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

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a

L2π

b

2πL

c

L2π

d

L2π

answer is A.

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Detailed Solution

By the principle of continuity A1v1=A2v2 According to question, A1=L2v1=2gy and A2=πR2&v2=2g4y∴L22gy=πR22g4y or L2=2πR2 or R=L2π
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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