A rectangular tank is filled to the brim with water. When a hole at its bottom is unplugged, the tank is emptied in time T. If the tank is half-filled with water, it will be emptied in time

The velocity of efflux through a hole is given by
$v=\sqrt{2gh}$
where h is the height of the tank. If the hole is at the top of the tank, v is obviously zero. Therefore, the average velocity of efflux $v_a=\frac{1}{2}\times \sqrt{2gh}=\sqrt{\frac{gh}{2}}$.
If the volume of water in the tank, when it is full, is $\text{V}$ and $\mathrm{A}$ the cross-sectional area of the hole, then time taken by the tank to be emptied is
$T=\frac{V}{A{v}_a}=\frac{\sqrt{2}V}{A\sqrt{gh}}$
When the tank is half-full, V is replaced by $\frac{V}{2}$ and h is replaced by $\frac{h}{2}$. Therefore, time taken now is
$T^{\text{'}}=\frac{\sqrt{2}V/2}{A\sqrt{gh/2}}=\frac{V}{A\sqrt{gh}}=\frac{T}{\sqrt{2}}$