Reynolds Number
Re = ρVL/µ with one-click air or water properties, or your own fluid.
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The engineering
Reynolds number is the ratio of inertia to viscosity — the single number that decides whether flow slides in ordered layers or churns. Below ~2,300 in a pipe it's laminar; above ~4,000, turbulent; in between, moody. For wings and hulls the transition thresholds differ, but the number still rules.
It's also the passport for scale models: match Re and the flow pattern around a 1:10 model is honestly the full-scale one. Mismatch it and your beautiful wind-tunnel drag polar describes an aircraft that doesn't exist — the reason cryogenic and pressurized tunnels were built.
Where this math comes from
Osborne Reynolds dyed a filament of water inside a glass pipe in 1883 and watched it stay a thread, then shatter into eddies as flow sped up — and showed the changeover obeyed one dimensionless group, whatever the fluid or pipe. George Stokes had supplied the viscous theory (1851); Reynolds supplied the criterion.
Arnold Sommerfeld attached Reynolds' name to the group in 1908, and Prandtl's boundary-layer theory (1904) explained why it governs: viscosity only matters in thin layers whose fate Re decides. It remains the first number any fluids engineer computes, usually before breakfast.
- 1851George Gabriel StokesViscous-flow theory — the µ in the denominator.
- 1883Osborne ReynoldsDye-filament experiment finds the transition criterion.
- 1904Ludwig PrandtlBoundary-layer theory explains why Re governs.
- 1908Arnold SommerfeldCoins the name 'Reynolds number'.
See the full timeline of the math behind every calculator →
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