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 both holes are the same. Then, R is equal to
A. `2piL`
B. `(L)/sqrt(2pi)`
C. L
D. `(L)/(2pi)`

Answer 1

Correct Answer - B
Velocity of efflux when the hole is at depth h, `v=sqrt(2gh)`
Rate of flow of water from square hole `Q_(1) = a_(1)v_(1) = L^(2) sqrt(2gy)`
Rate of flow of water from circular hole `Q_(2) = a_(2)v_(2) = piR^(2) sqrt(2g(4y))`
and according to problem `Q_(1) = Q_(2) implies L^(2) sqrt(2gy) = piR^(2) sqrt(2g(4y)) implies R = (L)/sqrt(2pi)`