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 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 $L/\sqrt{2\pi }$

Flow of water out of the holes per second are same-

$A_1{V}_1=A_2{V}_2{L}^2\sqrt{2gy}=\sqrt{2g\left(4y\right)}\left(\pi R^2\right)L^2=2\pi R^{2}L=\sqrt{2\pi }RR=\frac{L}{\sqrt{2\pi }}$