Question

A wide vessel of uniform cross-section with a small hole at the bottom is filled with a $40\text{cm}$ thick layer of water and $30\text{cm}$ thick layer of kerosene. The relative density of kerosene is $0.8$. The initial velocity of flow of the water streaming out of the hole is -

• A. $\frac{2}{\sqrt{5}}{\text{ms}}^{-1}$
• B. $\frac{4}{\sqrt{5}}{\text{ms}}^{-1}$
• C. $\frac{6}{\sqrt{5}}{\text{ms}}^{-1}$
• D. $\frac{8}{\sqrt{5}}{\text{ms}}^{-1}$

Answer 1

The correct option is D $\frac{8}{\sqrt{5}}{\text{ms}}^{-1}$

Let us suppose, initial velocity of flow of water streaming out of the hole is $v$.
According to the question -


On applying Bernoulli's Equation -
$p_o+{\rho }_{k}g{h}_k+{\rho }_{w}g{h}_w=p_o+\frac{1}{2}{\rho }_w{v}^2$
$\Rightarrow 0.8\rho \times 10\times 0.3+\rho \times 10\times 0.4=\frac{1}{2}\rho v^2$
$\Rightarrow v=\sqrt{\frac{64}{5}}=\frac{8}{\sqrt{5}}\text{m/s}$