A fixed cylindrical tank having large cross-section area is filled with two liquids of densities p and 2p and in equal volumes as shown in the figure. A small hole of area of cross-section $a= \sqrt{6} cm²$ is made at height h/2 from h 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.

 $P_{atm}+\rho gh+0=P_2+0+0$
 $\Rightarrow P_2=P_{atn}+\rho gh$ …..(i)

Again applying Bernoulli's equation at section 2
$P_2+0+2\rho g\times \frac{h}{2}=P_{atm}+\frac{1}{2}2\rho V^2$  …(ii)
$\Rightarrow V=\sqrt{2gh}$        …(iii)
This is required velocity of efflux Applying continuity equation between 3 and 4 cross-section,
aV = a₁V₁ ...(iv)
Again applying Bernoulli's equation between (iii) and (iv)
$P_{atm}+\frac{1}{2}\left(2\rho \right)V^2+2\rho g\times \frac{h}{2}=P_{atm}+\frac{1}{2}\left(2\rho \right)V_1^2+0$  
 
 $$\begin{gathered} \Rightarrow V_1^2=3gh \\ {a}_1=\frac{aV}{V_1}=\frac{\sqrt{6}.\sqrt{2gh}}{\sqrt{3gh}}=2c{m}^2 \end{gathered}$$
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