# Valve Sizing for Liquid

## formula

### flow rate

\(Q = C_v \sqrt {\frac {\Delta p} {SG} }\)

Where:

\(Q\) = flow rate capacity, gpm

\(C_v\) = flow coefficient

\(\Delta p\) = pressure differential, psi

\(SG\) = specific gravity of fluid (water at 60°F = 1.0000)

### flow coefficient

\(C_v = Q \sqrt {\frac{SG} {\Delta p} }\)

Where:

\(C_v\) = flow coefficient

\(Q\) = flow rate capacity, gpm

\(SG\) = specific gravity of fluid (water at 60°F = 1.0000)

\(\Delta p\) = pressure differential, psi

### actual required cv

\(C_{vr} = K_v C_{v} \)

Where:

\(C_{vr}\) = corrected sizing coefficient required for viscous applications

\(K_v\) = viscosity correction factor

\(C_v\) = flow coefficient

### maximum flow rate assuming no viscosity correction

\(Q_{m} = C_{vr} \sqrt{ \frac {\Delta p}{SG } } \)

Where:

\(Q_{m}\) = maximum flow rate, assuming no viscosity correction required, gpm

\(C_{vr}\) = corrected sizing coefficient required for viscous applications

\(\Delta p\) = pressure differential, psi

\(SG\) = specific gravity of fluid (water at 60°F = 1.0000)

### predict actual flow rate

\(Q_{p} = \frac {Q_m}{K_v } \)

Where:

\(Q_{p}\) = predicted flow rate after incorporating viscosity correction, gpm

\(Q_{m}\) = maximum flow rate, assuming no viscosity correction required, gpm

\(K_{v}\) = viscosity correction factor

### corrected size coefficient

\(C_{vc} = \frac {C_{vr}} {K_v} \)

Where:

\(C_{vc}\) = Cv flow coefficient including correction for viscosity

\(C_{vr}\) = corrected sizing coefficient required for viscous applications

\(K_v\) = viscosity correction factor

### predicted pressure drop

\(\Delta p_p = SG \left( \frac {Q} {C_{vc} } \right)^2 \)

Where:

\(\Delta p_p \) = predict pressure differential drop for viscous liquids

\(SG\) = specific gravity of fluid (water at 60°F = 1.0000

\(Q\) = flow rate capacity, gpm

\(C_{vc}\) = Cv flow coefficient including correction for viscosity

### maximum allowable pressure drop

\(\Delta p_a = K_m \left( p_i \;-\; r_c p_v \right) \)

Where:

\(\Delta p_a \) = maximum allowable pressure differential for sizing purposes, psi

\(K_m\) = valve recovery coefficient from manufacturer’s literature

\(p_i\) = body inlet pressure, psia

\(r_c\) = critical pressure ratio

\(p_v\) = vapor pressure of liquid at body inlet temperature, psia

### pressure drop at which cavitation damage will begin

\(\Delta p_c = Ca \left( p_i \;-\; p_v \right) \)

Where:

\(\Delta p_c \) = pressure differential drop at which cavitation damage will begin, psi

\(Ca \) = dimensionless Cavitation Number index used in determining \(\;\Delta p_c \)

\(p_i\) = body inlet pressure, psia

\(p_v\) = vapor pressure of liquid at body inlet temperature, psia