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A square hole of side length l  is made at a depth of y  and a circular hole s made at a depth of 4y  from the surface of water tank, kept on a horizontal surface. If equal amount of water comes out of the vessel through the holes per second. Then the radius of circular hole is equal to (r,l<

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a

l2

b

l2

c

lπ

d

l2π

answer is D.

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Detailed Solution

Equation of continuity at 1 and 2,r1=A1v1and r2=A2v2it is given thatr1=r2(r= rate of flow of liquid through the holes).∴  A1v1=A2v2Where the velocities of efflux are,v1=2gy  and v2=2g(4y)And areas of cross-section of the holes are,A1=l2  and A2=πR2Putting all the values, we obtain,l2(2gy)={2g(4y)}πR2∴  R=l/2π
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A square hole of side length l  is made at a depth of y  and a circular hole s made at a depth of 4y  from the surface of water tank, kept on a horizontal surface. If equal amount of water comes out of the vessel through the holes per second. Then the radius of circular hole is equal to (r,l<