Hydraulics and Fluid Mechanics in ME
When a body is placed over a liquid, it will sink down if

Gravitational force is less than the up-thrust of the liquid
None of these
Gravitational force is equal to the up-thrust of the liquid
Gravitational force is more than the up-thrust of the liquid

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

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Hydraulics and Fluid Mechanics in ME
The discharge through a channel of trapezoidal section is maximum when

The sloping side is equal to half the width at the top
Width of channel at the top is equal to twice the width at the bottom
The sloping side is equal to the width at the bottom
Depth of channel is equal to the width at the bottom

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