Question

A hole is made at the bottom of a tank filled with water. If total pressure at the bottom of the tank is three atmosphere, then the velocity of efflux at the bottom is (1 atm = ${10}^{5}N/m^2$)

• A. $\sqrt{400}m/s$
• B. $\sqrt{200}m/s$
• C. $\sqrt{600}m/s$
• D. $\sqrt{500}m/s$

Answer 1

The correct option is A $\sqrt{400}m/s$

Given,

$\begin{array}{c}P=1000kg/m^3\\ P=3atm=3\times {10}^{5}N/m^2\\ P_0=1atm={10}^{5}N/m^2\end{array}$

Pressure due to liquid column is

$P-P_0=\rho gh$

velocity of flux $V=\sqrt{2gh}$

$\begin{array}{c}V=\sqrt{2\frac{\left(p-P_0\right)}{\rho }}\\ =\sqrt{\frac{2\left(3\times {10}^5-{10}^5\right)}{1000}}\\ =\sqrt{\frac{4\times {10}^5}{1000}}\\ =\sqrt{400}m/s\end{array}$

Hence,

option $A$ is correct answer.