Head loss in full-flow conduits: Which named formula is the general, dimensionally consistent relation used across fluids, sizes, and Reynolds numbers?

Introduction / Context:
Estimating head loss in pipes is central to sizing pumps and pipelines. Among various equations, one is broadly applicable to different fluids, diameters, and flow regimes because it uses a friction factor tied to Reynolds number and roughness.

Given Data / Assumptions:

• Steady, incompressible flow in closed conduits running full.
• Commercial pipes with known roughness and diameter.

Concept / Approach:

The Darcy–Weisbach equation: h_f = f * (L/D) * (V^2 / (2g)). The friction factor f is obtained from the Moody chart or correlations (e.g., Colebrook–White), thus accommodating laminar and turbulent regimes and various roughness levels.

Step-by-Step Solution:

Verification / Alternative check:

Handbooks and standards recommend Darcy–Weisbach for accuracy and universality; specialized equations are used only within their calibration limits.

Why Other Options Are Wrong:

• Hazen–Williams/Manning: empirical, limited to certain fluids/conditions.
• Nikuradse: provided roughness/experimental insights, not the standard design head-loss formula.
• Chezy alone: lacks modern friction factor generality.

Common Pitfalls:

• Using Hazen–Williams outside its calibration range.
• Forgetting temperature/viscosity effects when not using Darcy–Weisbach.

Final Answer:

Darcy–Weisbach formula.