Question

The density of liquid contained in the tank of area $0.5m^2$ is $1200$ $kg/m^2$. It has a hole of area $1$ $c{m}^2$ near the bottom. A load of $30$kg is applied on the liquid at the top. Find the velocity of efflux when the height of liquid level is $75$cm above the bottom.
(Take, $g=10m/s^2$).

• A. $2m/s$
• B. $4m/s$
• C. $6m/s$
• D. $8m/s$

Answer 1

The correct option is B $4m/s$

Let the velocity of efflux at point $2$ is v.
Given, $a=1c{m}^2,A=0.5m^2=0.5\times {10}^{4}c{m}^2$
Applying continuity equation,
AV$=$av
$V=\frac{a}{A}v$
Since, $a<<A,V<<c,V^2$ is negligible
Pressure at $1$. $p_1=p_o+\frac{mg}{A}$
$=p_o+\frac{30\times 10}{0.5}$
$=p_o+600$
Pressure at $\left(2\right)$.
$p_2=p_o$
where, $p_o$ is atmospheric pressure
Applying Bemoulli's equation between $\left(1\right)$ and $\left(2\right)$
$p_1+pgh+\frac{1}{2}\rho V^2=p_2+\frac{1}{2}\rho v^2$
$V^2$ is negligible, then
$p_0+600+1200\times 10\times 0.75$
$=p_0+\frac{1}{2}\times 1200v^2$
$600v^2=9600\Rightarrow v^2=16\Rightarrow v=4m/s$.