Questions: Pipe Roughness: Absolute and Relative Effects on Friction

Question 1

Two pipes carry the same fluid at the same fully turbulent flow rate. Pipe A has diameter 50 mm and Pipe B has diameter 500 mm. Both are made of the same material with identical absolute roughness ε = 0.5 mm. Which pipe has the higher friction factor?

• A. Pipe B (500 mm), since larger pipes have more total surface area in contact with the fluid
• B. They have identical friction factors, since absolute roughness ε is the same for both
• C. Pipe A (50 mm), since it has higher relative roughness (ε/D = 0.01 vs. 0.001)
• D. Pipe A (50 mm), since smaller pipes inherently have higher flow resistance at any roughness

Answer: (C)

The friction factor in turbulent flow depends on relative roughness ε/D, not absolute roughness ε alone. Pipe A has ε/D = 0.5/50 = 0.01, while Pipe B has ε/D = 0.5/500 = 0.001 — a tenfold difference. On the Moody chart, Pipe A traces a much higher friction factor curve. Option B is the classic misconception: same material does not mean same friction factor unless the diameters match, because the roughness bumps loom much larger relative to the flow channel in the smaller pipe.

Question 2

A pump engineer is designing a system for very low flow velocity (well within the laminar or smooth-turbulent regime). The pipe is made of a rough material. Which statement best describes the effect of pipe roughness in this regime?

• A. High roughness always increases the friction factor, regardless of the flow regime
• B. In the hydraulically smooth regime, roughness projections are submerged within the viscous sublayer and have little effect on friction
• C. Relative roughness is irrelevant at low Reynolds numbers; only absolute roughness matters
• D. The pipe behaves as fully rough once any roughness is present, so friction is independent of Re

Answer: (B)

The viscous sublayer — the thin laminar layer adjacent to the wall — thickens as Reynolds number decreases. When the sublayer is thicker than the roughness height ε, the bumps are fully submerged and do not disrupt turbulent flow. The pipe is hydraulically smooth, and friction depends only on Re (not ε). This is the left portion of the Moody chart. Roughness only matters once the sublayer shrinks below ε, which happens at higher Re. Option A confuses the fully rough regime behavior with all regimes.

Question 3

In the fully rough turbulent regime of pipe flow, increasing the flow velocity (and thus Reynolds number) does not change the friction factor.

• T. True
• F. False

Answer: True

This is a key result from the Moody chart. When Re is large enough that the viscous sublayer is negligibly thin compared to ε, the roughness elements protrude fully into the turbulent core and generate eddies whose magnitude is independent of viscosity. Friction losses are then proportional to velocity squared, meaning the friction factor — defined as the ratio of head loss to velocity head — becomes constant. On the Moody chart, the fully rough curves are horizontal at large Re. The friction factor depends only on ε/D in this regime.

Question 4

A pipe with a larger absolute roughness value (ε) will generally have a higher friction factor than a pipe with a smaller ε, regardless of pipe diameter.

• T. True
• F. False

Answer: False

Friction factor in turbulent flow is governed by relative roughness ε/D, not absolute roughness ε. A large-diameter pipe with high absolute roughness can have a lower friction factor than a small-diameter pipe with low absolute roughness if its relative roughness is smaller. For example, a 1000-mm pipe with ε = 1 mm (ε/D = 0.001) will have a lower friction factor than a 20-mm pipe with ε = 0.1 mm (ε/D = 0.005). The physical reason is that what matters is how large the bumps are relative to the flow channel, not their absolute size.

Question 5

Explain why engineers use relative roughness (ε/D) rather than absolute roughness (ε) alone when predicting friction losses in turbulent pipe flow.

Model answer: The friction losses in turbulent pipe flow depend on how large the roughness elements are relative to the flow channel diameter, not on their absolute size. A roughness height of 0.1 mm creates much more disruption in a 10-mm pipe (ε/D = 0.01) than in a 100-mm pipe (ε/D = 0.001), because in the small pipe the bumps occupy a much larger fraction of the cross-section and cause more severe disturbance to the velocity profile. Relative roughness captures this scaling; absolute roughness alone does not.

The physical mechanism reinforces this: in the fully rough regime, the friction factor depends only on the ratio of roughness height to pipe diameter because the eddies generated by roughness elements scale with ε, while the mean flow scales with D. When ε/D is small, roughness effects are minor; when ε/D is large, they dominate. This is why the Moody chart plots friction factor against both Re and ε/D — both parameters matter, and ε alone tells you nothing without knowing D.