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
The depth of centre of pressure (h) for a vertically immersed surface from the liquid surface is given by (where IG = Moment of inertia of the immersed surface about horizontal axis through its centre of gravity, A = Area of immersed surface, and x = Depth of centre of gravity of the immersed surface from the liquid surface)

(IG/x̅) - Ax̅
(IG/Ax̅) - x̅
(IG/Ax̅) + x̅
(Ax̅/IG) + x̅

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Hydraulics and Fluid Mechanics in ME
A tank of uniform cross-sectional area (A) containing liquid upto height (H1) has an orifice of cross-sectional area (a) at its bottom. The time required to bring the liquid level from H1 to H2 will be

2A × (√H₁ - √H₂)/Cd × a × √(2g)
2A × √H₂/Cd × a × √(2g)
2A × (√H3/2 - √H3/2)/Cd × a × √(2g)
2A × √H₁/Cd × a × √(2g)

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