Question

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

• A. $\sqrt{85}m/s$
• B. $\sqrt{88}m/s$
• C. $\sqrt{92}m/s$
• D. $\sqrt{98}m/s$

Answer 1

Answer: (C)

$\sqrt{92}m/s$

Let $d_w$ and $d_0$ be the densities of water and oil, respectively. Then the pressure at the bottom of the tank is $h_w{d}_{w}g+h_0{d}_{0}g$.

Let this pressure be equivalent to pressure due to water of height h. Then,
$h{d}_{w}g=h_w{d}_{2}g+h_0{d}_{0}g$
$\therefore h=h_w+\frac{h_0{d}_0}{d_w}=1+\frac{4\times 0.9}{1}$
$=1+3.6=4.6m$

According to Toricelli's theorem,
$v=\sqrt{2gh}=\sqrt{2\times 10\times 4.6m/s}=\sqrt{92}m/s$