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 following equation:
Where:
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.
This flow resistance, often expressed as a unit-less parameter,
which may be obtained by substituting
An example in open channel flow
Due to complex behavior of fluids around some of the structures such as orifices, gates, and weirs etc., some assumptions are made for the theoretical analysis of the stage-discharge relationship. For example, in case of gates, the pressure at the gate opening is non-hydrostatic which is difficult to model; however, it is known that the pressure at the gate is very small. Therefore, engineers assume that the pressure is zero at the gate opening and following equation is obtained for discharge:
where:
Q = Discharge
g = Acceleration due to gravity
However, the pressure is not actually zero at the gate; therefore, discharge coefficient, Cd is used as follows: