Darcy-Weisbach vs Hazen-Williams
Two ways to calculate pipe pressure drop: the physically general Darcy-Weisbach equation (density, viscosity, Reynolds number, roughness, friction factor) and the empirical Hazen-Williams water-flow formula (C-factor). When each is used, why Hazen-Williams is water-only, and why Darcy-Weisbach is the default for general engineering work.
Definition
Darcy-Weisbach and Hazen-Williams are two methods for estimating pressure drop (or head loss) in a pipe. Darcy-Weisbach is broadly physics-based: it works from the fluid density and viscosity, the Reynolds number, the pipe roughness, and a friction factor, so it applies to any Newtonian fluid in any unit system. Hazen-Williams is an empirical formula tuned specifically to water flowing at ordinary temperatures, in which all of the resistance is bundled into a single roughness coefficient C that depends only on the pipe material and condition.
Why it matters
Choosing the wrong method, or mixing their inputs, is a common source of pressure-drop errors. Hazen-Williams is quick and is entrenched in water-distribution and fire-water practice, where its C-factors are well tabulated. But because it ignores viscosity and is calibrated only for water in turbulent flow, it goes wrong for oils, hot or cold liquids, gases, slurries, or any markedly different fluid. Darcy-Weisbach has no such restriction, which is why it is the default for general process and mechanical engineering. Knowing which assumptions sit behind each formula tells you when a Hazen-Williams answer can be trusted and when it cannot.
Formula
Units involved
- •ΔP — pressure drop in Pa, kPa, bar, or psi
- •h_f — head loss in m or ft of fluid
- •f — Darcy friction factor, dimensionless
- •ρ — density, kg/m³; v — velocity, m/s; μ — viscosity, Pa·s
- •C — Hazen-Williams coefficient, dimensionless (≈ 100–150 for water pipe)
- •Q — volumetric flow, m³/s; D — diameter, m; L — length, m (SI form)
Concept diagram
Worked example
Water flows at Q = 0.05 m³/s through a 200 mm (D = 0.2 m) pipe, 100 m long, with Hazen-Williams C = 130. Estimate the head loss using the Hazen-Williams formula (SI form).
- 01Q^1.852 = 0.05^1.852 = 3.894 × 10⁻³
- 02C^1.852 = 130^1.852 ≈ 8,223
- 03D^4.87 = 0.2^4.87 ≈ 3.941 × 10⁻⁴
- 04Numerator = 10.67 × 100 × 3.894 × 10⁻³ = 4.155
- 05Denominator = 8,223 × 3.941 × 10⁻⁴ = 3.241
- 06h_f = 4.155 / 3.241 = 1.28 m
Head loss ≈ 1.28 m of water over the 100 m run — valid because the fluid is water near ambient temperature.
Common mistakes
- •Applying Hazen-Williams to a non-water fluid (oil, hot water, glycol, gas, slurry) — it has no viscosity term and is calibrated for water only.
- •Treating the C coefficient as interchangeable with a Darcy friction factor or an absolute roughness — they are different quantities and cannot be swapped.
- •Using the SI Hazen-Williams constant (10.67) with US-unit inputs, or vice versa — the numeric constant is unit-system specific.
- •Assuming the two methods must agree exactly; even for water they differ somewhat because Hazen-Williams is empirical and not a function of Reynolds number.
- •Reaching for Hazen-Williams as a universal design rule — for general engineering, Darcy-Weisbach is the correct default.
When to use the calculator
Use the Pipe Pressure Drop calculator (which applies Darcy-Weisbach with an internally computed friction factor) for general fluids and conditions, and the Darcy-Weisbach Pressure Drop calculator when you already have a friction factor. This site does not provide a Hazen-Williams calculator; the formula above is shown for comparison only.