Free · Physics models
Turbulent Pipe Friction Factor Approximation
Estimate the Darcy friction factor for turbulent pipe flow from Reynolds number and relative roughness.
- Formula & worked example
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Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
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Formula and method
Reynolds number = 100000.00; Roughness relative = 0.0010000000; friction = 0.022589779.
fD ≈ 0.0055[1+(20000 ε/D + 10⁶/Re)¹ᐟ³]; Re = ρvD/μ.
Worked example
Enter these known values and leave the other values blank.
- Hydraulic diameter (D)
- 0.1 m
- Surface roughness (k)
- 0.0001 m
- Density (ρ)
- 1000 kg/m³
- Velocity (V)
- 1 m/s
- Dynamic viscosity (μ)
- 0.001 Pa⋅s
- Reynolds number (Re)
- 100000
- Friction factor (f)
- 0.02259
- Relative roughness (k/D)
- 0.001
Assumptions and limitations
- Estimate the Darcy friction factor for turbulent pipe flow from Reynolds number and relative roughness.
- This explicit empirical approximation is not an iterative Colebrook solution. Its retained domain is 4000 < Re < 5×10⁸ and 0 < ε/D < 0.01.
- Use dynamic viscosity and hydraulic diameter with a mean positive flow speed. The result is Darcy factor, four times the Fanning factor; entrance and minor losses are excluded.
- Inputs and inverse outputs share the displayed unit selectors. Clear a known field to solve for it, and lock quantities that must remain fixed. Singular inverses may have no finite result.
Common questions
Can I use it for laminar flow?
No. For fully developed laminar flow in a circular pipe, Darcy factor is 64/Re.
Is this Fanning factor?
No. Divide the Darcy result by four for the Fanning convention.
References
Estimate the Darcy friction factor for turbulent pipe flow from Reynolds number and relative roughness. This explicit empirical approximation is not an iterative Colebrook solution. Its retained domain is 4000 < Re < 5×10⁸ and 0 < ε/D < 0.01. Use dynamic viscosity and hydraulic diameter with a mean positive flow speed. The result is Darcy factor, four times the Fanning factor; entrance and minor losses are excluded.