enter application information above )

Spec Sheet : --
Notepad : --
Valve sizing calculations for a liquid. ISA / EN method.

Figure 33. Valve Sizing Method Options

Selecting the Desired

Calculation Type
After a valve sizing method has been selected, the specifier

selects the type of calculation that will be performed. Refer to
Figure 34. Choices include valve sizing, fluid velocity
calculations, and various noise calculations.

ALTA Velocity
ALTP Increased Velocity LpA
ALTQ LpA vs Q

Figure 34. Available Calculation Types
Overview of Sizing Procedures
Valve Sizing Screen - Selecting

the Valve Sizing & LpA option
brings up the sizing screen. This screen is divided into several
sections as shown in Figure 35 below.
Rev 1.41 NRM ISA / EN Gas ValveSizing
Liquid & Service Conditions Valve Specifications
Gas Xt --
Tc --degF
Pc --psia
SG
Fk
P1
dP --psig
Q --psid
T --degF Calculated Results
--lb / h
Cv --
Intermediate Results Approve LpA -- dB(A)
dP Choked --psid
Y dP / P1 --
Z
Notes :
Gas name (optional). Press [F4] for a list of gases.
Figure 35. Valve Sizing Screen for the ISA Gas Valve Sizing Method

Fluid and Service Conditions - Inthis section, the specifier enters

the fluid type, and fluid properties such as critical pressure,
critical temperature, and Fk. Service conditions are also entered
in this section.
Intermediate Results - Any
intermediate results that the software
calculates are displayed in 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 xT and sizing data for the valve and
piping if piping corrections are necessary.
Calculated Results - After all fluid properties, service conditions,
and valve data are entered in the appropriate locations, the
specifier presses the function key F2 to calculate the required
control valve Cv. The results of the sizing calculations appear in
the calculated results section. In addition to valve Cv, other
important information such as the ∆Pchoked and the pressure
drop ratio (x) is also shown.
Selecting Options
F3 Options - During the sizing procedure, the specifier may

choose from several different sizing options by pressing the
function key F3. The options menu for the ISA Gas method is
shown in Figure 36. Options are toggled by highlighting the
appropriate line and pressing enter. The option that is visible
when the option menu is stored (by pressing the escape key) is
the option that will be used.
Gas Xt --
Tc --degF
Pc --psia
SG --
Fk OPTIONAL SELECTION
P1 Solve for Cg. Cs or Cv
dP
T CalculateZ
Q Omit Fp & Xtp ults
LpA(SPL)OFF
Pipe : Size / Sched --
Intermediate Results Warnings ON -- dB (A)
--psid
Y --
Z dp / p1
Gas name (optional). Press [ F4 ] for a list of gases.

Figure 36. Calculation Options for the ISA Gas Valve Sizing Method

F3 Options for the ISA Gas Sizing Method - Options for the gas
sizing method are as follows:
Line 1: Solve for Cg, Cs, or Cv. Other options: Solve for Flow,
Solve for ∆P (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 OFF
F3 Options for the ISA Vapor Sizing Method - Optionsfor the vapor
sizing method are the same as for the gas method, except that
there is no option for calculating Z. Recall that compressibility
effects are not considered when the vapor form of the equation.
Options and Input Fields - Asvarious options are selected, the
input fields on the sizing screen will change; for example, if the
option to calculate Z is selected, the software will require values
for critical pressure and temperature, and it will display the
calculated value of Z.
Units-Selection - As
explained previously, engineering units can
be changed globally through the selection of Units from the
Config heading on the main menu. The specifier may also
change units for any input parameter by placing the cursor on
that parameter and pressing F8. Pressing F8 produces a sub-
menu (refer to Figure 37) of available options.


Gas Xt --
Tc --degF
Pc --psia
SG --
Fk
P1 --psig
dP --psid
T --degF
Q -- alculated Results
lb / h
scfh v --
Intermediate Results MMscfd ppox LpA -- dB (A)
scfm P Choked --psid
Y kg / h P/ P1 --
Z Nm3 / h
scfd
Fluid flow through valve.

Figure 37. Line-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 the ISA equations. The Fisher
Universal Gas Sizing Equation gained popularity immediately
after its introduction in 1951 because it was easier to use than
other techniques that were available at that time. During this
era, specifiers sized valves manually, either by calculation or
with slide 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 calculator
because of its straightforward, non-iterative nature. Today,
control valve specifiers size valves with 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 flow process in a similar fashion and they
give nearly identical results. with rare exception, any
discrepancies in calculated results are within the limits of
accuracy of any sizing technique. In virtually 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 region between linear flow and choked flow.
This approach eliminates the need to calculate the value of
an expansion factor (Y).
• Terms to account for the influences of piping factors,
compressibility, and specific heat ratios other than 1.0 are
not included in the basic equation; instead, they are
considered on an as-needed basis.
The Fisher Universal Sizing equation for an ideal gas is as
follows:
520   3417  ∆P 
Q= Cg P1 C2 SIN    (87)
GTZ  1 2
 C C P1 
Degrees
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 began with the basic liquid sizing equation (see
Equation 88).
∆P
Q(GPM) = Cv (88)
G
Adding a Constant to Change from GPM to SCFH - The first step in
adapting the equation for use with compressible fluids is to add
a conversion factor to change units from gallons-per-minute to
cubic-feet-per-hour. In addition, specific gravity is related in
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 pressure drop ratio is identical
to the x term in the ISA equation. The result is as follows:
∆P
Qscfh = 59. 64 Cv P1 (89)
P1

