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Question

Water is flowing through a channel (lying in a vertical plane) as shown in the figure. Three sections A,B and C are shown. Section B and C have equal areas of cross- section. If PA,PB and PC are the pressures at A,B and C respectively, then


  1. PA<PB=PC
  2. PA<PB<PC
  3. PA>PB>PC
  4. PA>PB=PC


Solution

The correct option is B PA<PB<PC
Applying Bernoulli's principle and equation of continuity.
Comparing points A and B (the vertical elevation h is same for both),
AAVA=ABVB (equation of continuity)
AA<AB
VA>VB
PA+12ρV2A+ρgh=PB+12ρV2B+ρgh  (Bernoulli's equation)
VA>VB
In accordance with Bernoulli's equation,
12ρV2A>12ρV2B
PA<PB     ...(1)
Now comparing C and B
Area of cross-section AB=AC
VB=VC=V, from equation of continuity
PB+12ρV2+ρghB=PC+12ρV2+ρghC
(Applying Bernoulli's equation between points B and C)
PB+ρghB=PC+ρghC
hB>hC
PB<PC ...(2)
Using Eq.(1) and (2) we get,
PA<PB<PC

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