Question

A square hole of side length l is made at a depth of y and a circular hole is made at a depth of 4y from the surface of water in a water tank kept on a horizontal surface. If equal amount of water comes out of the vessel through the holes per second then the radius of the circular hole is equal to (l<<y)

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

$A_1{v}_1$ = $A_2{v}_2$ , asd equal amount of water comes out.

Where the velocities of efflux $v_1$ = $\sqrt{2gy}$ and

$v_2$ = $\sqrt{2g\left(4y\right)}$ & the area of cross section of the holes are $A_1$ =$l^2$ and $A_2$ = $\pi R^2$.

Putting all the values, we obtain

$\left(l^2\right)\sqrt{2gy}=\left\{\sqrt{2g\left(4y\right)}\right\}\pi R^2$

$\Rightarrow R=\frac{l}{\sqrt{2\pi }}$.