Provisions for Any Specific Gravity and Temperature - with

the
inclusion of a modification that is based upon Charles' Law for
gasses, the equation is generalized to account for any gas at
any temperature as shown in Equation 90.
∆ P 520
Q scfh= 59. 64 Cv P1 (90)
P1 GT
Where:
520 = The product of the specific gravity and the absolute
temperature of air at standard conditions (i.e., the
specific gravity is 1.0 and the temperature is 520
degrees Rankine, which corresponds to 60 degrees
F).
G = The specific gravity of the flowing gas at standard
conditions (60 degrees F and 14.7 psia).
T = The temperature of the flowing gas in degrees
Rankine.
Equation Limits
Pressure Drop Ratio Limits - Equation90 predicts a flow rate that is

a linear function of the square root of the pressure drop ratio
(the same as the flow rate that is predicted by the x term in the
ISA equation); however, at pressure drop ratios that are greater
than approximately 0.02, tests show smaller and smaller
incremental increases in actual flow for every incremental
increase in the pressure drop ratio. Refer to Figure 38.
Critical Flow - Tests
also indicate a point of critical flow, which is
the same as choked flow in ISA terminology. Critical flow is
defined as the point where increasing the pressure drop ratio by
reducing downstream pressure does not produce any increase
in flow rate.

Figure 38. Actual 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 flow rate. As it turns out, critical flow
is a function of valve geometry. a comparison of plots that relate
critical flow to the pressure drop ratio for two different valve
styles illustrates the concept. Refer to Figure 39. Note that the
two valves have identical Cv ratings, but one of the valves is a
high recovery type and the other valve is a low recovery type.
Figure 39. Critical Flow for Low and High Recovery Valves
Low Recovery Valves (or globe style valves) reach critical flow at a
pressure drop ratio of 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 predict critical flow in both high and low recovery
valves, Fisher Controls developed a standard for testing flow
capacity with air as well as with water. From these tests, a gas
sizing coefficient Cg was defined that relates gas critical flow to
the absolute inlet pressure. Cg is experimentally determined for
each valve style and size; therefore, Cg can be used to
accurately predict critical flow (using air as a test fluid) with the
following:
Qcritical = Cg P1 (91)
To make the critical flow equation useful for any gas at any
temperature, the correction factor that was shown previously is
applied:
520
GT
Blending the Two Equations
Impracticality of Using Two Equations - at this point, Fisher had two

equations. See Figure 40.
Equation a (see Equation 93) accurately predicted flow at very
low pressure drop ratios only. Note that this equation uses the
flow coefficient Cv.
∆P 520
Q = 59. 64 C v P1 (93)
P1 GT
Equation B (see Equation 94) predicted critical flow only. Note

that this equation uses the flow coefficient Cg.
520
GT
Although the equations provided utility, neither equation
accounted for the transition region between low flow conditions
and critical flow; i.e.,
when ∆P/P1 > 0.02 and Q < Qcritical. In addition, the process of
using two equations and two flow coefficients was inefficient.

Figure 40. Predicting Low Flow and Critical Flow

Tests and Data Plotting - To
arrive at a single equation, Fisher
Controls completed an extensive testing procedure to analyze
flow versus pressure relationships in the region between low
pressure drop ratios and critical (choked) flow. Tests were
performed on high recovery valves, low recovery valves, and
valves that can be called intermediate recovery valves. Test
results were normalized with respect to critical flow, and data
was plotted.
Sine Curve - Analysis
revealed that the test points in the transition
region between low flow and critical flow fell on a curve that
closely approximates the first quarter cycle of a standard sine
curve. See Figure 41 below.

Figure 41. Tested Values of Flow Compared to a Sine Curve

Combining the Equations - Capitalizing on this finding, Fisher
Controls used a sine function to mathematically model flow in
the transition region. The sine function effectively 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 degrees so that the equation does not predict
decreasing flow after critical flow is achieved.
520   3417  DP 
Q= Cg P1 SIN   
 (95)
GT   C1  P1  Degrees
The C1 Factor
Note the inclusion of the C1 factor in Equation 96.
520   3417  ∆P 
Q= Cg P1 SIN    (96)
GT   C1  P1 
Degrees

Role of C1 - The role of C1 is to allow the use of a single sizing

coefficient (Cg) in a universal equation that combines the
equation that is used to calculate the flow of incompressible
fluids (Equation 97) with the equation that is used to calculate
the critical flow of a gas (Equation 98). a fundamental obstacle
in blending Equations 97 and 98 is that the liquid flow equation
uses the flow coefficient Cv, while the gas flow equation uses
the flow coefficient Cg.
∆P 520
Liquid Flow Q = 59. 64 C v P1 (97)
P1 GT
520
Q= Cg P1
Gas Flow GT (98)
Equations 97 and 98 could have been combined in their original

forms; however, the specifier would have to supply both the Cv
coefficient and the Cg coefficient. During the development of the
Fisher equation, the decisions were made that a single
coefficient would be used and that a factor to account for the
differences in liquid and gas flow through a particular valve
would be included in the equation. The factor C1 is used for this
purpose. As shown in Equation 99, C1 is defined simply as the
ratio of the gas flow coefficient, Cg to the liquid flow coefficient,
Cv.
Cg
C1 = (99)
Cv
Differences in Gas and Liquid Capacity - In

order to better
understand the significance of the C1 term, consider a
comparison of the Cg and Cv flow coefficients for a high
recovery valve, and the Cg and Cv flow coefficients for a low
recovery valve that are shown in Table 7.
Liquid flow (Cv) is heavily influenced by valve geometry (i.e.,
whether the flow path is tortuous or streamlined). Gas flow (Cg)
is largely a function of the flow area of the valve. The difference
in the factors that determine capacity for liquid flow and for gas
flow 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).

