Question

A small hole of area of cross-section $2m{m}^2$ is present near the bottom of a fully filled open tank of height 2 $m$. Taking $g=10m/s^2$ , the rate of flow of water through the open hole would be nearly

• A. $12.6\times {10}^{–6}{m}^3/s$
• B. $8.9\times {10}^{–6}{m}^3/s$
• C. $2.23\times {10}^{–6}{m}^3/s$
• D. $6.4\times {10}^{–6}{m}^3/s$

Answer 1

The correct option is A $12.6\times {10}^{–6}{m}^3/s$

Velocity of efflux, $v=\sqrt{2gh}$
Volume flow rate, $Q=Av=A\sqrt{2gh}=\left(2\times {10}^{-6}\right){\left(2\times 10\times 2\right)}^{1/2}=4\sqrt{10}\times {10}^{-6}{m}^3/s\approx 12.6\times {10}^{-6}{m}^3/s$