# Water Flow Rate Through a Valve

Written by Jerry Ratzlaff on . Posted in Fluid Dynamics

### Water Flow Rate Through a Valve formula

$$\large{ p_1 - p_2 < F_l^2 \left( p_1 - F_f \; p_{av} \right) \rightarrow }$$

(Eq. 1)  $$\large{ Q_w = C_v \; \sqrt { \frac{ p_1 \;-\; p_2 }{ SG } } }$$

$$\large{ p_1 - p_2 \ge F_l^2 \left( p_1 - F_f \; p_{av} \right) \rightarrow }$$

(Eq. 2)  $$\large{ Q_w = C_v \; F_l \; \sqrt { \frac{ p_1 \;-\; F_f \; p_{av} }{ SG } } }$$

Where:

$$\large{ Q_w }$$ = water flow rate

$$\large{ p_{av} }$$ = absolute vapor pressure of the water at inlet temperature

$$\large{ F_f }$$ = liquid critical pressure ratio factor

$$\large{ p_1 }$$ = primary pressure

$$\large{ F_l }$$ = liquid pressure recovery factor (= 0.9)

$$\large{ p_2 }$$ = secondary pressure

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

$$\large{ SG }$$ = water specific gravity