Hydraulic roughness criteria: Two pipes are said to have the same hydraulic roughness when which dimensionless parameter is equal for the two pipes?

Introduction / Context:
In turbulent pipe flow, the friction factor depends on Reynolds number and roughness effects. Properly characterizing hydraulic roughness is key to using the Moody chart and Colebrook–White equation for pressure drop calculations.

Given Data / Assumptions:

• Commercial pipes with uniformly distributed roughness height k.
• Same flow regime comparison (turbulent).
• Focus on geometric similarity of roughness effect.

Concept / Approach:
Hydraulic roughness impact on friction scales with the nondimensional parameter k/D, known as relative roughness. Two pipes with the same k/D plot along the same family of curves on the Moody chart, yielding comparable friction behavior at the same Reynolds number. Absolute roughness alone is insufficient because diameter D also influences the effect of roughness on flow.

Step-by-Step Solution:

Verification / Alternative check:
On the Moody chart, lines of constant k/D overlay friction factor behavior; identical k/D aligns pipes to identical roughness curves.

Why Other Options Are Wrong:

• Absolute roughness: Different diameters would yield different ε and different friction behavior.
• Friction coefficient equality: This depends on both Re and k/D; equality at one Re does not define hydraulic roughness generically.
• All (a), (b) & (c): Overbroad; only relative roughness is the defining equality.

Common Pitfalls:
Using absolute roughness tables without accounting for pipe diameter; misreading Moody chart scales or regimes (hydraulically smooth vs fully rough).

Final Answer:
relative roughness