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Question

The area of two holes A and B are 2a and a respectively. The holes are at depths H3 and 2H3 from the surface of water. Find the correct option(s) -


A
The velocity of efflux at hole B is 2 times the velocity of efflux at hole A
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B
The velocity of efflux at hole B is 2 times the velocity of efflux at hole A
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C
The discharge is same through both the holes
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D
The discharge through hole A is 2 times the discharge through hole B
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Solution

The correct option is D The discharge through hole A is 2 times the discharge through hole B
Given,
Area of hole A, AA= 2a
Area of hole B, AB= a


Velocity of efflux -
For hole A :
vA=2g×H3 ......(1)
[ v=2gh ]
For hole B :
vB=2g×2H3 ......(2)
From (1) and (2),
vB=2vA .......(3)

Discharge of efflux -
For hole A :
QA=2a×vA ......(4)
[ Q=Av ]
For hole B:
QB=a×vB=a×2vA ......(5)
[ from (3) ]
From (4) and (5),
QA=2QB
Hence, option B and D are correct.

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