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. The, R is equal to :

• A. (a) L /\sqrt{2\pi}
• A. (b) 2pL
• A. (c) L
• A. (d) L / 2p

Answer 1

(a)

Velocity of efflux at a depth h is given by v =$\sqrt{2gh}$. Volume

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

\ a₁v₁ = a₂v₂

or (L²)$\sqrt{2g(y)}$= pR²$\sqrt{2g(4y)}$

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