Solve the implicit Colebrook-White equation for the Darcy-Weisbach friction factor f, with Swamee-Jain comparison and regime classification.
Pipe Networks · FrictionColebrook-White Equation (implicit)
Implicit in f — solved by fixed-point iteration starting from the Swamee-Jain explicit guess.
Special Cases
Swamee-Jain Explicit Approximation
Valid for 3×10³ < Re < 3×10⁸ and 10⁻⁶ < ε/D < 10⁻². Error typically < 3% vs Colebrook-White.
Flow Regime Classification
| Regime | Re range | f formula |
|---|---|---|
| Laminar | < 2 300 | f = 64/Re |
| Transitional | 2 300–4 000 | Unstable — CW result uncertain |
| Smooth turbulent | > 4 000, ε/D≈0 | 1/√f = −2log(2.51/(Re√f)) |
| Transitionally rough turbulent | > 4 000 | Colebrook-White (full form) |
| Fully rough turbulent | > 4 000, Re→∞ | 1/√f = −2log(ε/3.7D) |
Typical Pipe Roughness ε
| Material | ε (m) | ε (mm) |
|---|---|---|
| PVC / glass / drawn tubing | 1.5×10⁻⁶ | 0.0015 |
| Commercial steel | 4.6×10⁻⁵ | 0.046 |
| Galvanized steel | 1.5×10⁻⁴ | 0.15 |
| Cast iron | 2.6×10⁻⁴ | 0.26 |
| Concrete | 1×10⁻³ | 1.0 |