A large cylindrical tank has a hole of area A at its bottom. Water is oured in the tank by a tube of equal cross sectional area A ejecting water at the speed v.

Options

A. Water level in tank keeps on rising
B. No water can be stored in the tank.
C. Water level will rise to a height `v^(2)//2g` and then stop.
D. The water level will be oscillating.

Answer

C

Explanation

Initially the water flowing olut will be less than that flowing into it. Hence the water level will go on rising. When the water level is `h`, the velocity of effux `sqrt(2gh)`. When this becomes equal to the velocity of inflow, the level will become steady as the area of cross section of the filling tube and area of across section of the hole equal. This height given by Torricelli's theorem
`v=sqrt(2g)` or `(v^(2))/(2g)=h`