A tank is filled with water of density ${10}^3\mathrm{kg}/{\mathrm{m}}^3$ and oil of density $0.9\times {10}^3\mathrm{kg}/{\mathrm{m}}^3$ . The height of water layer is 1m and that of the oil layer is 4 m. The velocity of efflux from an opening in the bottom of the tank is

Let ${\rho }_w$ and ${\rho }_o$ be the densities of water and oil, respectively. 

Then the pressure at the bottom of the tank is given as,

${\mathrm{P}}_{\mathrm{B}}={\mathrm{h}}_{\mathrm{W}}{\mathrm{\rho }}_{\mathrm{w}}\mathrm{g}+{\mathrm{h}}_0{\mathrm{\rho }}_0\mathrm{g}$

Let this pressure be equivalent to pressure due to water of height h. Then,

$h{\rho }_{w}g=h_w{\rho }_{w}g+h_0{\rho }_{0}g$

$\Rightarrow \mathrm{h}={\mathrm{h}}_{\mathrm{w}}+\frac{{\mathrm{h}}_0{\mathrm{\rho }}_0}{{\mathrm{\rho }}_{\mathrm{w}}}=1+\frac{4\times 0.9}{1}=1+3.6=4.6 \mathrm{m}$

According to Toricelli's theorem,

$\mathrm{v}=\sqrt{2\mathrm{gh}}=\sqrt{2\times 10\times 4.6}=\sqrt{92} \mathrm{m}/\mathrm{s}$