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 PA<PB=PCPA<PB<PCPA>PB>PCPA>PB=PC

Solution

## The correct option is B PA<PB<PCApplying 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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