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 |
Need density, specific weight or vapor pressure too? See the full water properties table (0–100°C / 32–212°F).
Sources: White, F.M., Fluid Mechanics. Munson et al., Fundamentals of Fluid Mechanics. Viscosity values: standard water property tables.
Worked examples: one turbulent, one laminar
12-in pipe, Q = 1.5 cfs, water at 50°F (ν = 1.41×10⁻⁵ ft²/s)
1-in drain line, V = 0.1 ft/s, same water
The first case is typical: water in civil infrastructure is almost always turbulent, so the Reynolds number mainly tells you to use a turbulent friction relation. The second case is where the check matters. Small, slow flows include drain lines, chemical feed tubing, and seepage through a filter or sand bed. In those, laminar flow is real, and the turbulent friction relations do not apply.
Common mistakes
- Plugging dynamic viscosity μ into V·L/ν. Dynamic viscosity μ (lb·s/ft² or Pa·s) goes with density in ρVL/μ. Kinematic viscosity ν (ft²/s or m²/s) goes alone in VL/ν. Mixing them makes Re off by a factor of about 1.94 in US units (the density of water in slugs/ft³).
- Applying the pipe threshold (2,100) to an open channel that uses R as the length. With L = R, the laminar limit is about 500. With L = 4R, the pipe thresholds apply again. Check which convention a source uses.
- Using 20°C viscosity for cold water. Viscosity at 5°C is 52% higher than at 20°C. For winter design of treatment processes and settling, that changes the answer.
- Reading Reynolds number as the sub/supercritical test. That is the Froude number. A channel can be turbulent and either sub- or supercritical.
When this card doesn’t apply
The thresholds are for Newtonian fluids in steady, fully developed flow. Sludges, slurries and drilling muds are non-Newtonian and need a rheological model and a modified Reynolds number. Flow through porous media uses a particle-diameter Reynolds number. In that case Darcy’s law holds only below Re of roughly 1–10. Entrance regions, pulsating flow and flow with heat transfer transition at different values.
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.