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