How to Find the Darcy Friction Factor: Moody, Colebrook, and Swamee-Jain
The Moody diagram is a picture of the Colebrook-White equation. Laminar shortcut, implicit iteration, explicit fits, and a worked Re–ε/D example.
Key takeaways
- Always compute Re before you touch a Moody chart.
- Laminar: f = 64/Re. Roughness does not matter.
- Colebrook is the industrial standard; Swamee-Jain and Haaland are ~1–2% explicit fits.
- ε is equivalent sand roughness, not a measured peak-to-valley height.
Head loss is easy once you have f. Getting f is the part that trips people: laminar vs turbulent, ε/D, and an implicit log equation that textbooks wave at a Moody chart. This article walks the calculation in the order you should actually do it.
Start with Reynolds number
- Re < 2300 — laminar. f = 64/Re. Roughness does not matter.
- 2300–4000 — transitional. Avoid designing here; f is uncertain and can jump.
- Re > 4000 — turbulent. f depends on Re and ε/D.
Example: V = 1.8 m/s, D = 0.15 m, water 20 °C. Re = 1.8 × 0.15 / 1e-6 = 2.7×10⁵ — firmly turbulent. If you had used 5 °C water, Re ≈ 1.8×10⁵, still turbulent, but f is a little higher.
Open solver: Reynolds number calculatorColebrook-White
f appears on both sides, so you iterate. A good seed is Swamee-Jain; three or four updates usually settle to engineering precision. The Moody chart is simply this equation drawn for families of ε/D.
Explicit approximations
Both stay within about 1–2% of Colebrook over the usual turbulent range. Use them in spreadsheets and network codes. For a reported design value, iterate Colebrook once and cite it.
Open solver: Colebrook / Swamee-Jain / HaalandRoughness catalogue
| Material | ε (mm) | ε (m) |
|---|---|---|
| Drawn tubing / PVC / PE | 0.0015 | 1.5×10⁻⁶ |
| Commercial steel | 0.045 | 4.5×10⁻⁵ |
| Galvanized iron | 0.15 | 1.5×10⁻⁴ |
| Cast iron | 0.26 | 2.6×10⁻⁴ |
| Concrete (smooth to rough) | 0.3–3 | 3×10⁻⁴–3×10⁻³ |
| Corrugated metal | 3–30 | up to 0.03 |
ε is equivalent sand roughness, not a profilometer reading. Biofilm and scale move you up the Moody chart faster than most textbooks admit. Relative roughness is ε/D — a 0.045 mm steel wall on a 1 m main is almost hydraulically smooth; the same wall on a 20 mm tube is not.
Open solver: Water properties and roughness catalogueOpen solver: Interactive Moody diagramFrequently asked questions
f appears inside the log and under a square root. There is no algebraic rearrangement. Iterate from a Swamee-Jain seed; four updates are usually enough.