# Discharge Coefficient

Written by Jerry Ratzlaff on . Posted in Fluid Dynamics

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

## Discharge Coefficient formulas

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

### Where:

$$\large{ C_d }$$ = discharge coefficient

$$\large{ A_c }$$ = area cross-section of flow constriction

$$\large{ \rho }$$  (Greek symbol rho) = density of fluid

$$\large{ \dot m_f }$$ = mass flow rate

$$\large{ \pi }$$ = Pi

$$\large{ d }$$ = pipe inside diameter

$$\large{ \Delta p }$$ = pressure drop across constriction

$$\large{ Q }$$ = volumetric flow rate