In the figure shown, velocity and pressure of the liquid at cross section 2 respectively are given by (if $P_{0}$ is the atmospheric pressure)

\sqrt{2 h g}, P_{0} + \frac{ρ h g}{2}

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\sqrt{h g}, P_{0} + \frac{ρ h g}{2}

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\sqrt{\frac{h g}{2}}, P_{0} + \frac{3 ρ h g}{4}

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\frac{\sqrt{h g}}{2}, P_{0} + \frac{3 ρ h g}{4}

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Solution

The correct option is C $\sqrt{\frac{h g}{2}}, P_{0} + \frac{3 ρ h g}{4}$
Velocity of the liquid just after coming out of section 3 is
$v_{3} = \sqrt{2 g h}$
Using continuity equation at section '2' and section '3'
$\frac{A}{2} v_{2} = \frac{A}{4} v_{3} v_{2} = \frac{1}{2} v_{3} = \sqrt{\frac{h g}{2}}$
Now using Bernoulli's theorem at section 2 and at the opening end of section 3:
$P_{0} + \frac{1}{2} ρ {v_{3}}_{3}^{2} = P_{2} + \frac{1}{2} ρ {v_{2}}_{2}^{2} P_{2} = P_{0} + \frac{1}{2} ρ ({v_{3}}_{3}^{2} - {v_{2}}_{2}^{2}) = P_{0} + \frac{1}{2} ρ (2 g h - \frac{g h}{2}) P_{2} = P_{0} + \frac{3 ρ g h}{4}$

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In the figure shown, velocity and pressure of the liquid at cross section 2 respectively are given by (if P0 is the atmospheric pressure)

In the figure shown, velocity and pressure of the liquid at cross section 2 respectively are given by (if $P_{0}$ is the atmospheric pressure)