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 \(\large{\frac{ft^3}{sec}}\) \(\large{\frac{m^3}{s}}\)

 

P D Logo 1

Tags: Coefficient Equations Flow Equations Orifice and Nozzle Equations