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

Answer

A

Explanation

By the principle of continuity
`A_1v_1 = A_2v_2`
According to question, `A_1 = L^2`
`v_1 = sqrt(2gy)`
and `A_2 = pi R^2`
`v_2 = sqrt(2 g 4y)`
`therefore L^3 sqrt(2gy) = pi R^2 sqrt(2 g 4y)`
or `R . L/(sqrt(2pi))`