Discharge Coefficient

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