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?

Easy

A

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

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

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

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

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,
$P + \frac{1}{2} ρ v^{2} = constant$
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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