GATE 2017 ME (ME1) – Question 16

Fluid Mechanics · Control-volume analysis of mass, momentum and energy · 1 mark · Multiple choice

For steady viscous incompressible flow through a constant-diameter circular pipe, the fully developed mean velocity is constant. Which statement about mean velocity in the developing region is true?

It increases until flow is fully developed.
It is constant and equals the fully developed mean velocity.
It decreases until flow is fully developed.
It is constant but always lower than the fully developed mean velocity.

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Show answer and explanation

Correct answer: (B) It is constant and equals the fully developed mean velocity.

Explanation

Steady incompressible continuity fixes the volume flow $Q$ through every cross-section. Since the pipe area A is constant, the cross-sectional average $\overline V=Q/A$ is unchanged. The velocity profile develops, but this does not change its average. Thus B.

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