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Q.

Which one of the following statements is correct? When a fluid passes through the narrow part of non-uniform pipe,

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a

its velocity increases but its pressure decreases

b

its velocity and pressure both increase

c

its velocity decreases but its pressure increases

d

its velocity and pressure both decrease

answer is D.

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Detailed Solution

Consider two points A and B in the pipe at the same horizontal level. At point A, let a1 be the area of cross-section of the pipe, v1 the velocity of fluid flow and p1 the fluid pressure. Let a2,v2 and p2 be the corresponding quantities at point B. Then from Bernoulli's theorem, we have
p1+12ρv12=p2+12ρv22  or  p1-p2=12ρv22-v12            (i)
If a2<a1, it follows from continuity equation a1v1=a2v2,  that  v1>v2.

From Eq. (i), it follows that p2<p1. Hence, at the narrow part of the pipe, the fluid velocity increases but its pressure decreases, which is choice (4).

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Which one of the following statements is correct? When a fluid passes through the narrow part of non-uniform pipe,