Cv Flow Coefficients & Valve Sizing

Cv Flow Coefficients & Valve Sizing

The flow coefficient, Cv, is the volume (in gallons) of water at 60° F that will flow per minute through a valve with a pressure drop of 1 psi across the valve. Numerically this definition can be expressed as

Cv = F ÷ √ΔP                                                 

The use of the flow coefficient offers a standard method of comparing valve capacities and sizing valves for specific applications that is widely accepted by industry. The general definition of the flow coefficient can be expanded into equations modeling the flow of liquids, gases and steam as follow

Liquid flow

F = Cv√ΔP ÷ S         Cv = F ÷ √(ΔP ÷ S)               ΔP = S (F ÷ Cv)2            

Gas flow

When the downstream pressure (P₂) is greater than 53% of the inlet pressure (P₁), the following formula apply

F = 1,391 Cv√(P₂ΔP ÷ S T)     Cv = F ÷ 1,391√(P₂ ΔP ÷ S T)       ΔP = ST (F ÷ 1,391 Cv)2 ÷ P₂

When the downstream pressure is equal to or less than *53% of the inlet pressure (P₁), the following formula apply

F = 695.4 Cv P₁ ÷ √(S T)             Cv = F√(S T) ÷ 695.4 P₁        P₁ = F√(S T) ÷ 695.4 Cv

Steam flow

When the downstream pressure (P₂) is greater that 57% of the inlet pressure (P₁), the following formula apply:

F = 3 Cv√(P₂ΔP ÷ X)                 Cv = F ÷ 3√(P₂ΔP ÷ X)                     ΔP = X (F ÷ 3 Cv)2 ÷ P₂

When the downstream pressure (P2) is equal or less than 57% of the inlet pressure (P1), the following formula apply

F = 3 Cv P₁ ÷ 2√(X)            Cv = 2 F√(X) ÷ 3 P₁                   P1 = 2 F√(X) ÷ 3 Cv

Note: Equations are for saturated steam

Definitions

Cv               Flow coefficient or flow capacity rating of valve

F               Rate of flow in USGPM for liquids, SCFH for gases, and lbs/hr for steam.

(T                Absolute temperature in degrees Rankine (°R) (460 + degrees Fahrenheit(°F

S                Specific gravity (relative to air or water

P₁               Inlet pressure, PSIA

P₂               Downstream pressure, PSIA

ΔP              Pressure drop across the valve, PSI

X                Quality of steam in decimal form. i.e. 80% quality = 0.80

USGPM      U.S. gallons per minute

SCFH         Standard cubic feet per hour

PSI             Pounds per square inch

(PSIA          Pounds per square inch absolute (PSIA = PSI + 14.7)

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