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

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

Where:

 Units English SI
\(\large{ C_d }\) = 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 \(\large{ dimensionless \; constant }\)
\(\large{ d }\) = 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 \(\large{\frac{ft^3}{sec}}\) \(\large{\frac{m^3}{s}}\)

 

Related Discharge Coefficient formula

\(\large{ C_d =   \frac { Q_o }  { A_o \; \sqrt { 2 \; G \; h }     }   }\) (orifice area) (orifice gravitational constant)

Where:

\(\large{ C_d }\) = discharge coefficient

\(\large{ A_o }\) = orifice area

\(\large{ h }\) = orifice center of head

\(\large{ Q_o }\) = orifice flow rate

\(\large{ G }\) = orifice gravitational constant

 

Tags: Equations for Coefficient Equations for Flow Equations for Orifice and Nozzle