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Physics

Fluid-Mechanics

Easy

Question

A cylinder containing water up to a height of h cm has a hole of cross-section area a cm² at its bottom. It is counterpoised in a balance. When water just begins to flow out, the initial change in weight is

$2 gha$
$\sqrt{2 g h a}$
$\sqrt{g h a}$
None

The correct answer is: $2 text gha end text$

Let y be the initial velocity of efflux of water.
Initial volume of water flowing out per sec = av
Initial mass of water flowing out per sec $equals a v d equals a v cross times 1 equals a v$
Rate of change of momentum $equals left parenthesis a v right parenthesis v equals a v squared$
Initial downward force on the outflowing water =av²
Reaction acts upwards on the cylinder
Initial upward reaction = av²
Now $v equals square root of 2 g h end root$
Initial decrease in weight $equals a cross times 2 g h equals 2 g h a$

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