# 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 formula

$$\large{ C_d = \frac { \dot m_f } { \rho \; Q } }$$
Symbol English Metric
$$\large{ C_d }$$ = discharge coefficient $$\large{ dimensionless }$$
$$\large{ \rho }$$  (Greek symbol rho) = density of fluid $$\large{\frac{lbm}{ft^3}}$$ $$\large{\frac{kg}{m^3}}$$
$$\large{ \dot m_f }$$ = mass flow rate $$\large{\frac{lbm}{sec}}$$ $$\large{\frac{kg}{s}}$$
$$\large{ Q }$$ = volumetric flow rate $$\large{\frac{ft^3}{sec}}$$ $$\large{\frac{m^3}{s}}$$