Question

A wide vessel with a small hole in the bottom is filled with water and kerosene. Neglecting the viscosity, find the velocity of the water flow, if the thickness of the water layer is equal to $h_1=30cm$ and that of the kerosene layer to $h_2=20cm$.Density of kerosene $=600\mathrm{kg}/m^3$

• A. $5.74{ms}^{-1}$
• B. $1.91{ms}^{-1}$
• C. $2.87{ms}^{-1}$
• D. $3.82{ms}^{-1}$

Answer 1

Answer: (C)

$2.87{ms}^{-1}$

since, the density of water (1000 kg/m^3) 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 $v=\sqrt{2(h_1+h_2\frac{{\rho }_2}{{\rho }_1})g}$

$v=\sqrt{2(0.3+0.2\frac{600}{1000})g}=2.87m/s$