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. The value of R is

Explanation

`:.` Velocity `v= sqrt(2gh)`
`:.` Quantity at square hole `(Q_(1)) = v_(1)A_(1)`
`:. Q_(1) = sqrt(2gy) xx L^(2)`
Again quantity at circular hole `(Q_(2)) = v_(2)A_(2)`
`:. Q_(2) = sqrt(2g xx 4y) xx pi r^(2) or Q_(2) = sqrt(8gy) xx pi r^(2)`
Given `Q_(1) = Q_(2)` (according to the equation of continuity )
`:. sqrt(2gy) xx L^(2) = sqrt(8gy) xx pi r^(2)`
or `L^(2) = 2pi r^(2) or r= (L)/(sqrt(2pi))`