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Question

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 the two holes are the same. Then value of R is:

A
L2π
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B
2πL
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C
L2π
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D
L2π
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Solution

The correct option is A L2π
By principle if continuity: A1v1=A2v2
As per quesiton: A1=L2;v1=2gy and
A2=πR2, v2=2g4y
So,
L22gy=πR22g4y
L2=2πR2
R=L2π

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