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Mechanical Properties Of Fluids

Question
CBSEENPH11018949

A tank is filled with liquid upto height H as shown. There is an orifice at a depth h below the surface of water. Find the horizontal range of water on the ground.


Solution
We have, the escaping liquid analogous to horizontal projectile.
The relation between vertical distance y by which projectile falls and horizontal distance x where it falls is, 
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where,  u is horizontal velocity of projection.
Here,  
Vertical distance, y = (H-h)
Initial velocity,space straight u space equals space square root of 2 gh end root
Horizontal range, x = R = ?
therefore space space space space space space space space left parenthesis straight H minus straight h right parenthesis space equals space 1 half fraction numerator g R squared over denominator 2 g h end fraction

rightwards double arrow space space space space space space space space space straight R squared equals left parenthesis straight H minus straight h right parenthesis left parenthesis 4 straight h right parenthesis

rightwards double arrow space space space space space space space space straight R space equals space 2 square root of left parenthesis straight H minus straight h right parenthesis left parenthesis straight h right parenthesis end root