Question

A hole is made at the bottom of the tank filled with water (density $1000{\text{kg/m}}^3$). If the total pressure at the bottom of the tank is 3 atmosphere (1 atmosphere = ${10}^5{\text{N/m}}^2$), then the velocity of efflux is

• A. $\sqrt{200}\text{m/s}$
• B. $\sqrt{400}\text{m/s}$
• C. $\sqrt{500}\text{m/s}$
• D. $\sqrt{800}\text{m/s}$

Answer 1

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

We know that velocity of efflux, $v=\sqrt{2gh}$.
At the bottom of tank pressure is 3 atmosphere. So, total pressure due to water column
$h\rho g=2\times {10}^5$ (two atmosphere)
$\Rightarrow gh=\frac{2\times {10}^5}{\rho }=\frac{2\times {10}^5}{{10}^3}=2\times {10}^2$

$\Rightarrow v=\sqrt{2\times 2\times {10}^2}=\sqrt{400}\text{m/sec}$