Darcy-Weisbach vs Hazen-Williams: Which Head-Loss Equation Should You Use?
Darcy-Weisbach is the general friction formula. Hazen-Williams is a water-only shortcut. Here is when each one is valid, a worked comparison, and how they connect through f.
Key takeaways
- Darcy-Weisbach works for any Newtonian fluid once f is known.
- Hazen-Williams hides viscosity and is fitted on cool turbulent water.
- The two formulas scale differently with velocity (V² vs V^1.85).
- Never mix the US 1.318 constant with SI metres.
Two formulas dominate pipe-friction homework and water-network models: Darcy-Weisbach and Hazen-Williams. They answer the same question — how much head do you lose along a pipe — but they are not interchangeable. Choosing the wrong one is one of the most common sources of silent error in student work and in poorly documented GIS models.
Darcy-Weisbach is the general law
The friction factor f comes from Reynolds number and relative roughness ε/D. In laminar flow f = 64/Re exactly (Hagen–Poiseuille). In turbulent flow you iterate Colebrook-White or read a Moody diagram. That extra step is the price of a formula that still works for oil, glycol, air at low Mach, and hot water.
Worked sketch: D = 0.2 m, L = 100 m, V = 2 m/s, f = 0.02. Then h_f = 0.02 × (100/0.2) × 4 / (2 × 9.81) = 2.04 m. For water, ΔP ≈ 20 kPa. Change V to 3 m/s and the loss jumps by (3/2)² = 2.25, not by 1.5.
Open solver: Darcy-Weisbach calculatorHazen-Williams is a water shortcut
Hazen-Williams was fitted on water near 15 °C in turbulent pipes. It hides viscosity: there is no Reynolds number. That is convenient for municipal models and fire-flow spreadsheets, and dangerous for anything else. C = 150 for new PVC is not a viscosity correction; if the water is 4 °C or the fluid is not water, the answer drifts.
| Material / condition | Typical C | Notes |
|---|---|---|
| New PVC / PE | 140–150 | Smooth; C falls as slime builds |
| New cement-lined DI | 130–140 | Common distribution default |
| Unlined CI, moderate tuberculation | 100–110 | Field-test before you trust it |
| Old tuberculated CI | 60–80 | Hazen-Williams is optimistic if you leave C = 130 |
Side-by-side comparison
| Item | Darcy-Weisbach | Hazen-Williams |
|---|---|---|
| Fluids | Any Newtonian | Water only |
| Temperature | Through μ(T) and ρ(T) | Assumed ~15 °C |
| Laminar flow | Exact (f = 64/Re) | Not valid |
| Velocity scaling | h ∝ V² | h ∝ V^1.85 |
| Roughness input | ε (mm) + Re | Single C |
| Best use | Pumps, oil, HVAC, academia | Water networks with tested C |
A practical rule
- Water distribution, 10–25 °C, turbulent, C from a trusted table → Hazen-Williams is acceptable.
- Any other fluid, temperature swing, laminar or transitional flow, or academic work → Darcy-Weisbach.
- If you already have f from Colebrook or Moody, stay with Darcy. Do not convert to C unless a code demands it.
- Fire-flow models that were calibrated in C should stay in C, or you will break the calibration.
How they connect through f
Equating the two head-loss expressions at one Q gives an equivalent Darcy f. That f is a snapshot. Because Hazen-Williams is V^1.85 and Darcy is V², a pipe that “matches” at 20 L/s will not match at 50 L/s. Pump-system curves, water hammer, and variable-speed stations should start from Darcy.
Open solver: Colebrook-White friction factorOpen solver: Moody diagramFrequently asked questions
No. C was calibrated on water. Use Darcy-Weisbach with a Reynolds number and roughness for any other fluid, or for water far from 10–25 °C.