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 $\text{second}$ from 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 $\frac{L}{\sqrt{2\pi }}$

As, it is given that the discharge of water is same through both the holes

$\therefore A_1{v}_1=A_2{v}_2$

Where, $A_1,A_2$ are the cross-section area of square and circular holes respectively.

And, $v_1,v_2$ are the velocities of efflux through square and circular holes respectively.

$\Rightarrow A_1\sqrt{2g{h}_1}=A_2\sqrt{2g{h}_2}$

$\Rightarrow A_1^2{h}_1=A_2^2{h}_2$

$\Rightarrow \left(L^2{)}^2\right(y)=(\pi R^2{)}^2\left(4y\right)$

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

Hence, option $\left(\text{A}\right)$ is correct.