Table 7. Comparison of Cv, Cg, and C1 Values

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 C1 = Cg/Cv
= 4680/254 =4680/135
=18.4 =34.7
Locating C1 Values - Manufacturers that use C1 values determine
them by test, and they publish 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 sine function is essentially used as a multiplier
with the simple equation for critical flow. Refer to Equation 100.
520   3417  ∆P 
Q= C P SIN   
GT g 1   C1  P1 
Degrees (100)
Predicts Qcritical Serves as a multiplier
Low Pressure Drop Ratio Example - Assuming a C1 value of 35 and

a pressure drop ratio of 0.02, the value of the bracketed terms is
as follows:
  3417  
SIN  0. 02  = SIN [98 × 0.141]Degrees =
  35   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, at the end of the first quarter cycle, tends
towards its maximum value of 1.0. If the result of the sine
function is 1.0, the equation is functionally reduced to the
equation for critical flow as illustrated in the following equation.
520   3417  ∆P  ∆P
If Q = C g P1 SIN    and = 1. 0
GT   C1  P1  P1
Degrees
102)
  3417   520
then SIN   1 ≈ SIN 90° = 1. 0 and Q = C g P1
 35   GT
(103)
Intermediate Pressure Drop Ratios - at intermediate pressure drop

ratios, the sine function models 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 is based on the ideal gas laws. As was
discussed previously, real gas behavior can differ markedly from
ideal behavior.
Real Gasses - The real gas form of the Fisher equation uses two
correction factors. The corrections are for compressibility and
for the ratio of specific heats. Both corrections are 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 gas does not follow the ideal gas law of
pV = RT, the term Z is used to correct the ideal gas equation.
pV = ZRT (104)
The value of Z can be determined from generalized

compressibility charts (refer back to Figure 32) after establishing
the reduced pressure and temperature with the use of the
P T
Preduced = actual and Treduced = actual (105)
Pcritical Tcritical
The Z term is included in the equation as follows:

520   3417  ∆P 
Q= Cg P1 SIN   (106)
GTZ  C  P1 Degrees
 1
C2 and the Ratio of Specific Heats - In the Fisher equation,

allowance is made for thermodynamic properties (the ratio of
specific heats) with the term C2. C2 serves the same function as
the Fk factor in the ISA equations. C2 is included in the equation
as follows:
520   3417  ∆P 
Q= Cg P1 C2 SIN    (107)
GTZ  1 2
 C C P1 
Degrees
In the ISA equation, the Fk factor suggests a linear relationship

between k and Fk (i.e., Fk = k/1.4). This relationship is typically
valid for k values between 1.2 and 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 is not
precisely linear. for a specific value of k, the specific value of C2
can be determined from the chart that is shown in Figure 42.
Figure 42. C2 Factor Versus k

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

  3417  ∆P 
Q = 1. 06 d1P1 Cg SIN   (108)
 C  P1  Degrees
 1
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 vapor applications.
Special Steam Equation (Below 1000 PSIG) - Because steam
applications are quite common, a special form of the equation,
which is shown in Equation 109, is also available.
 Cs P1    3417  ∆P 
QLB/HR = SIN    (109)
 1+ 0. 00065 T sh    C1  P1 
Degrees
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 Controls publishes Cs values for most valves.
The relationship between Cs, Cg, and Cv is as follows:
Cg
Cs = therefore Cg = Cs x 20 (110)
20
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 that predict flow rate, any of the equations
that are used to predict flow can be arranged to solve for the
required control valve Cg as shown in Equation 111.
Q scfh
Cg = (111)
520  3417 ∆P 
P1 C2 SIN
GTZ C C P1 
 1 2 Degrees

Initial Assumptions for C1 Values - When solving for Cg, the

specifier must initially select a valve style and estimate a value
of C1. After calculating Cg and selecting a specific valve type
and size, the actual C1 values for the selected valve are used in
the equation to ensure maximum accuracy. Specifiers typically
use initial (estimated) C1 values of approximately 35 for
standard globe style valves, and C1 values of approximately 15
to 20 for ball and butterfly valves.
Converting Cg to Cv - It may occasionally be desirable to convert a
flow coefficient from Cg to Cv; for example, it may be useful to
size non-Fisher valves by means of the Fisher Sizing Program,
or it may be useful to convert Cg to Cv for comparative studies
of capacity or other valve attributes. Recall that C1 is calculated
as follows:
Cg
C1 = (112)
Cv
Therefore, after a Cg has been calculated, it can be converted to

Cv as follows:
Cg
Cv = (113)
C1
Comparison of Fisher and ISA

Gas Sizing Equations
Both the ISA and the Fisher equations model the same process
and typically produce nearly identical results. Although minor
differences in the calculated flow coefficient may occur, the use
of either equation will virtually always lead the specifier to the
same valve size. The table below summarizes how the two
equations account for various aspects of flow through the
control valve.

Table 8. Comparison of ISA and Fisher Sizing Terms
Parameter ISA Equation Fisher Equation

Flow equation   3417  ∆P 
x 520
Cg P1 C2 SIN   
q = N7 Fp C v p 1 Y Q=
GTZ   C1 C2 
 P1 
G g T1 Z Degrees
Cg
Cg (air test) C v =
Flow Coefficient Cv (water test) C1
Flow when ∆P ∆P
∆P / p1 ≤ 0. 02 Cv (liquid equation) Cv (liquid equation)
p1 p1
Critical Flow for p1 xT p1 Cg
Specific Valve Published Cg tested at critical
Style Published xT tested by
manufacturer flow
Fluid Expansion Y x Sine function
Piping Factor FP factor Swaged capacities for rotary-
Calculated by specifier or shaft valves published in sizing
tested and published by information
manufacturer Can use FP
Compressibility pV pV
Z= Z=
(real gasses) RT RT
Thermodynamic Fk xT C2
behavior (k)

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 sizing methods as shown in Figure 43.
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 be 1.4. 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 factors and 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 that there is no option for the piping factor
correction. Fluid density is entered in terms of lbs/ft3 or kg/m3,
and there are options for the use of Z and C2 factors. The vapor
method is also commonly used for steam.
Fisher Steam - The Fisher Steam method uses the special
equation for steam applications under 1 000 psig.
Fisher Real Gas
Fisher Ideal Gas FISHER SIZING PROGRAM Rev 1.41
Fisher Water
Fisher Pulp Tag :

ISA / EN Gas
ISA / EN Vapor
ISA / EN Liquid or [ F10 ] to enter application information above )
Valve Sizing : Fisher Real Gas File : 2FIG28

Spec Sheet : --
Notepad : --
Valve sizing calculations for a real gas, Fisher method.

