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

Options

A. `2 pi L`
B. `(L)/sqrt(2pi)`
C. L
D. `L/(2pi)`

Answer

B

Explanation

Velocity of efflux when the hole is a t 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))`
According to problem, `Q_(1) = Q_(2)`
`implies L^(2) sqrt(2gy) = pi R^(2)sqrt(2g(4y)) implies R = (L)/(sqrt(2pi)`.