Question

A tank is filled with water of density $1g$ per $c{m}^3$ and oil of density $0.9g$ per $c{m}^3$ The height of water layer is $100cm$ and of the oil layer is $400cm$ . If $g=980cm/s^2$ , then the velocity of efflux from an operating in the bottom of the tank is :

• A. $\sqrt{900\times 980}cm/s$
• B. $\sqrt{1000\times 980}cm/s$
• C. $\sqrt{920\times 980}cm/s$
• D. $\sqrt{950\times 980}cm/s$

Answer 1

Answer: (C)

Pressure at the bottom of tank must equal pressure due to water of height $h$.
Let $d_w$ and $d_o$ be the densities of water and oil,
then the pressure at the bottom of the tank
$=h_w{d}_{w}g+h_0{d}_{0}g$
Let this pressure be equivalent to pressure due
to water of height $h$. Then
$h{d}_{w}g=h_w{d}_{w}g+h_0{d}_{0}g$
$\therefore h=h_w+\frac{h_0{d}_0}{d_w}$
$=100+360=460$
According to Toricelli’s theorem,
$v=\sqrt{2gh}=\sqrt{2\times 980\times 460}$
$=\sqrt{920\times 980}cm/s$