Figure 43. Valve Sizing Methods

Selecting a Calculation Type
After a specific valve sizing method has been selected, the

specifier can choose the type of information that is being
sought. As shown in Figure 44, choices include valve size, fluid
velocity, and various noise calculations.
Rev 1.41 Fisher Real Gas Sizing

ALTA Velocity
ALTP Increased Velocity LpA
ALTQ LpA vs Q

Figure 44. Selection of a Calculation Type
Overview of Sizing Procedures
Valve Sizing Screen - Selecting the Valve Sizing & LpA option
brings up the actual sizing screen, which is illustrated in
Figure 45. The sizing screen is divided into four distinct
sections.
Rev 1.41 NRM Fisher Real Gas ValveSizing
Gas C1 --
Tc --degF
Pc --psia
SG
Fk
P1 --psig
dP --psid
T --degF
Q --lb / h Calculated Results
Cv --
Intermediate Results Approve LpA -- dB(A)
dP CCritical --psid
Y dP / P1 --
C2
Gas name (optional). Press [F4] for a list of gases.

Figure 45. Valve Sizing Screen for the Fisher Real Gas Sizing Method

F3 Options
Fisher Ideal Gas - As shown in Figure 46 below, there are no

sizing options for the Ideal Gas Method that affect how the flow
coefficient is determined.
Rev 1.41 NRM Fisher Ideal Gas Valve Sizing
Gas C1 --
SG --
k(optional) --
Service Conditions
OPTIONAL SELECTION
P1
dP Solve for Cg. Cs or Cv
T LpA(SPL)OFF
Q Pipe : Size / Sched ults
Warnings ON
--
ApproxLpa -- dB (A)
dpCritical --psid
dP / P1 --

Figure 46. Calculation Options for the Fisher Ideal Gas Sizing Method
Fisher Real Gas - The calculation options for the Fisher Real Gas
Method (see Figure 47) present the specifier with several
choices for the use of Z and C2 factors. The choices 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)


Gas C1 --
Tc --degF
Pc --psia
SG
k OPTIONAL SELECTION
P1
dP Solve for Cg. Cs or Cv
T LpA(SPL)OFF
Q Pipe : Size / Sched ults
CalculateZ, C2
Warnings ON --
-- dB (A)
Intermediate Results dpCritical --psid
dP / P1 --
Z
C2

Figure 47. Calculation Options for the Fisher Real Gas Sizing Method
Fisher Vapor - As shown in Figure 48, there are no sizing options
for the Fisher Vapor Method that affect the calculation of the
flow coefficient.
Vapor Name C1 --
P1 --psig
dP
Density OPTIONAL SELECTION
W
M(optional)
LpA(SPL)OFF
k(optional) Pipe : Size / Sched ults
T(optional) Warnings ON
--
ApproxLpA -- dB (A)
dpCritical --psid
dP / P1 --
Vapor name (optional).

Figure 48. Calculation Options for the Fisher Vapor Sizing Method
Fisher Steam - The only option in the Fisher Steam Method is the
choice of whether the specifier will input steam temperature or
assume that the steam is saturated. See Figure 49.


P1 --psig C1 --
dP --psid
T --degF
Qs
OPTIONAL SELECTION

Intermediate Results
Input Temperature
TSaturation LpA(SPL)OFF ults
Pipe : Size / Sched
Warnings ON --
-- dB (A)
dpCritical --psid
dP / P1 --
Valve inlet pressure .
Figure 49. Calculation Options for the Fisher Steam Sizing Method
Options and Input Fields - As various options are selected, the
input fields on the sizing screen will change; for example, if the
option to calculate Z is selected, the software will require values
for critical pressure and temperature. Refer to Figure 50.
Units-Selection - As explained previously, engineering units can
be changed globally by selecting Units from the Config heading
on the main menu; in addition, the specifier may change the
units for any input parameter by placing the cursor on that
parameter and pressing F8. Figure 50 illustrates the available
units options for fluid temperature.
Rev 1.41 NRM Fisher Steam Valve Sizing
Service Conditions Valve Specifications
P1 --degF C1 --
dP --psia
T --
Qs -- degR
degF
degC
degK
Intermediate Results
Calculated Results
TSaturation
Cs --
Appox LpA -- dB (A)
dP Critical --psid
dP/ P1 --
Fluid flowing temperature .

Figure 50. Pull-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 must calculate and enter information that
describes both the physical size of the valve and information
that describes the capacity of the valve. for purposes of
illustration, the discussion that follows is based on the ISS for
globe and angle control valves (Refer to Saudi Aramco 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 size are 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 a particular valve style and size is included in the
appropriate valve specification bulletin.
Capacity Ratings
Capacity at Minimum, Normal,
and Maximum Flow Conditions
Cv at Minimum, Normal, and Maximum Flow Conditions is specified

on lines 62 through 64.
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 62 through 64. Each value is simply the
calculated Cv at each flow condition divided by the 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 the percent of valve travel that provides the
minimum Cv requirement, and the upper value of 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 Cv at normal flow conditions.

