Reynolds Number

Definition

The dimensionless number predicting whether fluid flow is smooth (laminar) or chaotic (turbulent).

$Re = \frac{\rho v L}{\mu}$

Symbol: $Re$ · Unit: dimensionless

Technical definition

Re = ρvL/μ (density × velocity × characteristic length / viscosity). Low Re (<~2300 in pipes) means viscous forces dominate → laminar; high Re means inertial forces dominate → turbulent. Enables scale modeling (same Re = same flow behavior).

Example

Honey pouring has Re ~ 1 (laminar); a jet airliner at cruise has Re ~ 10⁸ (turbulent boundary layers) — same equation, wildly different regimes.

Common confusion

There is no single universal critical Reynolds number — ~2300 is for pipe flow; flat plates transition around 5×10⁵. The threshold depends on geometry, so always specify the setup.