Question

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

• A. $1.3m{s}^{-1}$
• B. $3.3m{s}^{-1}$
• C. $5.3m{s}^{-1}$
• D. $7.3m{s}^{-1}$

Answer 1

The correct option is B $3.3m{s}^{-1}$

Applying Bernoullis therom across point (1) and (2),
$P_0+\frac{20\times 10}{0.5}+1000\times 10\times 0.5=P_0+\frac{1}{2}\times 1000\times V^2$
[$A_1{V}_1=a_1{v}_1$ from continuity equation]
$\Rightarrow 400+5000=500\times V^2$
$\Rightarrow \frac{5400}{500}=v^2\Rightarrow V^2=10.8m/s$
$\Rightarrow V\approx 3.3m/s$