Water stands at a depth H in a tank whose side walls are vertical. A hole is made in one of the walls at a height h below the water surface. The stream of water emerging from the hole strikes the floor at a distance R from the tank, where R is given by

Let h be the depth of the hole below the free surface of water. (see Fig).

According to Torricelli's theorem, the velocity of efflux v of water through the hole is given by
$v=\sqrt{2gh}$                (i)
The height through which water falls is
$S=H-h$
If t is the time taken by water to strike the floor, then
$$\begin{gathered} S=\frac{1}{2}g{t}^2 \\ \text{ or } H-h=\frac{1}{2}g{t}^2 \\ \text{ giving } t=\sqrt{\frac{2(H-h)}{g}} \left(ii\right) \end{gathered}$$
The distance R where the emerging stream strikes the floor is given by
$R=v t$
Substituting for v and t from Eqs. (i) and (ii), we get
$R=\sqrt{2gh}\times \sqrt{\frac{2(H-h)}{g}}=2\times \sqrt{h(H-h)}$