A fluid is in streamline flow across a horizontal pipe of variable area of cross section. For this which of the following statements is correct?

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The velocity is maximum at the narrowest part of the pipe and pressure is maximum at the widest part of the pipe.

Velocity and pressure both are maximum at the narrowest part of the pipe.

Velocity and pressure both are maximum at the widest part of the pipe.

The velocity is minimum at the narrowest part of the pipe and the pressure is minimum at the widest part of the pipe.

answer is A.

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Detailed Solution

According to equation of continuity, A v=constant Therefore, velocity is maximum at the narrowest part and minimum at the widest part of the pipe. According to Bernoulli's theorem for a horizontal pipe,P+12ρv2= constant Hence, when a fluid flow across a horizontal pipe of variable area of cross-section its velocity is maximum and pressure is minimum at the narrowest part and vice versa.

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