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.