# Discharge Coefficient

## Description

In a nozzle or other constriction, the discharge coefficient (also known as coefficient of discharge) is the ratio of the actual discharge to the theoretical discharge, i.e., the ratio of the mass flow rate at the discharge end of the nozzle to that of an ideal nozzle which expands an identical working fluid from the same initial conditions to the same exit pressures.

Mathematically the discharge coefficient may be related to the mass flow rate of a fluid through a straight tube of constant cross-sectional area through the equation shown here.

This parameter is useful for determining the irrecoverable losses associated with a certain piece of equipment (constriction) in a fluid system, or the “resistance” that piece of equipment imposes upon the flow.

Related formulas## Variables

C_{d} | discharge coefficient through the constriction (dimensionless) |

ṁ | mass flow rate of fluid through constriction (kg/s) |

A | cross-sectional area of flow constriction (m^{2}) |

ρ | density of fluid (kg/m^{3}) |

Δ_{P} | pressure drop across constriction (N/m^{2}) |