Consider fully developed laminar flow in a circular pipe of a fixed length:

1) The friction factor is inversely proportional to Reynolds number

2) The pressure drop in the pipe is proportional to the average velocity of the flow in the pipe

3) The friction factor is higher for a rough pipe as compared to a smooth pipe

4) The pressure drop in the pipe is proportional to the square of average of flow in the pipe.
Which of the above statements are correct?

Question

Question

This question was previously asked in

ESE Mechanical 2016 Paper 1: Official Paper

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Answer 1

Explanation

Friction factor of laminar flow and turbulent flow is given as,

\(for\;Laminar\;flow,\;f = \frac{{64}}{{Re}}\)

∴ The friction factor is inversely proportional to Reynold's Number

\(for\;Turbulent\;flow,\;f = \frac{{0.316}}{{R{e^{1/4}}}}\)

The pressure drop in a fully developed laminar flow through pipe is given as,

\(\Delta P = \frac{{32\mu {V_{mean}}L}}{{{D^2}}}\)

∴ ΔP is proportional to mean velocity or average velocity in pipe.

In laminar flow, the friction factor is independent of roughness because boundary layer covers the roughness.