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Question

A cylindrical vessel with a cross sectional area A has a small hole of area a at the bottom. A liquid is filled in the vessel upto a height H. Find the time taken to empty the tank.


A
t=aA2Hg
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B
A2Hg
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C
Aa2Hg
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D
AaHg
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Solution

The correct option is C Aa2Hg

Let at any time t, the height of the liquid be y, and in (t+dt) time, the level of the liquid will be (ydy).

As per equation of continuity,
A1v1=A2v2
a2gy=A(dydt)
where, dydt is the rate of decrease in the level of liquid.
y=0y=Hdyy=aA2gt=Tt=0dt
[2y]0H=aA2g[t]T0
T=Aa2Hg is the time taken to empty the tank.
Thus, option (c) is the correct answer.

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