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 the two holes are the same. Then value of $R$ is:

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

Answer 1

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

By principle if continuity: $A_1{v}_1=A_2{v}_2$

As per quesiton: $A_1=L^2;v_1=\sqrt{2gy}$ and

$A_2=\pi R^2$, $v_2=\sqrt{2g4y}$

So,

$L^2\sqrt{2gy}=\pi R^2\sqrt{2g4y}$

$\Rightarrow L^2=2\pi R^2$

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