# Water Flow Rate Through a Valve

on . Posted in Fluid Dynamics

### Water Flow Rate Through a Valve formula

$$Q_w \;=\; C_v \; \sqrt { p_1 - p_2 \;/\; SG }$$     (Water Flow Rate through a Valve)

$$C_v \;=\; Q_w \; \sqrt{ SG } \;/\; \sqrt{ p_1 - p_2 }$$

$$p_1 \;=\; ( Q_w^2 \; SG \;/\; C_v^2 ) + p_2$$

$$p_2 \;=\; p_1 - ( Q_w^2 \; SG \;/\; C_v^2 )$$

$$SG \;=\; C_v^2 \; ( p_1 - p_2 ) \;/\; Q_w^2$$

Symbol English Metric
$$Q_w$$ = water flow rate $$ft^3\;/\;sec$$ $$m^3\;/\;s$$
$$C_v$$ = valve flow coefficient $$dimensionless$$ $$dimensionless$$
$$p_1$$ = primary pressure $$lbf\;/\;in^2$$ $$Pa$$
$$p_2$$ = secondary pressure $$lbf\;/\;in^2$$ $$Pa$$
$$SG$$  = water specific gravity $$dimensionless$$ $$dimensionless$$

### Water Flow Rate Through a Valve formula

$$Q_w \;=\; C_v \; F_l \; \sqrt { p_1 - F_f \; p_{av} \;/\; SG }$$     (Water Flow Rate through a Valve)

$$C_v \;=\; \sqrt{ SG \; ( Q_w \;/\; F_l )^2 \;/\; p_1 - ( F_f \; p_{av} ) }$$

$$F_l \;=\; \sqrt{ SG \; ( Q_w \;/\; C_v )^2 \;/\; p_1 - ( F_f \; p_{av} ) }$$

$$p_1 \;=\; SG \; ( Q_w \;/\; C_v \; F_l )^2 + ( F_f \; p_{av} )$$

$$F_f \;=\; p_1 - ( SG \; ( Q_w \;/\; C_v \; F_l )^2 ) \;/\; p_{av}$$

$$p_{av} \;=\; p_1 - ( SG \; ( Q_w \;/\; C_v \; F_l )^2 ) \;/\; F_f$$

$$SG \;=\; p_1 - ( F_l \; p_{av} ) \;/\; ( Q_w \;/\; C_v \; F_l )^2$$

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