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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.
In fluid dynamics, the Reynolds number (Re) is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between inertial and viscous forces. [2] At low Reynolds numbers, flows tend to be dominated by laminar (sheet-like) flow , while at high Reynolds numbers, flows tend to be turbulent .
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.
Now to use the eq.(4), the flow field entering the orifice plate must be free of swirl and exhibit a fully developed flow profile. API 14.3 (1990) and ISO standards determined the Coefficient of Discharge by completing numerous calibration tests where the indicated mass flow was compared to the actual mass flow to determine coefficient of ...
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 coefficient of discharge of Venturi meter ranges from 0.93 to 0.97. The first large-scale Venturi meters to measure liquid flows were developed by Clemens Herschel, who used them to measure small and large flows of water and wastewater beginning at the very end of the 19th century. [6]
Increased viscosity lowers this drain rate; this is reflected in the discharge coefficient, which is a function of the Reynolds number and the shape of the orifice. [ 25 ] The Bernoulli grip relies on this principle to create a non-contact adhesive force between a surface and the gripper.
Note: the Strickler coefficient is the reciprocal of Manning coefficient: Ks =1/ n, having dimension of L 1/3 /T and units of m 1/3 /s; it varies from 20 m 1/3 /s (rough stone and rough surface) to 80 m 1/3 /s (smooth concrete and cast iron). The discharge formula, Q = A V, can be used to rewrite Gauckler–Manning's equation by substitution for V.