Physics Foundations · Topic 2 of 6
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Reynolds number
The single dimensionless number that predicts whether flow is laminar or turbulent.
What you’ll learn
- What the Reynolds number represents physically
- How to compute it and read the result
- Why microchannels almost always sit at low Re
The concept
The Reynolds number, Re, is the ratio of inertial forces to viscous forces in a flow. A high Re means inertia dominates and turbulence is likely; a low Re means viscosity dominates and the flow is smooth and laminar.
Re = ρvDₕ/μ combines density, mean velocity, a length scale (the hydraulic diameter), and viscosity. Because microchannels have a tiny Dₕ and modest velocities, Re is usually well below 100 — firmly laminar.
By convention, pipe flow is laminar below Re ≈ 2000 and turbulent above ≈ 4000, with a transitional band between. These thresholds are calibrated for circular pipes; other cross-sections shift them, so treat them as guidelines.
Why it matters
A single quick calculation tells you which flow regime you are in — and therefore which design rules and mixing strategies apply.
The equation
Dimensionless ratio of inertial to viscous forces.
Variables
| Symbol | Variable | Unit |
|---|---|---|
| Re | Reynolds number | — |
| ρ | Fluid density | kg/m³ |
| v | Mean velocity | m/s |
| Dₕ | Hydraulic diameter | m |
| μ | Dynamic viscosity | Pa·s |
Worked example
Water (ρ = 1000 kg/m³, μ = 1.0 mPa·s) at v = 0.01 m/s in a 100 µm channel:
Re = (1000)(0.01)(100×10⁻⁶) / (1.0×10⁻³) = 1.0
Re = 1 → laminar, as expected for a microchannel.
Try it yourself
Put these numbers into the reynolds number calculator and see the result for your own channel.
Open the Reynolds number calculator →Common mistakes
Watch out for:
- Mixing unit systems — always convert to SI first, or you can be off by factors of ten.
- Using a plain diameter for a rectangular channel; use the hydraulic diameter Dₕ instead.
Keep going
Related concepts
Related tools
Further reading
- A standard fluid-mechanics textbook chapter on the Reynolds numberPlaceholder — a specific, verified reference will be added.
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Reynolds number
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