Question

In the figure shown the velocity and pressure of the liquid at the cross section $\left(2\right)$ are given by (If $p_0$ is the atmospheric pressure)

• A. $\sqrt{2hg},p_0+\frac{\rho hg}{2}$
• B. $\sqrt{hg},p_0+\frac{\rho hg}{2}$
• C. $\sqrt{\frac{hg}{2}},p_0+\frac{3\rho hg}{4}$
• D. $\frac{\sqrt{hg}}{2},p_0+\frac{5\rho hg}{4}$

Answer 1

The correct option is C $\sqrt{\frac{hg}{2}},p_0+\frac{3\rho hg}{4}$

Applying Bernouli's equation between A and B

$P_0+\rho gh+\frac{1}{2}(0{)}^2=P_0+\rho g(0)+\frac{1}{2}\rho V_S^2\Rightarrow V_3=\sqrt{2gh}$

Applying equation of continuity between Band C-

$\frac{A}{2}{V}_2=\frac{A}{4}\sqrt{2gh}\Rightarrow V_2=\sqrt{\frac{gh}{2}}$

Appplying Bernouli's equation between B and C

$P_0+\rho g\left(0\right)\frac{1}{2}\rho V_3^2=P_2+\rho g\left(0\right)+\frac{1}{2}\rho V_2^2{P}_0+\frac{1}{2}\rho \left(2gh\right)=P_2+\frac{1}{2}\rho \frac{gh}{2}{P}_0-\frac{1}{4}\rho gh+\rho gh=P_2{P}_2=P_0+\frac{3\rho gh}{4}$