Reynolds Number

Also known as Re · laminar or turbulent

Re = \frac{\rho v D}{\mu}

Re =

ρ =

v =

D =

μ =

Enter your known values, leave one input blank, and solves for the missing one. Try different units for next level excitement!

Learning zone

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

Re = \frac{\rho v D}{\mu}

Where

$Re$ = Reynolds number
$\rho$ = Fluid density
$v$ = Flow velocity
$D$ = Characteristic length
$\mu$ = Dynamic viscosity

Missing one of these? Work it out first, then come back

Reynolds number — Laminar Friction Factor (f = 64/Re), Swamee–Jain Friction Factor
Fluid density — Dynamic Pressure (q = ½ρv²), Buoyant Force (Archimedes' Principle)
Flow velocity — Volumetric Flow Rate (Q = Av), Dynamic Pressure (q = ½ρv²)
Characteristic length — Nusselt Number, Biot Number
Dynamic viscosity — Poiseuille's Law, Stokes' Drag (F = 6πμrv)

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.