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Accelerating Containers

In the figure...

Question

In the figure, an idea liquid flow through the tube, this is of uniform cross section. The liquid has velocities $v_{A}$ and $v_{B}$ , and pressures $P_{A}$ and $P_{B}$ at the point $A$ and point $B$ , respectively. Then

v_{A} = v_{B}

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v_{A} > v_{B}

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P_{A} > P_{B}

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P_{B} > P_{A}

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Solution

The correct options are
A $v_{A} = v_{B}$
D $P_{B} > P_{A}$
Applying Bernoulli's equation keeping pressure energy and potential energy constant, we get,
$\frac{1}{2} ρ V_{A}^{2} = \frac{1}{2} ρ V_{B}^{2} \Rightarrow V_{A} = V_{B}$
However, with the height difference between points $A$ and $B$ causes a difference in pressure $P_{A} & P_{B}$ where $P_{A} = ρ g h_{A}$ and $P_{B} = ρ g h_{B}$ and since $h_{B} > h_{A} > P_{b} > P_{A}$
where $h =$ depth of point.

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