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Question

A container has a small hole at its bottom. Area of cross-section of the hole is A1 and that of the container is A2. Liquid is poured into the container at a constant rate of Q m3/s. The maximum level of liquid in the container will be -

A
Q22g A1A2
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B
Q22g A21
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C
Q2g A1A2
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D
Q22g A22
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Solution

The correct option is B Q22g A21
Given,
Rate of inflow, Qin=Q m3/s ........(1)
According to question -


We know that, level in the container is maximum when rate of inflow = rate of outflow.
Rate of outflow, Qout=Av ........(2)
where A is the area of the hole and v is the velocity of efflux.
From (1) and (2) -
A1v=Q [ A=A1, given ]
A12gh=Q
h=Q22gA21

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