A wide vessel of uniform cross-section with a small hole in the bottom is filled with 40 cm thick layer of water and 30 cm thick layer of kerosene. The relative density of kerosene is 0.8. The initial velocity of flow of water streaming out of the hole is (take g = 10 ms^-2 ) 

Let ${\rho }_w$ and ${\rho }_k$ be the densities of water and kerosene. 

The initial weight of the liquid in the vessel $=h_w{\rho }_w$$ag+h_k {\rho }_{k }ag$ where $h_w$ and $h_k$ are the thicknesses of water and kerosene layers and a is the cross-sectional area of the vessel. Let this weight be equivalent to water layer of thickness $h$, then

                 $\begin{array}{r}h{\rho }_{w}ag=h_w{\rho }_{w}ag+h_k{\rho }_{k}ag\end{array}$

              $or h=\left\{h_w+h_k\left(\frac{{\rho }_k}{{\rho }_w}\right)\right\}$ 

                             $= 0.4 + 0.3 X 0.8 = 0.64 m$

From Torricelli's theorem, the velocity of efflux is

                        $$\begin{gathered} v=\sqrt{2gh} \\ =\sqrt{2\times 10\times 0.64}=\frac{8}{\sqrt{5}}m{s}^{-1} \end{gathered}$$