# Valve Sizing for Liquid

Written by Jerry Ratzlaff on . Posted in Valve

## Valve Sizing for Liquid

### flow rate Formula

$$Q = C_v \sqrt {\frac {\Delta p} {SG} }$$

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 Formula

$$C_v = Q \sqrt {\frac{SG} {\Delta p} }$$

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 Formula

$$C_{vr} = K_v C_{v}$$

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 Formula

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

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 Formula

$$Q_{p} = \frac {Q_m}{K_v }$$

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 Formula

$$C_{vc} = \frac {C_{vr}} {K_v}$$

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 Formula

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

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 Formula

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

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 Formula

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

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