Question

A container having a small orifice in the bottom is filled with water and kerosene as in figure. Neglecting the viscosity, find the velocity of the water flow (in $\text{m/s}$ upto 2 decimals) if the thickness of the water layer is $h_1=30\text{cm}$ and that of the kerosene layer is $h_2=20\text{cm}$.
Take ${\rho }_{\text{water}}=1\frac{g}{{\text{cm}}^3},{\rho }_{\text{kerosene}}=0.80\frac{g}{{\text{cm}}^3}$

Answer 1

Applying Bernoulli's equation for a point 1 just inside the orifice and point 2 just outside the orifice.
$P_{\text{atm}}+{\rho }_{w}g{h}_1+{\rho }_{k}g{h}_2=P_{\text{atm}}+\frac{1}{2}{\rho }_w{v}^2$ (Just inside the orifice velocity is negligible)
$\Rightarrow v=\sqrt{2(h_2\frac{{\rho }_k}{{\rho }_w}+h_1)g}$
$\Rightarrow v=\sqrt{2\left(0.2\right(0.8)+0.30)9.8}=\sqrt{9.016}$
$\Rightarrow v=3\text{m/s}$