Question

A fixed cylindrical tank having large cross-section area is filled with two liquids of densities $\rho$ and $2\rho$ and in equal volumes as shown in the figure. A small hole of area of cross section $a=\sqrt{6}c{m}^2$ is made at height h'(h' < h) from the bottom.

Answer 1

Applying the Bernoulli's equation for the given setup:

$P_0+\frac{1}{2}\times 2\times \rho v^2=P_0+2\rho g+\frac{h}{2}+\rho gh$

So, velocity of efflux comes out to be $v=\sqrt{2gh}$

Now, for the distance covered in vertical direction:

$\frac{1}{2}g{t}^2=\frac{h}{2}$

So, $t=\sqrt{\frac{h}{g}}$

So, the ranfe of the efflux will be:

$R=v\times t$

$R=\sqrt{2}h$