Choose an input mode, set pipe roughness, and select a correlation. The layout adapts: three columns on large screens, two on medium, one on mobile.
These sample cases use the Haaland approximation to illustrate typical values.
| Re | ε/D | Correlation | f (Darcy) |
|---|---|---|---|
| 100000 | 0.000200 | Haaland | 0.018735 |
| 200000 | 0.002000 | Haaland | 0.024253 |
| 5000000 | 0.010000 | Haaland | 0.037991 |
Flow-rate mode: v = Q / A, with A = π·D²/4, then compute Re.
Turbulent (Colebrook–White): 1/√f = −2·log10( (ε/D)/3.7 + 2.51/(Re·√f) ).
Explicit options: Swamee–Jain, Haaland, and Blasius (smooth pipe).
- Select an input mode: direct Re, velocity-based, or flow-rate-based.
- If computing Re, enter diameter and viscosity values.
- Set pipe roughness as ε/D, or enter ε with diameter.
- Choose a turbulent correlation for your application.
- Click Calculate to view results above the form.
- Use the CSV/PDF buttons to export your inputs and results.
1) Why the Darcy friction factor matters
In internal pipe flow, head loss scales with the Darcy factor f. Using Darcy–Weisbach, pressure drop rises linearly with f, pipe length, and velocity squared. A small friction factor error can shift pump sizing and energy cost estimates.
2) Reynolds number and regime boundaries
Re compares inertial and viscous effects. Laminar flow occurs below about 2300, where f follows 64/Re. Between 2300 and 4000, the flow is transitional and sensitive to disturbances. Above 4000, turbulent behavior dominates and roughness becomes important.
3) Relative roughness and its influence
Pipe roughness is captured by ε/D. Smooth pipes approach lower f values at high Re, while rough pipes maintain higher resistance. Typical ε for commercial materials ranges from a few micrometers to hundreds of micrometers, which can noticeably change ε/D for small diameters.
4) Colebrook–White as the reference model
The Colebrook–White equation is widely treated as a benchmark for turbulent flow in full pipes. It is implicit in f, so this calculator solves it iteratively. Iteration usually converges rapidly when starting from an explicit estimate, giving stable results across common Re and ε/D ranges.
5) When explicit formulas are practical
Explicit correlations avoid iteration and are convenient for spreadsheets and embedded systems. Haaland and Swamee–Jain approximate Colebrook well for many engineering cases. Blasius is intended for smooth pipes and moderate Reynolds numbers, so it should not be used when roughness is significant.
6) Typical friction factor ranges
For turbulent flow, Darcy friction factor often falls between about 0.008 and 0.08, depending on Re and ε/D. Very smooth, high-Re conditions can reach the lower end. Rougher pipes and lower turbulent Reynolds numbers push f upward, increasing pressure losses. For clean steel water pipes, f near 0.02 is typical.
7) Data sensitivity for design calculations
Because head loss scales with f·v², uncertainty in roughness, diameter, or velocity can dominate. Measuring internal diameter precisely matters because Re and ε/D both depend on D. Reporting the chosen correlation, inputs, and computed regime helps reviewers reproduce results.
8) Recommended workflow for reliable results
Start by computing Re from flow conditions, then confirm the regime. Enter ε/D directly when available, or use ε with diameter for consistent conversion. Compare at least two correlations for a quick sanity check. Export the CSV or PDF to document assumptions and outputs clearly.
1) Is this the Darcy or Fanning friction factor?
This calculator reports the Darcy friction factor. The Fanning friction factor is one quarter of the Darcy value. Always confirm which definition your textbook or software uses before comparing results.
2) What if my flow is in the transitional range?
Between about Re = 2300 and 4000, friction factor is uncertain and depends on disturbances and inlet conditions. Treat results as approximate and consider conservative design margins or testing when accuracy is critical.
3) Which correlation should I choose for turbulent flow?
Colebrook–White is a common reference when roughness is relevant. Haaland and Swamee–Jain are fast explicit options with good accuracy for many cases. Use Blasius only for smooth pipes and moderate Reynolds numbers.
4) How do I estimate roughness if I only know the pipe material?
Engineering handbooks often list typical absolute roughness values by material and condition. Convert ε to ε/D using the internal diameter. When data is uncertain, evaluate a range of ε to see the impact on f.
5) Why does changing diameter affect friction factor twice?
Diameter influences Reynolds number and relative roughness. Increasing D raises Re for fixed velocity and lowers ε/D for fixed ε. Both effects typically reduce friction factor, which can significantly decrease head loss.
6) Can I use this for non-circular ducts?
The correlations here assume circular pipes. For non-circular ducts, engineers often use hydraulic diameter with caution, but accuracy can vary. If you use hydraulic diameter, document the assumption and validate against references when possible.
7) What viscosity input should I use, ν or μ and ρ?
Use kinematic viscosity ν if it is available for your fluid and temperature. If you have dynamic viscosity μ and density ρ, the calculator computes Re using ρ·v·D/μ. Ensure units match the selected options.