Reynoldsnumber

The Reynolds number, denoted Re, is a dimensionless quantity that expresses the ratio of inertial to viscous forces in a fluid flow. For a Newtonian fluid, Re = rho v L / mu = v L / nu, with rho the density, v a characteristic velocity, L a characteristic length, mu the dynamic viscosity, and nu the kinematic viscosity. The choice of L and v depends on the problem; for internal flow, L might be a pipe diameter, while for external flow it could be a body length and wind speed.

Interpretation: Low Re implies viscous forces dominate and flows are typically laminar; high Re implies inertia dominates and the flow can become turbulent. Re helps predict flow regimes and compare model experiments with real systems.

Critical values vary with geometry and surface roughness; a common reference for pipe flow is about 2000–2300 for transition, but there is no universal threshold.

Applications: Re is used to assess similarity between models and prototypes, estimate pressure drops and drag, and guide design in engineering, aerodynamics, hydraulics, and physiology.

History: The concept is named after Osborne Reynolds, who studied laminar–turbulent transition in pipes in the 1880s.

Limitations: Re assumes Newtonian, incompressible, constant-property fluids. It may not predict behavior well for non-Newtonian, highly compressible, multiphase, or unsteady flows; in such cases other nondimensional parameters are needed.