Saudi Aramco 8020-711-ENG (8/89)
SAUDI ARABIAN OIL COMPANY

APPD.
INSTRUMENT SPECIFICATION SHEET - GLOBE/ANGLE CONTROL VALVES

1 Instrument Tag Number 2 P & ID No. Sht. No.
CERT.
3 Service ONSHORE / OFFSHORE ON-OFF / THROTTLING

4 ACTUATOR POSITIONER
GENERAL
5 Manufacturer
CHKD.
6 Model/Type Number
7 Material Requesition Number
8 Source AMS Stock Number
9 Overall Valve / Actuator Characteristic EQ % Linear Other
10 Line Size & Schedule 11 Electrical Area Classification
12 Fluid 49 Body Size / Port Size
13 Single / Two Phase / Flashing 50 Inlet Flange Size Rating/Style
14 Corrosive Components / Sand 51 Outlet Flange Size Rating/Style
15 Relative Density Liquid (Oper.Cond.) 52 Body and Bonnet Material
DESCRIPTION
16 Relative Density Gas (Standard Cond.) 53 Bonnet Std/Extended or Column Std

17 Operating Temperature °C (°F) 54 Gland Packing Material
18 Degree of Superheat (Steam) °C (°F) 55 Lubricator and Isolating Valve
19 Minimum Flow Rate 56 Stem Material
20 P(In) At Minimum Flow Rate kpa(ga)(paig) 57 Type of Plug Guiding
21 P(Out) At Minimum Flow Rate kpa(ga)(paig) 58 Plug / Cage Material
PROCESS DATA
22 Normal Flow Rate 59 Leakage Class (ANSI B 16.104)

23 P(In) At Normal Flow Rate kpa(ga)(paig) 60 Seat Type / Material
VALVE BODY
24 P(Out) At Normal Flow Rate kpa(ga)(paig) 61 Valve Plug Action Flow To: Close Open
25 Maximum Flow Rate 62 Cv at Min. Flow % of Rated Cv
JO/EWO
26 P(In) At Maximum Flow Rate kpa(ga)(paig) 63 Cv at Norm. Flow % of Rated Cv

27 P(Out) At Maximum Flow Rate kpa(ga)(paig) 64 Cv at Max. Flow % of Rated Cv
28 Vapor Pressure kpa(ga)(paig) 65 Rated Cv of Selected Valve
BY
29 Critical Pressure kpa(ga)(paig) 66 Throttling Range From / To%

DATE
30 ∆PAt Shut-Off kpa(paig) 67 Valve Opening at Normal Flow%

31 ∆PEffective Choked Flow kpa(paig) 68 Calc. Max. Noise Level at 1 m (3 ft)
32 ∆PCavitation Worst Case kpa(paig) 69 Noise Reducing Trim Required YES NO
NO.
33 Cavitation Service YES NO 70 Vibration Resistant Trim Required YES NO

REVISION 34 71 Cavitation Resistant Trim Required YES NO
Drawn Type (Pneum./Elec./Hydr.) and Size Face to Face Dimensionmm (in)
35 * 72
BY ..................... YES NO
36 Spring Range and Travel * 73 Wetted Parts Per NACE STD MR-01-75
Date .................. 37 Adjustible Stoper 74 Air Filter RegulatorType / Size
CHKD BY ............. 38 Positioner Type / Model Number * * 75 Air Req. Set Press. kpa(ga)(paig)
39 Positioner Bypass / Gauges 76 Volume Tank YES NO
ACCESSORIES
OPRG. DEPT.
ACTUATOR
40 Positioner Input Output 77 Trip Valve Lock Valves

BY ..................... 41 Positioner Action Direct Rev. 78 Solenoid Valve Type / Model No. *
Date .................. 42 Valve Action on Increase Signal Open Close 79 Number Solenoid Valve Req'd. *
43 Supply Max Avail/Min. Req'd kpa(ga)(paig) 80 Transducer Type / Model Number
ENG. DEPT. 44 Valve Action on Supply Failure Open Close Lock 81 Transducer Input mA / Output
BY ..................... 45 Cam Characterized YES NO 82 Handwheel TOP SIDE
46 Actuator Pressure Rating kpa(ga)(paig) 83 Lubricator YES NO
Date ..................
47 84 Fire Proofing YES NO
APPD. FOR 48 85
CONSTR.
BY ..................... NOTES:
1.THIS SPECIFICATION SHEET SHALL BE USED IN CONJUNCTION WITH 34-AMSS-711.
Date ..................
2.STANDARD CONDITIONS ARE 15¡C AND 101.325 kPa (60°F AND 14.73 psia).
CERTIFIED 3.VALVE SIZING SHALL COMPLY WITH ANSI/ISA S75.01. DETAILED CALCULATION SHEET SHALL BE SHOWN ON SHEET 2,
EITHER HANDWRITTEN OR AS COMPUTER PRINT-OUT.
BY ..................... 4.VENDOR TO CHECK SELECTION, SIZING AND MATERIALS OF VALVE AND ACTUATOR, AND SHALL RETURN ONE
COMPLETED (SEE * MARKS) OR CORRECTED COPY TO BUYER.
Date ..................
THIS DRAWING IS NOT

TO BE USED FOR ISS FOR PLANT NO. INDEX DRAWING NO. SHT. NO. REV. NO.
CONSTRUCTION OR
FOR ORDERING
MATERIALS UNTIL J DE - 1 OF 2
CERTIFIED AND
DATED
SAUDI ARABIA JO/EWO
Figure 51. The Saudi Aramco ISS

WORK AIDS
WORK AID 1: PROCEDURES THAT ARE USED TO MANUALLY SIZE

CONTROL 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:
G
Fisher: Cv =Q
∆P
q Gf
ISA: Cv =
N1 p1 − p2
To determine the appropriate value N1, refer to the table
below.
Constant Units that are Used in Equations

