Physics - Fluid Question with Solution | TestHub

Applying continuity equation at $1$ and $2$, we have

${\mathrm{A}}_1{\mathrm{V}}_1={\mathrm{A}}_2{\mathrm{V}}_2$        .....$\left(\mathrm{i}\right)$

Further applying Bernoulli’s equation at these two points, we have

$$

${\mathrm{P}}_0+\mathrm{pgh}+\genfrac{}{}{0.1ex}{}{1}{2}{\mathrm{pv}}_1^2={\mathrm{P}}_0+0+\genfrac{}{}{0.1ex}{}{1}{2}{\mathrm{pv}}_2^2 \dots \left(\mathrm{ii}\right)$

Solving Eqs. (i) and (ii), we have

${\mathrm{v}}_2^2=\genfrac{}{}{0.1ex}{}{2\mathrm{gh}}{1-\genfrac{}{}{0.1ex}{}{{\mathrm{A}}_2^2}{{\mathrm{A}}_1^2}}$

Substituting the values, we have

${\mathrm{v}}_2^2=\genfrac{}{}{0.1ex}{}{2\times 10\times 2.475}{1-{(0.1)}^2}=50 {\mathrm{m}}^2 {\mathrm{s}}^{-2}$