Hazen-Williams vs Darcy-Weisbach — when to use which
Hazen-Williams is empirical, water-only, and one closed-form expression. Darcy-Weisbach is physically grounded, fluid-agnostic, and iterative. Here's how to pick.
If you've spent any time sizing pipes you've met both equations. They produce similar numbers in their shared validity envelope and very different ones outside it. The short version: use Hazen-Williams for cold-water plumbing and irrigation; use Darcy-Weisbach for everything else.
The two equations, side by side
Hazen-Williams bundles roughness, viscosity, and a great deal of empirical curve-fit into a single coefficient C and one closed-form expression. No iteration. The exponents (1.852 on Q, 4.87 on d) are dimensionally odd because the equation isn't physically derived; it was fit to experimental data on commercial water mains in the 1900s.
Darcy-Weisbach is physically derived. The friction factor f depends on Reynolds number and relative roughness ε/D and requires iteration in the turbulent regime (Colebrook) or an explicit approximation (Haaland, Swamee-Jain). It works for any fluid given (ρ, μ).
Where they agree
Hazen-Williams was tuned for water around room temperature in commercial-grade pipes. In that envelope (Reynolds 10⁴–10⁷, water at 10–25 °C, smooth-to-medium roughness), the two equations agree to within roughly 5%. AWWA, ASPE, and IPC plumbing standards explicitly accept Hazen-Williams here.
Where they disagree
- Hot or cold water far from 20 °C. Water viscosity drops ~6× from 0 °C to 100 °C. Hazen-Williams's bundled C doesn't know about temperature; Darcy-Weisbach uses ν explicitly.
- Non-water fluids. Hazen-Williams is calibrated to water and isn't valid for glycol, oil, brine, or any other fluid.
- Laminar regime (Re < 2,300). Hazen-Williams's exponents misbehave in laminar flow. Darcy-Weisbach has the exact f = 64/Re solution.
- Very rough pipes. Hazen-Williams handles aged cast iron with a low C, but at very high ε/D the empirical fit becomes unreliable.
| Hazen-Williams | Darcy-Weisbach | |
|---|---|---|
| Form | Empirical, single expression | Physically derived, iterative |
| Fluid | Water only | Any Newtonian fluid |
| Temperature | ~10–25 °C, bundled into C | Any (handles ν explicitly) |
| Speed | Closed-form | ~6 Colebrook iterations |
| Code support | AWWA, ASPE, IPC | ASHRAE, Crane TP-410, fluid-mechanics texts |
| Use when | Domestic + irrigation cold water | Anything else |
Worked example: 100 ft of 2" copper at 50 GPM, 20 °C water
The flagship calculator gives:
Hazen-Williams (C = 140): head loss = 5.23 ft Darcy-Weisbach (ε = 1.5 µm, ν from NIST): head loss = 5.04 ft Δ ≈ 4%.
Inside the envelope, agreement is good. Now repeat at 80 °C:
Hazen-Williams: 5.23 ft (unchanged — it doesn't know about temperature) Darcy-Weisbach: 4.27 ft (lower viscosity → lower friction). Δ ≈ 22%.
At elevated temperature Hazen-Williams oversizes the friction. For a chiller-loop or hot-water retrofit, that's a real error you can avoid by switching to Darcy-Weisbach.
So why does anyone still use Hazen-Williams?
Convention and convenience. AWWA standards still spec it. ASPE design tables are built around C values. Most municipal water-main capacity calcs are stored in Hazen-Williams form. And in 1905 when there was no calculator, "look up C in a table and apply one expression" beat "iterate Colebrook by hand". The math hasn't changed in 120 years; what's changed is the cost of iteration.
Open the tools
- Hazen-Williams calculator — with material C-factor library and aged-pipe toggle
- Darcy-Weisbach calculator — Colebrook / Haaland / Swamee-Jain side-by-side
- Flagship pressure-drop calculator — multi-segment, fitting-aware, temperature-adjusted