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In a nozzle or other constriction, the discharge coefficient (also known as coefficient of discharge or efflux coefficient) is the ratio of the actual discharge to the ideal discharge, [1] 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.
Orifice plate showing vena contracta. An orifice plate is a thin plate with a hole in it, which is usually placed in a pipe. When a fluid (whether liquid or gaseous) passes through the orifice, its pressure builds up slightly upstream of the orifice [1] but as the fluid is forced to converge to pass through the hole, the velocity increases and the fluid pressure decreases.
The general definition of the flow coefficient can be expanded into equations modeling the flow of liquids, gases and steam using the discharge coefficient. For gas flow in a pneumatic system the C v for the same assembly can be used with a more complex equation.
For low viscosity liquids (such as water) flowing out of a round hole in a tank, the discharge coefficient is in the order of 0.65. [4] By discharging through a round tube or hose, the coefficient of discharge can be increased to over 0.9. For rectangular openings, the discharge coefficient can be up to 0.67, depending on the height-width ratio.
The fundamental difference between the orifice meter and the turbine meter is the flow equation derivation. The orifice meter flow calculation is based on fluid flow fundamentals (a 1st Law of Thermodynamics derivation utilizing the pipe diameter and vena contracta diameters for the continuity equation). Deviations from theoretical expectation ...
The choked velocity is a function of the upstream pressure but not the downstream. Although the velocity is constant, the mass flow rate is dependent on the density of the upstream gas, which is a function of the upstream pressure. Flow velocity reaches the speed of sound in the orifice, and it may be termed a sonic orifice.
If G represents stage for discharge Q, then the relationship between G and Q can possibly be approximated with an equation: Q = C r ( G − a ) β {\displaystyle Q=C_{r}(G-a)^{\beta }} where C r {\displaystyle C_{r}} and β {\displaystyle \beta } are rating curve constants, and a {\displaystyle a} is a constant which represents the gauge ...
The orifice plate formula in this article is an adaptation of the formula for a Venturi meter, where a pressure tap does exist in a plane of maximum fluid velocity. The formula below the line "Solving for Q:" in this article is the same as the last formula in this section: Venturi effect#Flow_rate .