# Valve Sizing for Liquid

Written by Jerry Ratzlaff on . Posted in Valve

## flow rate Formula

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

### Where:

$$\large{ Q}$$ = flow rate capacity, gpm

$$\large{ C_v}$$ = flow coefficient

$$\large{ \Delta p}$$ = pressure differential, psi

$$\large{ SG}$$ = specific gravity of fluid (water at 60°F = 1.0000)

## flow coefficient Formula

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

### Where:

$$\large{ C_v}$$ = flow coefficient

$$\large{ Q}$$ = flow rate capacity, gpm

$$\large{ SG}$$ = specific gravity of fluid (water at 60°F = 1.0000)

$$\large{ \Delta p}$$ = pressure differential, psi

## actual required cv Formula

 $$\large{ C_{vr} = K_v \;C_{v} }$$

### Where:

$$\large{ C_{vr}}$$ = corrected sizing coefficient required for viscous applications

$$\large{ K_v}$$ = viscosity correction factor

$$\large{ C_v}$$ = flow coefficient

## maximum flow rate assuming no viscosity correction Formula

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

### Where:

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

$$\large{ C_{vr}}$$ = corrected sizing coefficient required for viscous applications

$$\large{ \Delta p}$$ = pressure differential, psi

$$\large{ SG}$$ = specific gravity of fluid (water at 60°F = 1.0000)

## predict actual flow rate Formula

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

### Where:

$$\large{ Q_{p}}$$ = predicted flow rate after incorporating viscosity correction, gpm

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

$$\large{ K_{v}}$$ = viscosity correction factor

## corrected size coefficient Formula

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

### Where:

$$\large{ C_{vc}}$$ = Cv flow coefficient including correction for viscosity

$$\large{ C_{vr}}$$ = corrected sizing coefficient required for viscous applications

$$\large{ K_v}$$ = viscosity correction factor

## predicted pressure drop Formula

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

### Where:

$$\large{ \Delta p_p }$$ = predict pressure differential drop for viscous liquids

$$\large{ SG}$$ = specific gravity of fluid (water at 60°F = 1.0000

$$\large{ Q}$$ = flow rate capacity, gpm

$$\large{ C_{vc}}$$ = Cv flow coefficient including correction for viscosity

## maximum allowable pressure drop Formula

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

### Where:

$$\large{ \Delta p_a }$$ = maximum allowable pressure differential for sizing purposes, psi

$$\large{ K_m}$$ = valve recovery coefficient from manufacturer’s literature

$$\large{ p_i}$$ = body inlet pressure, psia

$$\large{ r_c}$$ = critical pressure ratio

$$\large{ p_v}$$ = vapor pressure of liquid at body inlet temperature, psia

## pressure drop at which cavitation damage will begin Formula

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

### Where:

$$\large{ \Delta p_c }$$ = pressure differential drop at which cavitation damage will begin, psi

$$\large{ Ca }$$ = dimensionless Cavitation Number index used in determining $$\;\Delta p_c$$

$$\large{ p_i}$$ = body inlet pressure, psia

$$\large{ p_v}$$ = vapor pressure of liquid at body inlet temperature, psia