A liquid ﬂows through a horizontal tube. The velocities of the liquid in the two sections which have areas of cross-section $A_{1}$ and $A_{2}$ , are $v_{1}$ and $v_{2}$ respectively. The difference in the level of the liquid in the two vertical tubes is h. Then

The volume of the liquid flowing through tube in unit time is

A_{1} v_{1}

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v_{2} - v_{1} = \sqrt{2 g h}

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v_{1}^{2} - v_{1}^{2} = 2 g h

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The energy per unit mass of the liquid is the same in both sections of the tube

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Solution

The correct options are
A The volume of the liquid flowing through tube in unit time is $A_{1} v_{1}$
C $v_{1}^{2} - v_{1}^{2} = 2 g h$
D The energy per unit mass of the liquid is the same in both sections of the tube
$\frac{P_{1}}{ρ} + \frac{v_{1}^{2}}{2} = \frac{P_{2}}{ρ} + \frac{v_{2}^{2}}{2}$
$P_{1} - P_{2} = \frac{ρ}{2} (v_{2}^{2} - v_{1}^{2})$
But $P_{1} - P_{2} = ρ g h = \frac{ρ}{2} (v_{2}^{2} - v_{1}^{2})$
or $v_{2}^{2} - v_{1}^{2} = 2 g h$ .

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A liquid flows through a horizontal tube. The velocities of the liquid in the two sections, which have have areas of cross section $A_{1}$ and $A_{2}$ , are $v_{1}$ and $v_{2}$ respectively. The difference in the levels of the liquid in the two vertical tubes is $h$ . Then :

A liquid flows through a horizontal tube. The velocities of the liquid in the two sections, which have areas of cross-section $A_{1}$ and $A_{2}$ are $v_{1}$ and $v_{2}$ respectively. The difference in the levels of the liquid in the two vertical tubes is $h$ .