Question

A large cylindrical tank has a hole of area A at its bottom. Water is poured in the tank by a tube of equal cross-sectional area A ejecting water at the speed v.
(a) The water level in the tank will keep on rising
(b) No water can be stored in the tank
(c) The water level will rise to a height v²/2g and then stop
(d) The water level will oscillate

Answer 1

(c) The water level will rise to a height v²/2g and then stop.

From the principle of continuity and Bernoulli's equation, ​we have:
$$\begin{gathered} v^2=2gh \\ \Rightarrow h=\frac{v^2}{2g} \end{gathered}$$

So, h is the maximum height up to which the water level will rise if the water is ejected at a speed v.