Question

The area of cross-section of a large tank is $0.5m^2$. It has an opening near the bottom having area of cross-section $1{cm}^2$. A load of $20kg$ is applied on the water at the top. Find the velocity of the water coming out of the opening at the time when the height of water level is $50cm$ above the bottom. Take $g=10m/s^2$

• A. $2.3m/s$
• B. $4.3m/s$
• C. $3.3m/s$
• D. $5.3m/s$

Answer 1

The correct option is C $3.3m/s$

$\text { Applying Bernoullis therom between points just inside and outside hole

$P_0+\frac{20\times 10}{0.5}+1000\times 10\times 0.5=P_0+\frac{1}{2}\times 1000\times V^2$

$[A_1{V}_1=a_1{v}_1\text{from continuity equation}]$

$\Rightarrow 400+5000=500\times V^2$

$\Rightarrow \frac{5400}{500}=v^2\Rightarrow V^2=10.8m/s$

$\Rightarrow V\approx 3.3m/s$