A large open tank has two small holes in its vertical wall as shown in figure. One is a square hole of side 'L' at a depth '4y' from the top and the other is a circular hole of radius 'R' at a depth 'y' from the top. When the tank is completely filled with water, the quantities of water flowing out per second from both holes are the same. Then, 'R' is equal to:
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a
L2π
b
2πL
c
2π L
d
L2π
answer is C.
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Detailed Solution
Let v1 and v2 be the velocity of efflux from square and circular hole respectively. S1 and S2 be cross-section areas of square and circular holes.v1 = 8gy and v2 = 2g(y)The volume of water coming out of square and circular hole per second isQ1 = v1S1 = 8gyL2; Q2 = v2S2=2gy πR2 Solve Q1=Q2∴ R = 2π. L