N w q p, ∆P d, D g1 n
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 the appropriate pages for the valve
types that are described in the Exercise. for each valve
type, browse through the Cv table and locate a valve size
that will provide the required capacity. Ensure that you
select a valve size that will provide the required Cv at a
percentage of travel that is consistent with the guidelines
that are given in Section 6.2.2 of SAES-J-700. The
guidelines are summarized in the table below.
Extrapolate the degrees of rotation or the percent of travel
that provides the required Cv.
for rotary-shaft valves, convert the degrees of rotation to
percent of travel by dividing the 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
Percent Travel at Normal Percent Travel at Maximum
Flow Characteristic
Flow Flow
Equal Percentage 85 93
Linear 75 90
Modified Parabolic 80 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 as follows:
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 "Valve Specifications."
P1 Use the value that is listed in the Exercise under the

heading "Service Conditions."
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 the required 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 and select the smallest valve size that will
provide the required Cv at a percentage of travel that is
consistent with the guidelines that are given in Section 6.2.2
of SAES-J-700 (refer to Work Aid 1A). Extrapolate and
record the percent of travel at which the Cv requirements 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 on Cv
Perform the following procedures to complete Exercise 1C:
1. Locate the appropriate pages in Fisher Catalog 10 for the
valve that is described in the Exercise. Ensure that you
locate the page for the line-to-body size ratio that is given
in the Exercise. Browse through the Cv column and locate
a valve that provides the maximum Cv at less than the
percent of travel guideline that is included in Section 6.2.2
of SAES-J-700.
Note: for rotary valves, the percentages of travel that are listed in Section 6.2.2 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 is described in the Exercise.
Calculate the required Cv through use of the following
equation:
Calculated C v
Re quired C v =
R
Using the required Cv that was just calculated, refer to the
appropriate page in Fisher Catalog 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-body size ratio. Also,
ensure that the selected valve provides the maximum required Cv at a
travel that is consistent with the guidelines that are listed in Section 6.2.2
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 the application that is
described. Use the following equation:
G
Cv =Q
∆P
2. To compensate for viscous effects, locate the Viscosity
Correction Nomograph in Fisher Catalog 10, Section 2,
pages 26 and 27 and follow the instructions that are
included in the nomograph. Use the value of Cv that was
calculated in step 1.


CONTROL VALVES FOR LIQUID APPLICATIONS
Work Aid 2A: Procedures that are Used to Computer Size Control
Valves for Water Applications
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 that are 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 (∆P). ∆P = P1 minus P2.
h. Locate the SG of water at 100 degrees F from the table
on page 135 of the Fisher 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 are requested 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 accurately entered.

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 FL
Globe and Angle 0.75 .87
Rotary-Shaft 0.45 0.67
f. Press F2 to calculate the valve sizing information. Record
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 Valve Handbook
g. Ensure that all service conditions and fluid properties are
accurately entered.
h. Press F2 to calculate the valve sizing information. Record
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 that follows or by selecting a value from the
table below:
Estimated FL = Estimated K m
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

Work Aid 2B: Procedures that are Used to Computer Size Control
Valves for Choked Flow
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 the maximum Cv at a
percentage of travel that is consistent with the guidelines
that are listed in Section 6.2.2 of SAES-J-700. (Refer to the
table in Work Aid 1A).
12. Record the information that is requested under the heading

"Initial Calculations and Valve Selection."
13. Using the Km of the initially selected, recalculate the valve

sizing information. Note that the calculated Cv may now
allow the selection of a smaller valve. To determine if a
smaller valve will pass the required flow, use the Km of the
smaller valve to recalculate the sizing information.
14. Record the information that is requested under the heading

"Final Calculations and Valve Selection."

Work Aid 2C:Procedures that are Used to Computer Size Control

Valves for Fluids in the 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 values of Pc, Pv, and SG for the liquid.
Enter these values in the proper fields on the calculation
screen. Note: The value of Pv that is included in the table
is for the fluid at a temperature of 100 degrees F;
however, this value of Pv will be used because 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 that is requested under the heading
Calculated Results.
a. Place the cursor on the appropriate fields and press the
F5 key to clear the values 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. From the pull-down menu, select Propane.
d. Press F2 to calculate the valve sizing information. Record
Calculated Results.


a. Without clearing the calculation screen, change the
temperature and the SG to to the values that are stated
in part 3.
b. Press F2 to calculate the valve sizing information. Record
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 the heading Calculated Results on the
Exercise Sheet, the information that is requested.

Work Aid 2D: Procedures that are Used to Computer Size Control
Valves with Piping Factor 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 the table 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 of travel (or degrees of rotation) that
is consistent with Section 6.2.2 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 of travel (or degrees of rotation) that
is consistent with Section 6.2.2 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.


of sizing methods.
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 Input Pv, 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 of the equation that follows or by
selecting a value from the table below:
Estimated FL = Estimated K m
g. Enter an assumed valve inlet size, d. Use the valve size
that was previously selected.
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 the necessary correction for piping
factors, ensure that you select a valve size from the table
that lists capacities for a 1:1 line-to-body size ratio. Also,
ensure that you select a valve size that is consistent with
the percentage of travel guidelines that are listed in
Section 6.2.2 of SAES-J-700. (Refer to the table in part 2
of Work Aid 1A.)

Work Aid 2E: Procedures Used to Computer Size Control Valves with
Viscosity Correction
of sizing methods.
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 are selected.
f. Enter the fluid name.
g. Ensure that the engineering units that are displayed on
the calculation screen match 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 in the Exercise.
l. Select a valve size that satisfies the Cv requirement
according to the travel guidelines that are given in
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 are selected.

c. Ensure that the engineering units that are displayed on

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 that satisfies the Cv requirement
according to the travel guidelines that are given in
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 are selected.
f. Note that the software may have calculated a value of FL

from the Km that was included in the previous
calculation. If the software has not calculated this value,
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 obtained from 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 that explains Fd values, press the F1
key twice, press "v" to view a list of valve sizing Help
Screens, select Valve Sizing: Sizing Parameters, and
press Page Down 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 appropriate value 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 above can provide the required
capacity. If it appears that a smaller valve can provide the
need capacity, change the value of d, calculate Cv, and
again refer to the sizing tables. Ensure that you select a
valve that is consistent with the guidelines in Section
6.2.2 of
SAES-J-700 (see the table in part 2 of Work Aid 1A).

