Question

A large vessel with a small hole at the bottom is filled with water and kerosene. The height of the water column is $20$ cm and that of the kerosene is $25$ cm. The velocity with which water flows out of the hole is ( density of kerosene =$0.8$ gm /cc) ( Neglect viscous force)

• A. $2m/s^{-1}$
• B. $4m/s^{-1}$
• C. $2.8m/s^{-1}$
• D. $3m/s^{-1}$

Answer 1

The correct option is D $3m/s^{-1}$

Since,the density of water is greater than that of kerosene oil, it will collect at the bottom.

Now, pressure due to water level equals $h_1{\rho }_{1}g$ and pressure due to kerosene oil level equals $h_2{\rho }_{2}g$. So, net pressure becomes $h_1{\rho }_{1}g+h_2{\rho }_{2}g$.

From Bernoulli's theorem, this pressure energy will be converted into kinetic energy while flowing through the whole $A$.

i.e. $h_1{\rho }_{1}g+h_2{\rho }_{2}g=\frac{1}{2}{\rho }_1{v}^2$

Hence,

$V=\sqrt{2\left(h_1+h_2\frac{{\rho }_2}{{\rho }_1}\right)g}=3m/s$.

$\therefore$ Option $D$ is correct.