Question

A tank is filled with two immiscible liquids of densities $2\rho$ and $\rho$ each of height $h$. Two holes are made to the side wall at $\frac{h}{2}$ and $\frac{3h}{2}$ from upper surface of the liquid, then the ratio of velocity of efflux of the liquids through the holes

• A. $\frac{\sqrt{2}}{3}$
• B. $\frac{\sqrt{3}}{1}$
• C. $\frac{3}{\sqrt{2}}$
• D. $\frac{1}{\sqrt{2}}$

Answer 1

The correct option is B $\frac{\sqrt{3}}{1}$

Let the velocity at hole is $v_1$

Height is $\frac{h}{2}$

Therefore velocity is, $v_1=\sqrt{2g\frac{h}{2}}$

Now pressure at hole 2 is

P= $h\rho g+\frac{h}{2}\times 2\rho g$

Applying Bernoulli's theorem, $P_o+2h\rho g=P_o+\frac{1}{2}\left(2\rho \right)v_2^2$

where $P_o$ is the atmospheric pressure

Velocity at hole 2 is $v_2=\sqrt{2g\frac{3h}{2}}=\sqrt{3gh}$

Now, $\frac{v_2}{v_1}=\frac{\sqrt{3gh}}{\sqrt{gh}}$

$\frac{v_2}{v_1}$= $\sqrt{3}:1$