A fixed cylindrical tank having large cross-section area is filled with two liquids of densities $\rho and2\rho$ 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 $\frac{h}{2}$ from the bottom. Find the area of cross-section of stream of liquid in $c{m}^2$ just before it hits the ground.

Applying Bernoulli’s equation at cross-section 1 and 2

$P_{atm}+\rho gh+0=P_2+0+0\Rightarrow P_2=P_{atm}+\rho gh\mathrm{.....}\left(i\right)$

Again applying Bernoulli’s equation at section 2 and 3.

$P_2+0+2\rho g+\frac{h}{2}=P_{atm}+\frac{1}{2}2\rho V^2\mathrm{....}\left(ii\right)\Rightarrow V=\sqrt{2gh}\mathrm{...}\left(iii\right)$

This is required velocity of efflux Applying continuity equation between  3 and 4 cross-section,  $aV=a_1{V}_1\mathrm{.......}\left(iv\right)$

Again applying Bernoulli’s equation between (iii) and (iv) $P_{atm}+\frac{1}{2}\left(2\rho \right)V^2+2\rho g\times \frac{h}{2}=P_{atm}+\frac{1}{2}\left(2\rho \right)V_1^2+0$

$\Rightarrow V_1^2=3gh{a}_1=\frac{nV}{V_1}=\frac{\sqrt{6}.\sqrt{2gh}}{\sqrt{3gh}}=2c{m}^2$