Darcy-Weisbach friction factor via Moody chart correlations. Laminar: f = 64/Re · Turbulent: Swamee-Jain approximation of Colebrook-White.
Fluid Mechanics IIOptional — compute ε/D from pipe material & diameter (auto-fills Relative roughness above)
Laminar flow (Re < 2 300):
Turbulent flow — Swamee-Jain approximation:
Valid for 10⁻⁶ ≤ ε/D ≤ 10⁻², 5 000 ≤ Re ≤ 10⁸. Error within ±3% of Colebrook-White.
Exact implicit form (Colebrook-White):
Requires iteration (3–10 passes from a Swamee-Jain starting guess).
Flow regime classification:
| Regime | Re range | Formula |
|---|---|---|
| Laminar | < 2 300 | f = 64/Re |
| Transitional | 2 300 – 4 000 | Uncertain — avoid if possible |
| Turbulent | > 4 000 | Colebrook-White / Swamee-Jain |
Common pipe roughness ε:
| Material | ε (mm) |
|---|---|
| Drawn tubing / PVC / Glass | 0.0015 |
| Commercial steel | 0.046 |
| Welded steel | 0.046 |
| Galvanized iron | 0.15 |
| Cast iron | 0.26 |
| Concrete (smooth) | 0.3 |
| Riveted steel | 2 |
Where: