Head loss due to pipe friction is the most fundamental calculation in design in the water industry, and two methods dominate practice: the empirical Hazen-Williams equation and the theoretically derived Darcy-Weisbach equation. Both are widely implemented in design software and both appear in standards, which makes choosing between them feel like a matter of preference. It is not.
Understanding the strengths and weaknessess of each approach prevents systematic errors in flow rate predictions, pump sizing, and pipeline pressure calculations.
The Darcy-Weisbach equation
Darcy-Weisbach is dimensionally consistent and derived from first principles. It expresses head loss as a function of pipe geometry, flow velocity, and a friction factor that captures the transition between laminar and turbulent flow regimes:
where f = Darcy friction factor (dimensionless)
L = pipe length (m) · D = internal diameter (m)
V = mean flow velocity (m/s) · g = 9.81 m/s²
The friction factor f is determined from the Moody diagram or calculated directly using the Colebrook-White equation, which accounts for both the Reynolds number (flow regime) and relative roughness (ks/D). For fully turbulent flow in rough pipes (most common in water distribution mains) the simplified Moody approximation is used in practice.
Roughness values: Design roughness ks should reflect the pipe material and age. New ductile iron: 0.3 mm. Aged or tuberculated iron: 1.0–3.0 mm. PE and PVC: 0.03 mm. Using new-pipe roughness for a 40-year-old main will significantly overestimate capacity.
The Hazen-Williams equation
Hazen-Williams is an empirical formula developed in the early 20th century to simplify hand calculations for water distribution design. It expresses head loss through a single roughness coefficient C, which bundles pipe material, condition, and implicitly, fluid properties into one number:
where C = Hazen-Williams roughness coefficient
R = hydraulic radius (m) · S = hydraulic gradient (m/m)
Typical C values range from 80 for badly corroded iron to 150 for smooth plastic pipe, with 100 commonly used as a conservative default for aged distribution mains.
Limitation: Hazen-Williams assumes fully turbulent flow in water at approximately 15–20°C. It gives increasingly inaccurate results for low-velocity flow, viscous fluids, non-circular sections, and temperatures significantly outside this range. It should not be used for fluids other than water.
Comparing the two methods
| Property | Darcy-Weisbach | Hazen-Williams |
|---|---|---|
| Theoretical basis | Derived from first principles | Empirical curve fit |
| Fluid applicability | Any Newtonian fluid | Water only |
| Flow regime | Laminar, transitional, turbulent | Turbulent only |
| Temperature sensitivity | Explicit via viscosity in Re | None (implicit in C) |
| Roughness input | ks (absolute roughness, mm) | C (empirical coefficient) |
| Computational complexity | Iterative (Colebrook-White) or explicit (Swamee-Jain) | Direct calculation |
| Typical use in UK practice | Detailed design, pumping mains | Distribution network modelling |
Which should you use?
For detailed hydraulic design, such as pumping main sizing, pressure loss across fittings, or any situation where fluid temperature or flow regime may vary, Darcy-Weisbach is the correct choice. The Colebrook-White friction factor approach is specified in several UK water industry standards (BS EN 805:2000, IGN 4-01-03) for this reason.
Hazen-Williams remains valid and useful for water distribution network modelling where C values have been calibrated against field measurements, and where the convenience of a single roughness coefficient outweighs the need for physical rigour. Most network modelling packages (WaterGEMS, InfoWorks WS) support both methods; Hazen-Williams is often the default because it was historically easier to calibrate.
The practical difference in head loss prediction between calibrated Hazen-Williams (C = 100) and Darcy-Weisbach (ks = 0.6 mm) for a 300 mm main at 1.0 m/s is typically under 5%. The risk of error is highest at the extremes: low-velocity trunk mains where laminar effects become relevant, and high-velocity emergency bypass pipework.
Key takeaways
- Use Darcy-Weisbach for pumping mains, detailed design, and any non-water fluid.
- Hazen-Williams is acceptable for calibrated distribution network models where C values reflect field conditions.
- Never use Hazen-Williams for laminar flow, elevated temperatures, or fluids other than water.
- Roughness values should reflect pipe age and condition — not new-pipe manufacturer data.
- Both methods are implemented in the draw engineering Pipe Head Loss calculator.