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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