Physics - Fluid Question with Solution | TestHub

According to Torricelli's law, the speed of efflux $v$ from an orifice is given by:

$v=\sqrt{2gh}$

where $h$ is the depth of the orifice below the free surface of the liquid.

From the given figure, let the depths of the orifices $O_1,O_2$, and $O_3$ from the free surface be $h_1,h_2$, and $h_3$ respectively. It is evident that:

$h_1<h_2<h_3$

Since the speed of efflux is directly proportional to the square root of the depth ($v\propto \sqrt{h}$), we have:

$\sqrt{2g{h}_1}<\sqrt{2g{h}_2}<\sqrt{2g{h}_3}$

$\Rightarrow V_1<V_2<V_3$

Answer: $V_1<V_2<V_3$