Work Aid 2F: Procedures that are Used to Computer Size Control
Valves with Viscosity and Piping Factor Correction
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 are selected.
f. Ensure that the engineering units that are displayed on
g. Enter the fluid properties and the service conditions.
h. Enter an estimated value of FL. an estimated value of FL
can be obtained from the 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 appropriate value 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 valve size that provides the required Cv
at a percentage of travel that is consistent with Section
6.2.2 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 valve will provide the maximum Cv
requirement.
Calculating Cv with Piping Factor Correction

a. Press F3. Ensure that the options Calculate FP and

Viscous Correction OFF are selected.
b. Initially assume that the required valve size is equal to
line size, and enter the appropriate 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 valve size. Evaluate the assumed valve
size as well as smaller sizes. If a smaller than initially
selected valve size appears to have sufficient capacity,
recalculate the valve sizing information with the use of
the appropriate value of d and the actual value of FL.
f. Record the selected valve size and the degrees of
rotation at which the valve provides the maximum Cv
requirements.
a. If the calculations that consider piping factors lead to the
selection of one valve size and the calculations that
consider the effects of laminar flow lead to the selection
of another valve size, select the larger valve.

Work Aid 2G: Procedures that are Used to Computer Size Control
Valves for Minimum, Normal, and Maximum Flow
Conditions
Use the following procedures to complete Exercise 2G:
Setup
a. Press ESCAPE until the valve sizing method menu appears.
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 options are set to LpA (SPL) OFF, Omit FP,
Viscous Correction OFF, Pipe: Size, Sched., Input Pv, and
Warnings 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 service conditions. To determine an
estimated value of FL, browse through the FL values that are
listed on the Catalog 12 page that describes the selected
valve type. Select a value of 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 information from the minimum flow calculation
screen to the normal flow calculation screen. Press ENTER.
e. Change the pressure and flow conditions to the values that
are given for the normal flow 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 information from 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 maximum flow 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 the selected valve. Locate the smallest
valve size that can provide the maximum Cv according to the
guidelines in Section 6.2.2 of SAES-J-700 (refer to the table
in part 2 of Work Aid 1A).

Valves for Minimum, 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 and LpA calculations are selected.
b. Press F3 and select the Calculate FP option. (Note that
selecting an option from this screen invokes the option for all
calculation screens (MIN, NRM, and MAX); selecting an
option from a particular sizing screen invokes the option for
that specific condition 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 piping factors. Refer to the appropriate Catalog
12 page, and compare the corrected Cv's that are displayed
on the screen to the Cv's that are published for the initially
selected valve. Ensure that the selected valve can provide
the Cv's that are required at the minimum and maximum flow
conditions according to the guidelines in Section 6.2.2 of
SAES-J-700 (refer to the table in part 2 of Work Aid 1A).
Record the valve size as requested 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 at which 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, and press 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 in step b., the degrees of rotation at
which the required Cv is obtained will be different and the
value of FL may have also changed; therefore, steps b. and
c. must be repeated. If the Cv's that were calculated in steps
b. and c. are the same (or nearly the same), record the
information that is requested on the Exercise Sheet, and
proceed to the next step.
e. Select the normal flow condition and note the value of the
calculated Cv. Perform steps 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 Exercise Sheet.
h. If it is necessary to review the calculated results, press F9.


CONTROL VALVES FOR GAS AND STEAM
APPLICATIONS
Work Aid 3A: Procedures that are Used to Computer Size Control
Valves for Ideal Gasses 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.
d. From the menu that appears, select the Valve Sizing and LpA
option.
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, Z cannot 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 Real Gasses 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.
c. From the menu that appears, select the Valve Sizing and LpA
option.
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 Vapors with the ISA Method
Perform the following procedures to complete Exercise 3C:
b. From the menu that appears, select the ISA Vapor method.
option.
d. Ensure that the engineering units on the calculation screen
match the units that are used to describe the service
conditions. If the units do not match for any field, move the
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 Steam with the ISA Method
Perform the following procedures to complete Exercise 3D:
b. From the menu that appears, select the ISA Vapor method.
option.
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 are used to describe the service
conditions. If the units do not match for any field, move the
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 the steam.
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 Ideal Gasses 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.
d. From the menu that appears, select the Valve Sizing and
LpA option.
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 that are used to describe the
service conditions. If the units do not match for any field,
move the cursor to that field, press the F8 key, and select
the desired units.
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

b. From the menu that appears, select the Fisher Real Gas
method.
LpA option.
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 Real Gasses with the Fisher Method
Perform the following procedures to complete Exercise 3F:
method.
LpA option.
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.

Valves for Vapors with 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.
LpA option.
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 Steam with 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.
LpA option.
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.
LpA option.
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 on Valve 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.
LpA option.
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 that appears, select N-Butane.
f. Enter the service conditions and the value of C1.
method.
LpA option.
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.
LpA option.
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 Flow Conditions
Setup
a. Press ESCAPE until the valve sizing method menu appears.
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 options are set to Input Z, Omit FP and xTP,
LpA (SPL) OFF, and Warnings OFF. Note that the FP option 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 the screen 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 for which 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 the desired option, and press ENTER. After the units for
the appropriate parameters have been selected, press
ESCAPE.
Initial Sizing
a. Select the MIN (minimum) condition and enter the required
sizing inputs. Assume ideal 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 the selected 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 information from the minimum flow calculation
screen to the normal flow calculation screen. Press ENTER.
e. Change the pressure and the flow conditions to the values
that are included in the application 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 information from 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 the application 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 maximum flow
condition. Ensure that you observe the percentage of travel
guidelines that are included in Section 6.2.2 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 and LpA calculations are selected.
b. Press F3 and select the Calculate FP option. (Note that
selecting an option from this screen invokes the option for all
calculation screens (MIN, NRM, and MAX); selecting an
option from a particular sizing screen invokes the option for
that specific condition 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 piping factors. Refer to the appropriate Catalog
12 page, and compare the corrected Cv's that are displayed
on the screen to the Cv's that are published for the initially
selected valve. Ensure that the initially selected valve has
adequate capacity and that it conforms to the guidelines in
Section 6.2.2 of SAES-J-700 (refer to the table in part 2 of
Work 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 which the Cv requirement will be met.

c. Extrapolate a value of xT for the percent travel that was

estimated in step b. Enter the extrapolated value of XT in the
appropriate field on the sizing screen, and press F2 to
calculate the sizing information.
d. If the Cv that was calculated in step c. is different than the
Cv that was calculated in step b., the percent of travel at
which the required Cv is obtained will be different and the
value of XT may have also changed; therefore, steps b. and
c. must be repeated. If the 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. Perform steps 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 DATA ON 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 the appropriate units
of measurement (mm or inches).

