Calculate the Darcy friction factor from the Colebrook equation using pipe roughness, diameter and Reynolds number, or solve in reverse for any missing input.
Related Calculators
- Siphon Flow Rate Calculator
- Filter Pressure Drop Calculator
- Pump Shaft Power Calculator
- Velocity To Pressure Calculator
- All Physics Calculators
Colebrook Equation Formula
The Colebrook equation estimates the Darcy friction factor for turbulent flow in a pipe. The calculator solves for the friction factor by iteration using the pipe roughness, pipe diameter, and Reynolds number.
For numerical solving, the equation can be rearranged into a root-finding form:
- f = Darcy friction factor, dimensionless
- ฮต = absolute roughness of the pipe wall
- D = inside pipe diameter
- Re = Reynolds number, dimensionless
- log10 = base-10 logarithm
The calculator converts the roughness and diameter inputs to meters before solving. Reynolds number and friction factor are dimensionless, so they do not need unit conversion.
Select the desired result and enter the displayed known values. For friction factor, supply roughness, diameter and Reynolds number; alternatively compute Reynolds number from velocity and kinematic viscosity. Inverse modes use the same equation. Colebrook results are restricted here to Re โฅ 4,000 and ฮต/D โค 0.05; transition is uncertain. Zero roughness is permitted except when solving diameter at fixed Re, where it is indeterminate.
Typical Pipe Roughness Values
Absolute roughness depends on pipe material, age, and condition. The values below are common reference ranges for clean commercial pipe.
| Pipe material | Typical absolute roughness ฮต | Meters |
|---|---|---|
| Drawn tubing, copper, brass, plastic | 0.0015 mm | 0.0000015 m |
| Commercial steel | 0.045 mm | 0.000045 m |
| Galvanized iron | 0.15 mm | 0.00015 m |
| Cast iron | 0.26 mm | 0.00026 m |
| Concrete | 0.3 mm to 3.0 mm | 0.0003 m to 0.003 m |
Flow Regime and Friction Factor Use
The Colebrook equation is intended for turbulent pipe flow. Check the Reynolds number before relying on the result.
| Reynolds number range | Flow regime | Friction factor note |
|---|---|---|
| Re < 2,300 | Laminar | Use f = 64 / Re instead of Colebrook. |
| 2,300 to 4,000 | Transitional | Results can be uncertain because flow may switch behavior. |
| Re > 4,000 | Turbulent | Colebrook is commonly used for Darcy friction factor. |
Example Problems
Example 1: Commercial steel pipe
Suppose you have a commercial steel pipe with:
- Absolute roughness: ฮต = 0.045 mm
- Diameter: D = 100 mm
- Reynolds number: Re = 100,000
Substitute into the Colebrook equation:
Solving iteratively gives:
f โ 0.02012
Example 2: Smoother pipe at high Reynolds number
Suppose you have:
- Absolute roughness: ฮต = 0.0015 mm
- Diameter: D = 50 mm
- Reynolds number: Re = 200,000
Convert the length values to meters:
- ฮต = 0.0000015 m
- D = 0.05 m
Then solve:
The resulting Darcy friction factor is approximately:
f โ 0.01588
FAQ
Is the Colebrook friction factor the Darcy or Fanning friction factor?
The Colebrook equation gives the Darcy friction factor. The Fanning friction factor is one-fourth of the Darcy friction factor:
If another equation or reference uses Fanning friction factor, do not mix it directly with a Darcy friction factor result.
Why does the Colebrook equation need iteration?
The friction factor appears on both sides of the equation, including inside a square root and a logarithm. Because of that, it cannot be solved directly with simple algebra. An iterative method starts with a guess for f, checks the equation, updates the guess, and repeats until the value changes very little.
Can you use the Colebrook equation for laminar flow?
No. For laminar pipe flow, use:
The Colebrook equation is used for turbulent flow, usually when Re is greater than about 4,000. For transitional flow, the result is less reliable because the flow is not fully laminar or fully turbulent.
