Question

Figure shows a large closed cylindrical tank containing water. Initially, the air trapped above the water surface has a height $h_0$ and pressure $2p_0$ where $p_0$ is the atmospheric pressure. There is a hole in the wall of the tank at a depth $h_1$below the top from which water comes out. A long vertical tube is connected as shown.
Find the height $h_2$ of the water in the long tube above the top initially.

Answer 1

The pressure of water above the water level of the bigger tank is given by

$P=(h_2+h_0)\rho g$

Let the atmospheric pressure above the tube be $P_0$

Total pressure above the tube $=P_0+P$

$=(h_2+h_0)\rho g+P_0$

This pressure initially is balanced by pressure above the tank $2P_0$.

$\Rightarrow 2P_0=(h_2+h_0)\rho g+P_0$

$\Rightarrow h_2=\frac{P_0}{\rho g}-h_0$