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Question

A vessel of area of cross section A has liquid to a height H. There is a hole at the bottom of vessel having area of cross-section a. The time taken to decrease the level from H1 to H2 will be:

A
Aa2g[H1H2]
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B
2gh
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C
2gh(H1H2)
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D
Aag2[H1H2]
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Solution

The correct option is A Aa2g[H1H2]
At height h the rate of discharge of liquid through hole at bottom is 2gh×a (by Bernoulli's principle).
Let in time dt level of water in tank decreases by dh.
Equating volumes, Adh=dt2gh×a
dt=Aa2gdhh
Integrating above we get,
t0dt=Aa2gH1H2dhh
t=Aa2gh1/21/2|H1H2=Aa2/g[H1H2]

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