Hazen-Williams vs. Darcy-Weisbach: when to use which

Published 2026-05-13

The short answer

Hazen-Williams is the right choice when fluid is water at typical municipal temperatures (40–75 °F / 4–24 °C), flow is fully turbulent, and you want a closed-form answer that fits in a calculator window.
Darcy-Weisbach is the right choice when any of those assumptions don't hold: non-water fluid, hot or cold service, low-Reynolds (laminar or transitional) flow, or any case where physical correctness matters more than computational convenience.

Both equations are correct in their respective regimes. Picking the wrong one isn't catastrophic — for water-only systems they typically agree within 10-15% — but the wrong choice does inject error you don't need to live with.

The two equations

Hazen-Williams (US units, head loss in feet over L feet of pipe):

h_f = 10.67 · L · (Q/C)^1.852 / D^4.87       (SI, h_f in m, Q in m³/s, D in m)
h_f = 0.2083 · (100/C)^1.852 · Q^1.852 / d^4.8655 · (L/100)   (US, Q in GPM, d in inches)

Darcy-Weisbach (any consistent unit system):

h_f = f · (L/D) · (V² / 2g)

The key difference: Hazen-Williams's C is a single empirical constant that bundles roughness + Reynolds-number dependence into one number. Darcy-Weisbach's f is a function of Reynolds number (Re) and relative roughness (ε/D), evaluated by either a graphical Moody chart, an iterative Colebrook-White equation, or an explicit approximation like Swamee-Jain.

Why Hazen-Williams works for water

Hazen-Williams is empirical — fitted to thousands of measurements of water in commercial pipe. It's accurate as long as you stay inside the conditions of the original dataset:

1. Water-only. Other fluids have different viscosities and densities; the C-factor doesn't map. 2. Turbulent flow. Re > ~10⁴. Below that, viscous effects dominate and the empirical fit breaks down. 3. Typical engineering temperatures. Fitted around room-temperature water. Hot or near-freezing water shifts viscosity enough to affect the relationship. 4. Pressure conduits. Not open-channel — that's Manning's territory.

Inside that envelope, H-W is fine. It's the standard choice for distribution mains, force mains, and irrigation. AWWA M22 (water service sizing) uses it. Most municipal water authority standards specify H-W with conservative C-factors.

Why you reach for Darcy-Weisbach

When you step outside the envelope above:

Cold-water service (chillers, ice rinks) where viscosity is significantly higher than 60 °F.
Hot-water service (boiler feed, hydronic heating) where viscosity is lower.
Glycol mixes for freeze protection — substantially different viscosity from water.
Hydrocarbon, refrigerant, or chemical service. H-W's C-factor isn't tabulated for these fluids — there's no single number you could legitimately plug in.
Slurries or viscous fluids where Reynolds drops into transitional or laminar regime at design flow.
Engineering-design contexts where you need to defend the calculation against "but that empirical fit was for water — what about cold-end-of-train conditions where temperature drops?". The answer "I used Darcy-Weisbach with the actual viscosity at design conditions" is harder to argue with than "I used Hazen-Williams with C=130".

In those cases, Darcy-Weisbach with the Swamee-Jain explicit formula gets you the friction factor without iteration:

f = 0.25 / [ log10( ε/(3.7·D) + 5.74/Re^0.9 ) ]^2

valid for 5×10³ ≤ Re ≤ 10⁸ and 10⁻⁶ ≤ ε/D ≤ 10⁻². Within 1% of the iterative Colebrook solution across that range — close enough that nobody iterates anymore.

A side-by-side calculation

250 GPM through 500 ft of 6" PVC pipe, water at 60 °F:

Hazen-Williams with C=150 (PVC):

h_f = 0.2083 · (100/150)^1.852 · 250^1.852 / 6^4.8655 · (500/100)
    ≈ 0.2083 · 0.470 · 27,625 / 6,113 · 5
    ≈ 2.21 ft

Darcy-Weisbach with ε = 5×10⁻⁶ ft (smooth PVC), v ≈ 2.84 ft/s, ν ≈ 1.21×10⁻⁵ ft²/s:

Re = v·D/ν = 2.84 × 0.5 / 1.21×10⁻⁵ ≈ 117,000
ε/D = 5×10⁻⁶ / 0.5 = 1×10⁻⁵
f (Swamee-Jain) ≈ 0.0179
h_f = 0.0179 · (500/0.5) · (2.84² / 64.4) ≈ 2.24 ft

Difference: about 1.5%. For municipal water at room temperature, the two equations agree closely enough that the choice is more about defensibility than accuracy.

Try both calculations →

A cold-water case where they disagree

Same 250 GPM, 500 ft, 6" PVC — but this time 35 °F chilled water. Viscosity at 35 °F is ν ≈ 1.71×10⁻⁵ ft²/s (≈40% higher than 60 °F water).

Hazen-Williams doesn't see the temperature change. Same C=150. Same answer: 2.21 ft.

Darcy-Weisbach:

Re = 2.84 × 0.5 / 1.71×10⁻⁵ ≈ 83,000   (lower Re due to higher viscosity)
f (Swamee-Jain) ≈ 0.0192   (about 7% higher)
h_f ≈ 2.40 ft

Now they differ by 9%. Hazen-Williams is under-predicting head loss because it doesn't know the water is colder. For a chilled-water loop where you're sizing the primary pump's TDH, picking the higher number means the pump still meets duty when you're running at design conditions.

Practical decision tree

Is the fluid water?
├── No  → Darcy-Weisbach.
├── Yes → Is it 40-75°F?
│         ├── No  → Darcy-Weisbach.
│         └── Yes → Is Re > 10⁴ at design flow?
│                   ├── No  → Darcy-Weisbach (or Manning's if open-channel).
│                   └── Yes → Hazen-Williams is fine.

When in doubt, run both. If they agree within 5%, you're inside H-W's comfort zone. If they disagree more, trust Darcy-Weisbach.

C-factor pitfalls

Even when H-W is the right choice, C-factor selection traps engineers:

New-pipe C is not service-life C. A new ductile-iron main might be C=130. After 20 years of municipal water with corrosion + tuberculation, that same main could be C=80. Design with the *aged* C unless you have a flushing/cleaning program.
C-factor shifts with Reynolds. H-W is calibrated around typical flow; at very low or very high Re the apparent C drifts. Most calc tools don't show this drift; you just get a wrong answer with a textbook coefficient.
C is not a material property. It's a property of (material × age × water chemistry × velocity). A C=120 in soft-water service might be C=90 with hard, high-iron water.

The conservative move: pick aged-pipe C (closer to 100 for steel/DI, closer to 140 for PVC/HDPE) and you'll never be embarrassed.

What to do next

1. Decide your fluid + temperature regime. Water at 40–75 °F in commercial pipe? Hazen-Williams is fine. Anything else? Darcy-Weisbach. 2. If Hazen-Williams: pick a defensible C-factor (aged values, not new-pipe brochure numbers). 3. If Darcy-Weisbach: get the actual viscosity at design temperature, compute Re, run Swamee-Jain. 4. If you're unsure, run both. Disagreement >5% is your signal that H-W isn't the right tool here.

Use the calculator's method toggle →

References

Hazen, A., & Williams, G. S. (1933). *Hydraulic Tables.* The original empirical fit.
Colebrook, C. F. (1939). *Turbulent flow in pipes...* The implicit f-equation Swamee-Jain approximates.
Swamee, P. K., & Jain, A. K. (1976). *Explicit equations for pipe-flow problems.* The closed-form approximation everyone uses.
AWWA M22, *Sizing Water Service Lines and Meters.*