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Reynolds Number

Also known as Re · laminar or turbulent

Re=ρvDμRe = \frac{\rho v D}{\mu}

Worked example: Water, 1 m/s, D = 5 cm, mu = 1 mPa*s → Re = 50000 — press Try an example to run it live, then adjust anything.

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Reynolds Number explained

vρμDRe

Osborne Reynolds injected dye into pipe flow in 1883 and watched it either glide in a smooth filament or erupt into eddies — and found one dimensionless group predicted which. Below about Re = 2300 pipe flow is laminar; above roughly 4000 it is turbulent. Water at 1 m/s in a 5 cm pipe gives Re = 1000 × 1 × 0.05 / 0.001 = 50 000: solidly turbulent, like nearly all industrial water flow.

Because only the combination ρvD/μ matters, a small model in a wind tunnel can faithfully stand in for a full-size aircraft as long as the Reynolds numbers match — the principle that makes scale testing legitimate.

Reynolds Number formula

Re=ρvDμRe = \frac{\rho v D}{\mu}
Where
  • ReRe= Reynolds number
  • ρ\rho= Fluid density (kg/m³)
  • vv= Flow velocity (m/s)
  • DD= Characteristic length (mm)
  • μ\mu= Dynamic viscosity (Pa·s)

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Part of this formula set

Pipe friction losses

9 formulasDarcy–Weisbach, Hazen–Williams, friction factors, minor losses and equivalent length — every way the trade computes head loss in pipe.