Question

A sealed tank has $2$-openings as shown below. One at near top and other at near bottom. Let height of water filled above the bottom opening is $h$ and a compressor producing a pressure $p$ is connected to top opening. Velocity of water obtained from lower opening is (take, atmospheric pressure $p_{a}$ such that $\left.p-p_{a}=\rho g h\right)$

• A. $\sqrt{2 g h}$
• B. $\sqrt{g h}$
• C. $2 \sqrt{g h}$
• D. $0$

Answer 1

Answer: (C)

Applying Bernoulli's theorem, at different parts of figure given below,
$p_{a}+\frac{1}{2} \rho v_{1}^{2}+\rho g y_{1}=p+\frac{1}{2} \rho v_{2}^{2}+\rho g y_{2}$
$=p+\rho g y_{2} \left[\because v_{2}=0\right]$
$v_{1}^{2}=\frac{2}{\rho}\left(p-p_{a}+\rho g\left(y_{2}-y_{1}\right)\right)\,\,\,....(i)$

Given, $ y_{2}-y_{1}=h$
Substituting the given value in Eq. (i), we get
$v_{1}=\sqrt{2 g h+\frac{2\left(p-p_{a}\right)}{\rho}}$
$=\sqrt{2 g h+\frac{2(\rho g h)}{\rho}}=2 \sqrt{g h}$