Calculator
Formula used
Relative roughness is the ratio of absolute roughness to internal diameter: ε/D.
- ε = absolute roughness (length, converted to meters)
- D = internal diameter (length, converted to meters)
- ε/D = dimensionless value used with friction correlations
How to use this calculator
- Select what you want to compute (ε/D, D, or ε).
- Optionally choose a material preset for typical roughness.
- Enter your remaining known values and units.
- Click Calculate to view results above the form.
- Use Download CSV or Download PDF for records.
Example data table
| Material (typical) | Absolute roughness ε (mm) | Internal diameter D (mm) | Relative roughness ε/D |
|---|---|---|---|
| Commercial steel | 0.045 | 100 | 0.00045 |
| Galvanized iron | 0.150 | 50 | 0.00300 |
| Cast iron | 0.260 | 150 | 0.00173 |
| Concrete | 0.300 | 300 | 0.00100 |
These values are typical, not guaranteed. Surface condition, scaling, and aging can change roughness.
Relative Roughness Guide
1) What relative roughness represents
Relative roughness is a dimensionless measure of how “textured” a flow passage is compared with its size. It is defined as absolute roughness, ε, divided by the internal diameter, D. Because it has no units, ε/D lets you compare different pipes and ducts fairly, even when their diameters and roughness values use different length units.
2) Why it matters in pressure-loss estimates
For internal flows, pressure loss is often estimated using a friction factor combined with the Darcy–Weisbach relationship. In laminar flow, friction factor depends mainly on Reynolds number and is largely insensitive to surface texture. In turbulent flow, however, ε/D strongly influences friction factor, so small changes can produce noticeable changes in head loss.
3) Typical roughness values as practical data
Engineers often start with typical ε values when measurements are unavailable. Smooth materials can be near 0.0015 mm, commercial steel is often around 0.045 mm, galvanized iron may be near 0.150 mm, and cast iron can be around 0.260 mm. Concrete can also be rough, commonly near 0.300 mm, but aging and deposits may increase it.
4) Diameter sensitivity and scaling effects
The same absolute roughness produces different ε/D values depending on diameter. For example, ε = 0.045 mm in a 100 mm pipe gives ε/D = 0.00045, while the same ε in a 25 mm pipe gives ε/D = 0.0018. This scaling is why small lines can show higher friction effects even with identical surface finish.
5) How ε/D is used with friction correlations
Once ε/D is known, it can be paired with Reynolds number in common turbulent-flow correlations and charts. Many workflows use the Moody diagram or an implicit relation such as the Colebrook equation. In fully rough turbulent conditions, friction factor becomes dominated by ε/D and becomes less sensitive to Reynolds number.
6) Measurement, specification, and uncertainty
Absolute roughness can come from manufacturer specifications, inspection data, or field measurements. Real systems can deviate due to corrosion, scaling, lining wear, or fouling. If you are sizing pumps or evaluating an existing system, it is often useful to test a range of ε values to see how sensitive results are.
7) Practical workflow for hydraulic design
A typical workflow is: choose a pipe material, estimate ε, compute ε/D, then calculate Reynolds number from flow conditions. Use both values to obtain friction factor, and finally compute head loss. This calculator handles unit conversions so you can focus on engineering decisions and keep assumptions consistent.
8) Limits and good modeling habits
Relative roughness is a key input for steady, single-phase internal flow models, but it is not a complete description of every real surface. Weld beads, fittings, valves, and bends add extra losses beyond straight-pipe friction. Use ε/D for straight runs, add minor-loss coefficients for components, and document your assumed ε values.
FAQs
1) What units should I use for ε and D?
Any length units work. The calculator converts them internally so ε and D are consistent. The output ε/D is dimensionless and can be used directly with friction charts and correlations.
2) Is relative roughness important for laminar flow?
Usually not. In laminar flow, friction factor is mainly controlled by Reynolds number. Surface texture becomes much more influential once flow is turbulent.
3) How do I pick ε if I do not have measurements?
Start with typical material values from reliable references or manufacturer data. Then perform a sensitivity check by varying ε up and down to see the impact on head loss.
4) Why does a smaller pipe often have higher ε/D?
Because ε/D scales with 1/D. With the same absolute roughness, reducing diameter increases the ratio, which can raise friction factor in turbulent flow and increase pressure losses.
5) Can deposits and corrosion change ε over time?
Yes. Scaling, corrosion, lining damage, or biofouling can increase effective roughness. For older systems, consider using a larger ε than new-pipe values.
6) Does this replace a friction factor calculator?
No. This tool computes ε/D, D, or ε. You can then use ε/D with Reynolds number in a friction-factor method such as a chart or correlation to compute head loss.
7) Should I use internal or nominal diameter?
Use internal diameter. Nominal size can differ from the true inside diameter, especially across schedules and materials. Using internal diameter improves accuracy for ε/D and flow calculations.