Question

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

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

Answer 1

Answer: (A)

$\sqrt{400}m/s$

Applying Bernoulli's equation to two points one on the surface and the other just outside the hole at the bottom,

$P_{atm}+\rho gh+\frac{1}{2}\rho v^2=P_{atm}+0+\frac{1}{2}\rho v^{\prime 2}$

Given,

$v=0$

Pressure difference between top and bottom is $2atm$ i.e equivalent of $20m$ of water column

$\therefore h=20$

$\frac{1}{2}\rho v^{\prime 2}=\rho gh$

$\therefore \frac{1}{2}\times 1\times v^{\prime 2}=10\times 20$

$\Rightarrow v^{\prime }=\sqrt{400}$