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. Then, R is equal to

• A. $\frac{L}{\sqrt{2\pi }}$
• B. $2\pi L$
• C. $L$
• D. $\frac{1}{2\pi }$

Answer 1

The correct option is A

$\frac{L}{\sqrt{2\pi }}$

Velocity of water coming out of square hole, $v=\sqrt{2gy}$
Velocity of water coming out of circular hole, $v^{\prime }=\sqrt{2g\times 4y}=2\sqrt{2gy}$
Now, $v{L}^2=v^{\prime }\pi R^2\Rightarrow \sqrt{2gy}\times L^2=2\sqrt{2gy}\times \pi R^2\therefore R=\frac{L}{\sqrt{2\pi }}$