Reynolds Number & Flow Regimes — Reference
The ratio of inertial to viscous forces — the single number that decides whether flow is laminar or turbulent, and therefore which friction relation applies.
Definition
Characteristic length L: pipe → diameter D (full-flow); open channel → hydraulic radius R = A/P. (Some texts use 4R for channels to align with the pipe definition — check which convention a threshold assumes.)
Flow Regime Thresholds
| System | Laminar | Transitional | Turbulent |
|---|---|---|---|
| Pipe flow (L = D) | < 2100 | 2100–4000 | > 4000 |
| Open channel (L = R) | < 500 | 500–2000 | > 2000 |
| Flow around a sphere/particle | < 1 | 1–1000 | > 1000 |
Kinematic Viscosity of Water
| Temp | ν (m²/s) | ν (ft²/s) |
|---|---|---|
| 5°C / 41°F | 1.52×10−6 | 1.63×10−5 |
| 10°C / 50°F | 1.31×10−6 | 1.41×10−5 |
| 20°C / 68°F | 1.00×10−6 | 1.08×10−5 |
| 30°C / 86°F | 0.80×10−6 | 0.86×10−5 |
Sources: White, F.M., Fluid Mechanics. Munson et al., Fundamentals of Fluid Mechanics. Viscosity values: standard water property tables.
Related cheat sheets and tools
Confirm the regime with the Reynolds tool, then pick the friction relation from the roughness card and compute loss in Darcy-Weisbach. For open channels, the specific-energy card covers the Froude side. For full network modeling, see HydroComplete.