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 $A_2v_1 = A_2v_2$ (Principle of continuity)
or $\ell^{2}\sqrt{2gh}=\pi r^{2}\sqrt{2g\times4h}$
$\left(Efflux velocity =\sqrt{2gh}\right)$
$\therefore r^{2}=\frac{\ell^{2}}{2\pi}$ or $r=\sqrt{\frac{\ell^{2}}{2\pi}}=\frac{\ell}{\sqrt{2\pi}}$