# Water Flow Rate Through a Valve

Written by Jerry Ratzlaff on . Posted in Fluid Dynamics

## Water Flow Rate Through a Valve formulas

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

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

Symbol English Metric
$$\large{ Q_w }$$ = water flow rate $$\large{\frac{ft^3}{sec}}$$ $$\large{\frac{m^3}{s}}$$
$$\large{ p_{av} }$$ = absolute vapor pressure of the water at inlet temperature $$\large{\frac{lbf}{in^2}}$$ $$\large{\frac{kg}{m-s^2}}$$
$$\large{ F_f }$$ = liquid critical pressure ratio factor $$\large{dimensionless}$$
$$\large{ p_1 }$$ = primary pressure $$\large{\frac{lbf}{in^2}}$$ $$\large{Pa}$$
$$\large{ p_2 }$$ = secondary pressure $$\large{\frac{lbf}{in^2}}$$ $$\large{Pa}$$
$$\large{ F_l }$$ = id pressure recovery factor (= 0.9) $$\large{dimensionless}$$
$$\large{ C_v }$$ = valve flow coefficient $$\large{dimensionless}$$
$$\large{ SG }$$ = specific gravity of water $$\large{dimensionless}$$ 