Question

A square hole of side length $l$ is made at a depth of $h$ and a circular hole of radius $r$ is made at a depth of $4h$ from the surface of water in a water tank kept on a horizontal surface. If $\ell <<h,r<<h$ and the rate of water flow from the holes is the same, then $r$ is equal to

• A. $\frac{\ell }{\sqrt{2\pi }}$
• B. $\frac{\ell }{\sqrt{3\pi }}$
• C. $\frac{\ell }{3\pi }$
• D. $\frac{\ell }{2\pi }$

Answer 1

Answer: (A)

As $A_2{v}_1=A_2{v}_2$ (Principle of continuity)
or ${\ell }^2\sqrt{2gh}=\pi r^2\sqrt{2g\times 4h}$
$\left(Effluxvelocity=\sqrt{2gh}\right)$
$\therefore r^2=\frac{{\ell }^2}{2\pi }$ or $r=\sqrt{\frac{{\ell }^2}{2\pi }}=\frac{\ell }{\sqrt{2\pi }}$