Discharge coefficient


In a nozzle or other constriction, the discharge coefficient 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
Where:
This parameter is useful for determining the irrecoverable losses associated with a certain piece of equipment in a fluid system, or the "resistance" that piece of equipment imposes upon the flow.
This flow resistance, often expressed as a dimensionless parameter,, is related to the discharge coefficient through the equation:
which may be obtained by substituting in the aforementioned equation with the resistance,, multiplied by the dynamic pressure of the fluid,.

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:
However, the pressure is not actually zero at the gate; therefore, discharge coefficient, C is used as follows: