Hydraulics and Fluid Mechanics in ME
The discharge through a large rectangular orifice is given by (where H1 = Height of the liquid above the top of the orifice, H2 = Height of the liquid above the bottom of the orifice, b = Breadth of the orifice, and Cd = Coefficient of discharge)

Q = (2/3) Cd × b × √(2g) × (H21/2 - H11/2)
Q = (2/3) Cd × b × √(2g) × (H23/2 - H13/2)
Q = (2/3) Cd × b × √(2g) × (H2 - H1)
Q = (2/3) Cd × b × √(2g) × (H22 - H12)

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Hydraulics and Fluid Mechanics in ME
For similarity, in addition to models being geometrically similar to prototype, the following in both cases should also be equal

ratio of inertial force to force due to viscosity
ratio of inertial force to force due to gravitation
ratio of inertial force to force due to surface tension
all the four ratios of inertial force to force due to viscosity, gravitation, surface tension, and elasticity

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Hydraulics and Fluid Mechanics in ME
Mach number is significant in

full immersion or completely enclosed flow, as with pipes, aircraft wings, nozzles etc
all of fhe above
supersonics, as with projectiles and jet propulsion
simultaneous motion through two fluids where there is a surface of dis-continuity, gravity force, and wave making effects, as with ship’s hulls

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