Inputs
Laminar: Re < 2300 Transitional: 2300 ≤ Re ≤ 4000 Turbulent: Re > 4000
Results
Enter inputs and press Calculate to see results.
Example Data
These example rows demonstrate typical ranges. Click Load Example to copy Case 1 into the form.
| Case | D (m) | Q (m³/s) | ρ (kg/m³) | μ (Pa·s) | ε (m) | Re | ε/D | f (Haaland) |
|---|---|---|---|---|---|---|---|---|
| 1 • Water @20°C, steel pipe | 0.10 | 0.0020 | 998.2 | 0.001002 | 0.000045 | |||
| 2 • Water, smooth pipe | 0.05 | 0.0004 | 998.2 | 0.001002 | 0 | |||
| 3 • Oil, moderate viscosity | 0.08 | 0.0005 | 870 | 0.02 | 0.000015 |
How to use this calculator
- Enter D, ρ, μ, and either Q or V.
- Provide pipe roughness ε or leave as zero for smooth pipe.
- Choose a method. “Auto” uses 64/Re when laminar, else Colebrook.
- Press Calculate. Review Re, ε/D, and the friction factor f.
- Export your results with Download CSV or Download PDF.
For transitional flows (2300–4000), results are uncertain; prefer fully laminar or fully turbulent conditions in design checks.
Formulas used
- Velocity
V = 4Q / (π D²) - Reynolds number
Re = ρ V D / μ - Relative roughness
ε/D - Laminar
f = 64 / Re - Colebrook–White solve for
fin
1/√f = -2 log10( (ε/D)/3.7 + 2.51/(Re√f) ) - Swamee–Jain
f = 0.25 / [log10((ε/D)/3.7 + 5.74/Re^0.9)]² - Haaland
f = 1 / [-1.8 log10(((ε/D)/3.7)^1.11 + 6.9/Re)]²
All formulas return the Darcy–Weisbach friction factor (not Fanning).
Typical Absolute Roughness (ε) Reference
Use these representative values when manufacturer data is unavailable. Adjust for aging, scaling, or lining conditions.
| Material / Pipe Type | ε (mm) | ε (m) |
|---|---|---|
| Glass / Drawn tubing (very smooth) | 0.0015 | 1.5×10⁻⁶ |
| Copper / Brass / PVC (smooth) | 0.0015–0.007 | 1.5–7.0×10⁻⁶ |
| Commercial steel (new) | 0.045 | 4.5×10⁻⁵ |
| Galvanized iron | 0.150 | 1.5×10⁻⁴ |
| Cast iron (new) | 0.260 | 2.6×10⁻⁴ |
| Concrete (smooth) | 0.300 | 3.0×10⁻⁴ |
| Concrete (rough / aged) | 1.500 | 1.5×10⁻³ |
Always prefer product-specific ε from vendor literature for critical work.
Flow Regimes & Method Guide
| Range | Regime | Recommended Approach | Notes |
|---|---|---|---|
| Re < 2300 | Laminar | f = 64/Re | Roughness negligible; validate fully developed profile. |
| 2300–4000 | Transitional | Colebrook with caution | Large uncertainty; avoid for design if possible. |
| Re > 4000, ε/D < 10⁻⁵ | Turbulent (hydraulically smooth) | Swamee–Jain or Haaland | Fast explicit estimates; good for quick iterations. |
| Re > 4000, ε/D ≥ 10⁻³ | Turbulent (fully rough) | Colebrook–White | Friction dominated by roughness; f ≈ function(ε/D). |
“Auto” mode selects laminar formula when Re < 2300, else Colebrook.
Pressure Drop & Head Loss Example
Relationship to friction factor (Darcy–Weisbach): Δp = f (L/D) (ρ V² / 2), hf = f (L/D) (V² / 2g).
| L (m) | D (m) | V (m/s) | ρ (kg/m³) | f | Δp (kPa) | hf (m) |
|---|---|---|---|---|---|---|
| 50 | 0.10 | 2.0 | 998 | 0.020 | 19.96 | ≈2.04 |
Use the computed f above to estimate line loss for your case.
Notes
- Input units are selectable per field and are converted internally to SI.
- For hydraulically smooth pipes, set ε = 0 to ignore roughness.
- For high-precision work, use Colebrook with an adequate convergence tolerance.
- Always validate outputs against design codes and project requirements.