Question

A tank with a small hole at the bottom has been filled with water and kerosene (specific gravity $0.8$). The height of water is $3m$ and that of kerosene $2m$. When the hole opened the velocity of fluid coming out from it is nearly: (take $g=10{ms}^{-2}$ and density of water ${10}^{3}kg{m}^{-3}$)

• A. $9.6{ms}^{-1}$
• B. $8.5{ms}^{-1}$
• C. $7.6{ms}^{-1}$
• D. $10.7{ms}^{-1}$

Answer 1

The correct option is A $9.6{ms}^{-1}$

Applying Bernoulli's law between the kerosene - water interface and the hole :

$P_0+({\rho }_{w}g{h}_1+{\rho }_{k}g{h}_2)+\frac{1}{2}{\rho }_w{v}_1^2=P_0+0+\frac{1}{2}{\rho }_w{v}_2^2$ (hole is at base so $h=0$)

$\Rightarrow 3\times {10}^{3}g+2\times 0.8\times {10}^{3}g=\frac{1}{2}\times {10}^3\times v_2^2$ ($v_1\approx 0$ as flow is very slow at interface)

$\Rightarrow v_2^2=9.2g$

$\Rightarrow v_2=\sqrt{92}$ (given : $g=10m/s^2$)

$\Rightarrow v_2=9.6m/s$