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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.
where the pressure loss per unit length Δp / L (SI units: Pa/m) is a function of: ρ {\displaystyle \rho } , the density of the fluid (kg/m 3 ); D H {\displaystyle D_{H}} , the hydraulic diameter of the pipe (for a pipe of circular section, this equals D ; otherwise D H = 4A/P for a pipe of cross-sectional area A and perimeter P ) (m);
f = 64/Re for laminar flow where Re is the Reynolds number. The frictional resistance, = using Poiseuille's law. Since they have same diameter and length in Fig. 3, their resistances are same, R 2 = R 3. Thus the velocities should be equal in two outlets or the flow rates should be equal according to the assumptions.
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 discharge. In all testing the common requirement was a fully developed flow profile entering the orifice plate. [8]
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.
Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena. [1] They include the Reynolds and the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed.
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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.