Question

Find the height of the water in the long tube above the top when the water stops coming out of the hole.

• A. $-2h_0$
• B. $h_0$
• C. $h_2$
• D. $-h_1$

Answer 1

The correct option is D $-h_1$

The pressure of the column present in the pipe is represented as:

$2P_0=(h_2+h_0)\rho g+p_0$

(Since liquids at the same level have the same pressure)

$p_0=h_2\rho g+h_0\rho g$

$h_2\rho g=P_0-h_0\rho g$

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

KE of the water $=$ Pressure energy of the water at the layer

$\frac{1}{2}m{v}^2=m\times \frac{P}{\rho }$

$v^2=\frac{2P}{\rho }=\frac{2}{\rho }[P_0+\rho g(h_1-h_0)]$

$v={\left[\frac{2}{\rho }\{P_0+\rho g(h_1-h_0)\}\right]}^{1/2}$

We know

$2P_0+\rho g(h_1-h_0)=P_0+\rho gX$

$\Rightarrow X=\frac{P_0}{\rho g}+(h_1-h_0)=h_2+h_1$

i.e., X is $h_1$ metre below the top or $X$ is $-h_1$ above the top.