GLOSSARY
g1 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 low recovery valve types.
C2 Term that is used in the Fisher Gas Sizing Equation to
account for the ratio of specific heats. C2 serves the same
function as Fk in 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
collapse in 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
fluid density 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
compacts molecules of the flowing gas.
critical flow Condition when gas flow is at sonic velocity and further
reductions in downstream pressure produce no increase in
flow rate.
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-vapor
transition.

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 term is used in conjunction with the Fisher Controls
nomograph that is 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 terms
of 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 the
direction 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
does not recover to a pressure above its vapor pressure.
Flashing commonly produces, in control valve components,
damage that has the appearance of erosion damage
(smooth, polished cavities on the affected components).

flow characteristic Relationship between flow through the valve and percent of
rated travel as the latter is varied from 0 to 100 percent. This
term is a special term. It should always be designated as
either inherent flow characteristic or installed flow
characteristic. Common flow characteristics are linear, equal
percentage, and quick opening.
flow coefficient (Cv) The number of U.S. gallons per minute of 60 degree F water
that will flow through a valve with a pressure drop of one
pound per square inch.
flow rate The amount (mass, weight, or volume) of fluid flowing
through a 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
is determined 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 Program
G 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
degrees F (15.6 degrees C).
Gg Gas specific gravity; ratio of density of gas at flowing
conditions to density of air at reference conditions; ratio of
molecular weight of a gas to molecular weight of air;
dimensionless.

high-recovery valve a valve design that dissipates relatively little flow-stream

energy because of streamlined internal contours and
minimal flow turbulence. Valves, such as rotary-shaft ball
and butterfly valves, are typically high-recovery valves. In
these designs, the pressure dip at the vena contracta is
larger than in low-recovery valves.
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,
while drag forces result in reduced velocity nearer the pipe
wall. Laminar flow is also referred to as viscous flow. The
term viscous flow is somewhat of a misnomer because
effects other than fluid viscosity can cause laminar flow.
low-recovery valve a valve design that dissipates a considerable amount of
flowstream energy because of turbulence created by the
contours of the flowpath. Globe valves are typical. In these
designs, the pressure dip at the vena contracta is not as
great as in 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.
Represented in the ISA equations with term FP.
pr The reduced pressure, determined by dividing the actual
pressure 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
compressibility factor, 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
that the control valve must be able to withstand.
pressure drop ratio Ratio of inlet pressure P1 to pressure drop across the valve.
pressure drop ratio The limiting value of x that is used in the ISA sizing
factor equations. Referred to with xT (t stands for terminal). The
value of xT is related to valve style and geometry. It is
determined by test and published with other valve sizing
information.
pressure drop, The pressure drop at which choked flow limits flow to Qmax.
allowable This term is used by Fisher Controls and others. It is
equivalent to the term "choked pressure drop" that is used in
the ISA equations.
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 the
term "allowable pressure drop" that is used by Fisher and
others.
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 rate
R 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 heat The factor that is used in the ISA gas sizing equations to
factor account for thermodynamic fluid behavior. It is represented
by Fk. Fk is equal to the ratio of the specific heat for the
flowing gas 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

represent the critical pressure ratio. The term rc is
equivalent to the term FF in the ISA sizing equations. The
critical pressure ratio and the fluid vapor pressure (Pv) are
used to estimate the fluid pressure at the vena contracta
according to: Pvc = rc Pv.
real gas a gas for which deviations form the ideal gas law are taken
into account.
SG specific gravity
sonic 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
SG and M.
specific heat ratio Represented with the term k. The ratio of the amount of heat
that is required to raise a mass of material 1 degree in
temperature to the amount of heat that is required to raise
an equal mass of a reference substance (usually water) 1
degree in temperature. Both measurements are made at a
specific temperature and at constant volume or pressure.
swage a piping expander or reducer that allows the installation of a
control valve in a pipeline whose diameter is greater than
the diameter 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
that provides the maximum Cv requirement.
Tr The reduced temperature, determined by dividing the actual
temperature of the fluid by the fluid's critical temperature.
The value of Tr and the value of Pr (the reduced pressure)
may be used to determine the value of the compressibility
factor, Z.
transitional flow a flow regime with characteristics of both laminar and
turbulent flow.
travel The amount of movement (linear or rotational) of the valve
closure member between the closed and open positions,
generally expressed in degrees of rotation for rotary-shaft
valves and in percent of travel for sliding-stem valves.

turbulent flow a flow regime characterized by turbulent eddies that occur

randomly in the fluid stream. Fluid velocity at the center of
the pipe and the velocity near the pipe wall are nearly equal.
vena contracta The location where cross-sectional area of the flowstream is
at its minimum size, where fluid velocity is at its highest
level, and fluid pressure is at its lowest level. (The vena
contracta normally occurs just downstream of the actual
physical restriction in a control valve.)
w Mass flow rate (lbs/hr, kg/s, etc.)
x Pressure drop ratio ( ∆P / p1 ); 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.
x
Y Expansion factor Y = 1− , where Fk = ratio of specific
3Fk x T
heats.
Z Compressibility factor; dimensionless.

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