Reynolds Number⚠ unverified
Physics / Fluids · Reynolds number of a flow (Re = ρ v L / μ)
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| density | ρ | kg/m^3 | 1000 | Fluid density |
| velocity | v | m/s | 1.0 | Characteristic flow speed |
| length | L | m | 0.1 | Characteristic length scale |
| viscosity | μ | Pa s | 0.001 | Dynamic viscosity |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| reynolds_number | Re | — | Reynolds number (dimensionless) |
The science & history
Understanding the Parameters
- $\rho$, $v$, $L$ — raise inertia ($\sim\rho v^{2}$ times area); larger → higher Re.
-
$\mu$ — higher viscosity lowers Re (more laminar tendency). Kinematic viscosity $\nu = \mu/\rho$ gives the equivalent form $\mathrm{Re} = v L / \nu$.
-
Re — pipe flow often transitions near $\mathrm{Re}_D \sim 2300$; airfoils use chord-based Re often $10^{5}$–$10^{7}$.
Derivation (Approaching a Proof)
From the Navier–Stokes equations, nondimensionalise length by $L$, velocity by $V$, time by $L/V$. The viscous term relative to inertia produces the group $\mu/(\rho V L) = 1/\mathrm{Re}$. Hence
$$\mathrm{Re} = \frac{\rho V L}{\mu}$$
measures inertia/viscosity. It is a similarity parameter, not a derived force by itself.
History
Osborne Reynolds’ pipe experiments (1880s) established Re as the transition criterion; it is now universal in fluid mechanics and CFD validation.
Related Concepts: Dynamic Pressure, Drag, Froude Number, Mach Number, Weber Number, Pipe Head Loss
Notes: Registry reynolds-number and cross-category duplicates (unverified). Choice of $L$ must
match the correlation you apply.