Colebrook Equation Calculator — Darcy Friction Factor
Calculate the Darcy-Weisbach friction factor (λ) for turbulent flow in pipes using the Colebrook-White equation. Supports Reynolds number or velocity-based input.
💧 Colebrook-White Friction Factor Calculator
The Colebrook equation is the most widely used implicit formula for calculating the Darcy friction factor in turbulent pipe flow. It combines the smooth-pipe and rough-pipe asymptotes into a single expression valid for the entire turbulent regime (Re > 4000).
where:
λ = Darcy friction factor (dimensionless)
Re = Reynolds number
ε = absolute roughness of pipe surface (m or ft)
D = hydraulic diameter (m or ft)
Input: Reynolds Number
Input: Velocity & Kinematic Viscosity
📊 Result
Darcy Friction Factor (λ):
—
dimensionless
About the Colebrook Equation
Published in 1939 by Cyril Colebrook and Cedric White, this equation is an implicit correlation that fits experimental data for friction factors in both smooth and rough pipes. Because λ appears on both sides of the equation, it must be solved iteratively. This calculator uses the Newton-Raphson method for fast convergence.
Common Pipe Roughness Values
| Pipe Material | Roughness ε (mm) | Relative Roughness (ε/D) for 100mm pipe |
|---|---|---|
| Drawn tubing (glass, copper) | 0.0015 | 0.000015 |
| Plastic (PVC, PE) | 0.001–0.007 | 0.00001–0.00007 |
| Commercial steel | 0.045 | 0.00045 |
| Galvanized iron | 0.15 | 0.0015 |
| Cast iron | 0.26 | 0.0026 |
| Concrete | 0.3–3.0 | 0.003–0.03 |
| Riveted steel | 0.9–9.0 | 0.009–0.09 |
Frequently Asked Questions
The friction factor λ appears on both sides of the equation — inside the logarithm and as the quantity being solved for. This means it cannot be rearranged into a direct formula and must be solved iteratively. The explicit Swamee-Jain equation is a common approximation.
The Colebrook equation is valid for turbulent flow only, typically Re > 4000. For laminar flow (Re < 2100), use λ = 64/Re. The transitional zone (2100–4000) is unpredictable.
The Darcy friction factor (λ) is 4 times the Fanning friction factor (f). The Colebrook equation gives the Darcy factor. Always check which one your pressure drop formula uses: ΔP = λ·(L/D)·(ρu²/2) for Darcy.
Yes — use the hydraulic diameter Dₕ = 4A/P (where A is cross-sectional area and P is wetted perimeter) instead of the actual diameter. This is a good approximation for turbulent flow.