Reynolds Number

Definition

The Reynolds number ($Re$) is a dimensionless quantity used to help predict flow patterns in different fluid flow situations. It quantifies the ratio of inertial forces to viscous forces.

Formula

$Re = \frac{\rho u L}{\mu} = \frac{u L}{\nu}$ where:

• $\rho$: Density
• $u$: Velocity
• $L$: Characteristic length
• $\mu$: Dynamic viscosity
• $\nu$: Kinematic viscosity

Physical Interpretation

• Low Re: Viscous forces dominate; flow is laminar.
• High Re: Inertial forces dominate; flow becomes turbulent.

Relationships

• Related: Navier-Stokes Equation, Turbulence and Mixing