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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 flow coefficient of a device is a relative measure of its efficiency at allowing fluid flow. It describes the relationship between the pressure drop across an orifice valve or other assembly and the corresponding flow rate. Mathematically the flow coefficient C v (or flow-capacity rating of valve) can be expressed as
Roark's Formulas for Stress and Strain is a mechanical engineering design book written by Richard G. Budynas and Ali M. Sadegh. It was first published in 1938 and the most current ninth edition was published in March 2020.
The proportionality coefficient is the dimensionless "Darcy friction factor" or "flow coefficient". This dimensionless coefficient will be a combination of geometric factors such as π , the Reynolds number and (outside the laminar regime) the relative roughness of the pipe (the ratio of the roughness height to the hydraulic diameter ).
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.
ξ is an empirical loss coefficient, which is dimensionless and has a value between zero and one, 0 ≤ ξ ≤ 1, ρ is the fluid density, v 1 and v 2 are the mean flow velocities before and after the expansion. In case of an abrupt and wide expansion, the loss coefficient is equal to one. [1]
Churchill equation [24] (1977) is the only equation that can be evaluated for very slow flow (Reynolds number < 1), but the Cheng (2008), [25] and Bellos et al. (2018) [8] equations also return an approximately correct value for friction factor in the laminar flow region (Reynolds number < 2300). All of the others are for transitional and ...
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