A wide vessel with a small hole at the bottom is filled with water (density $${\rho _1},$$ height $${h_1}$$) and kerosene (density $${\rho _2},$$ height $${h_2}$$ ). Neglecting viscosity effects, the speed with which water flows out is :

Solution :
$$\eqalign{ & {P_a} + \frac{1}{2}{\rho _1}v_1^2 + 0 \cr & = Pa + \frac{1}{2}{\rho _2}v_2^2 + \left( {{\rho _1}g{h_1} + {\rho _2}g{h_2}} \right) \cr & {\text{As}}\,{v_2} < < {v_1}. \cr & \therefore {v_1} = \sqrt {2g\left( {{h_1} + {h_2}\frac{{{\rho _2}}}{{{\rho _1}}}} \right)} \cr} $$