A tank is filled with water of density ${10}^3 \mathrm{kg}/{\mathrm{m}}^3$ and oil of density $9\mathrm{x}{10}^3 \mathrm{kg}/{\mathrm{m}}^3$. The height of water layer is 1 m and that of the oil layer is 4 m. The velocity of efflux from an opening in the bottom of the tank is

Let ${\mathrm{d}}_{\mathrm{w}} \mathrm{and} {\mathrm{d}}_0$ be the densities of water and oil, respectively.
Then the pressure at the bottom of the tank is ${\mathrm{h}}_{\mathrm{w}}{\mathrm{d}}_{\mathrm{w}}\mathrm{g}+{\mathrm{h}}_0{\mathrm{d}}_0\mathrm{g}$. Let this pressure be equivalent to pressure due to water of height h. Then,
${\mathrm{hd}}_{\mathrm{w}}\mathrm{g}={\mathrm{h}}_{\mathrm{w}}{\mathrm{d}}_{\mathrm{w}}\mathrm{g}+{\mathrm{h}}_0{\mathrm{d}}_0\mathrm{g}$
$$\begin{gathered} \therefore \mathrm{h}={\mathrm{h}}_{\mathrm{w}}+\frac{{\mathrm{h}}_0{\mathrm{d}}_0}{{\mathrm{d}}_{\mathrm{w}}}=100+\frac{400\times 0.9}{1} \\ = 100+360=460=4.6 \mathrm{m} \end{gathered}$$
According to Toricelli's theorem,
$\mathrm{v}=\sqrt{2\mathrm{gh}}=\sqrt{2\times 10\times 4.6}\mathrm{m}/\mathrm{s}=\sqrt{92}\mathrm{m}/\mathrm{s}.$