How it’s calculated
The Reynolds number is the ratio of inertial to viscous forces. For flow in a full circular pipe it uses the inside diameter and the average velocity.
| Re (pipe flow) | Regime used here |
|---|---|
| < 2,300 | Laminar |
| 2,300 – 4,000 | Transitional |
| > 4,000 | Turbulent |
These are typical engineering thresholds. Other references round differently: OpenStax uses about 2,000 and 3,000, and the U.S. DOE Fundamentals Handbook uses 2,000 and 3,500. Very smooth, disturbance-free pipes can stay laminar to higher Re.
Example (OpenStax University Physics, Example 14.9): air (ρ = 1.23 kg/m³, μ = 0.0181 mPa·s) moving at 0.15 m/s in an 18 cm duct: Re = 1.23 × 0.15 × 0.18 ÷ 1.81 × 10⁻⁵ ≈ 1,835, laminar.
Frequently asked questions
What Reynolds number is turbulent in a pipe?
Above about 4,000 the flow is fully turbulent; below about 2,300 it is laminar. In between it is transitional and can switch back and forth.
What is the difference between dynamic and kinematic viscosity?
Dynamic viscosity μ (Pa·s) is the fluid’s resistance to shear. Kinematic viscosity ν = μ/ρ (m²/s). 1 cP = 1 mPa·s; 1 cSt = 1 mm²/s.
Does temperature matter?
Strongly for liquids: water’s viscosity falls from 1.792 mPa·s at 0 °C to 0.282 mPa·s at 100 °C, so the same flow has a Reynolds number about 6 times higher when hot.
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Sources
- University Physics Vol. 1, 14.7 Viscosity and Turbulence — OpenStax
- DOE Fundamentals Handbook: Thermodynamics, Heat Transfer, and Fluid Flow, Vol. 3 (DOE-HDBK-1012/3-92) — U.S. Department of Energy
- Pipe Flows: Losses (ME 308 course notes, C. Wassgren) — Purdue University
- Reynolds Number (Beginner’s Guide to Aeronautics) — NASA Glenn Research Center
Formulas are taken from the free public references above. Results are provided “as is” for informational and educational purposes only. See our disclaimer.
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