First slide

Fluid dynamics

Question

Water having density ‘⍴’ is flowing (steadily) downwards in the given tube. What is the relation between P_A & P_B?

Moderate

A

P_A = P_B
B

P_A < P_B
C

P_A > P_B
D

P_A – P_B= ⍴gh

Solution

The fluid speed will be less at B according to the equation of continuity (Av = const).
An intuitive way to think about this problem is that pressure at B has to be greater than that at A as the pressure difference not only has to balance gravity (which is trying to increase its velocity), but also decrease fluid speed. Another way is to use the Bernoulli equation.
P_A + ρgh + 1/2 ρv_A² = P_B + 1/2ρ v_B². A_Av_A = A_Bv_B
P_B – P_A = ρgh + 1/2 ρv_A² – 1/2 ρv_B²—————–(1)
v_B < v_A(because A_B > A_A)
Therefore we can say that R.H.S of equation (1) is positive
which in turn shows that P_B – P_A > 0.

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