Question

A large open tank has two holes in the wall. One is a square hole of side $L$ at a depth h from the top and the other is a circular hole of radius $R$ at a depth $4h$ from the top, When the tank is completely filled with water, quantities of water flowing out per second from both holes are the same. Then $R$ is equal to

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

Answer 1

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

Since the water quantity from both the holes are equal, we have
$a_1{v}_1=a_2{v}_2$
$\Rightarrow L^2\sqrt{2gy}=\pi R^2\sqrt{2g\left(4y\right)}\because$ velocity of efflux at depth h is given by $v=\sqrt{2gh}$
$\Rightarrow R=\frac{L}{\sqrt{2\pi }}$