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Q.

A large open tank has two holes in the wall. One is a square hole of side L at a depth y from the top and the other is a circular hole of radius R at a depth 4y from the top. When the tank is completely filled with water, the quantities of water flowing out per second from both the holes are the same. Then R is equal to

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a

2πL

b

L2π

c

L

d

L2π

answer is B.

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Detailed Solution

Velocity of efflux when the hole is at depth h,v=2ghRate of flow of water from square holeQ1=a1v1=L22gyRate of flow of water from circular holeQ2=a2v2=πR22g(4y)According to problem, Q1 = Q2⇒L22gy=πR22g(4y)⇒R=L2π

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