First slide

Fluid dynamics

Question

In a vertical tube of variable cross section water is flowing as shown in figure. If p₁ and p₂ be respectively, then

Moderate

A

p₁ can never be equal to p₂
B

p₁ may be equal to p₂
C

p₂ is always greater than p₁
D

both 1 and 2 are right

Solution

By Bernoulli's equation
$p_{1} + \frac{1}{2} {ρv}_{1}^{2} = p_{2} + \frac{1}{2} {ρv}_{2}^{2} + ρgh \Rightarrow p_{1} - p_{2} = \frac{1}{2} ρ (v_{2}^{2} - v_{1}^{2}) + ρgh$
By continuity equation, $V_{1} > V_{2}$ . So the quantity $\frac{1}{2} ρ (v_{2}^{2} - v_{1}^{2})$ is always negative. So for some value of ‘h , $(p_{1} - p_{2})$ is zero.

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