# Discharge Coefficient

Written by Jerry Ratzlaff on . Posted in Fluid Dynamics

Discharge coefficient, abbreviated as $$C_d$$, also called coefficient of discharge, a dimensionless number, is the ratio of actual discharge to the theoretical discharge.

## Discharge Coefficient formulas

$$\large{ C_d = \frac { \dot m_f } { \rho \; Q } }$$

$$\large{ C_d = \frac { \dot m_f } { A_c \; \sqrt { 2 \; \frac{ \Delta p}{ \rho} } } }$$

$$\large{ C_d = \frac { \dot m_f } { d^2 \; \frac {\pi}{4} \sqrt { 2 \; \frac{ \Delta p}{ \rho} } } }$$

$$\large{ C_d = \frac { \dot m_f } { A_c \; \sqrt { 2 \; \rho \; \Delta p } } }$$

$$\large{ C_d = \frac { \dot m_f } { d^2 \; \frac {\pi}{4} \sqrt { 2 \; \rho \; \Delta p } } }$$

Symbol English Metric
$$\large{ C_d }$$ = discharge coefficient $$\large{ dimensionless }$$
$$\large{ A_c }$$ = area cross-section of flow constriction $$\large{ ft^2 }$$ $$\large{ m^2 }$$
$$\large{ \rho }$$  (Greek symbol rho) = density of fluid $$\large{\frac{lbm}{ft^3}}$$ $$\large{\frac{kg}{m^3}}$$
$$\large{ \dot m_f }$$ = mass flow rate $$\large{\frac{lbm}{sec}}$$ $$\large{\frac{kg}{s}}$$
$$\large{ \pi }$$ = Pi $$\large{3.141 592 653 589 793...}$$
$$\large{ d }$$ = pipe inside diameter $$\large{ in }$$ $$\large{ mm }$$
$$\large{ \Delta p }$$ = pressure drop across constriction $$\large{\frac{lbf}{in^2}}$$ $$\large{Pa}$$
$$\large{ Q }$$ = volumetric flow rate $$\large{\frac{ft^3}{sec}}$$ $$\large{\frac{m^3}{s}}$$