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…

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 both are the same. Then, find the value of R.

Sol: Velocity of efflux at a depth h is given by $\large v = \sqrt{2 g h}$

Volume of water flowing out per second from both the holes are equal

a1 v1 = a2 v2

$\large L^2 \sqrt{2 g (y)} = \pi R^2 \sqrt{2 g (4 y)}$

$\large R = \frac{L}{\sqrt{2 \pi}}$