Question

A large open tank has two holes in the wall. One is a square hold 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 the holes are the same. Then, $R$ is equal to:

• A. $L/\sqrt{2\pi }$
• B. $2\pi /L$
• C. $L$
• D. $L/2\pi$

Answer 1

The correct option is A $L/\sqrt{2\pi }$

Velocity of efflux at a depth h is given by $V=\sqrt{2gh}$
Given, by equation of continuity :$a_1{V}_1=a_2{V}_2$
$L^2\sqrt{2gy}=\pi R^2\sqrt{2g4y}$ or $R=L/\sqrt{2\pi }$