How does pipe roughness affect the friction factor and head loss?

• A. Higher roughness increases friction factor in turbulent flow, leading to greater head loss for a given length and diameter.
• B. Higher roughness decreases friction factor.
• C. Roughness only affects minor losses, not friction factor.
• D. Roughness has no effect on head loss.

Answer: (A)

In turbulent flow, the friction factor f depends on both the Reynolds number and the relative roughness ε/D. Increasing wall roughness makes the flow interact more with the pipe surface, stirring up more turbulence near the wall and increasing energy dissipation. Since head loss in the Darcy-Weisbach equation is h_f = f (L/D) (V^2/2g), a higher friction factor directly raises the frictional head loss for fixed length and diameter (and a fixed flow rate). So rougher pipes require more energy to push the same flow through the same length, resulting in greater head loss.

Note that in laminar flow the friction factor is determined only by Re (f = 64/Re) and roughness has no effect, but in typical hydraulic situations where turbulence dominates, roughness clearly increases f and thus head loss. The other statements conflict with this behavior because roughness does influence major, not just minor, losses, and it does not reduce the friction factor.