Question

Water stored in a tank flows out through a hole of radius 1mm at a depth 10 m below the surface of water.The rate of flow of water in $m^3/s$ will be

• A. $4.4\times {10}^{-5}$
• B. $4.4\times {10}^{-4}$
• C. $4.4\times {10}^{-3}$
• D. $4.4\times {10}^{-2}$

Answer 1

The correct option is A $4.4\times {10}^{-5}$

According to Torricelli's Theorem velocity of efflux i.e. the velocity with which the liquid flows out of a hole is equal to $\sqrt{2gh}$ where $h$ is the depth of the hole below the liquid surface. here $h=10m$
$\Rightarrow v=\sqrt{2\times 9.8\times 10}=\sqrt{196}=14m/s$
and rate of flow $=av=\pi (0.001{)}^2\times 14=4.4\times {10}^{-5}{m}^3/s$