Definition
The Reynolds number is a dimensionless parameter that characterizes the flow regime in fluid mechanics. It represents the ratio of inertial forces to viscous forces.
Mathematical Expression
Where:
- ρ = fluid density
- v = characteristic velocity
- L = characteristic length
- μ = dynamic Viscosity
- ν = kinematic viscosity (μ/ρ)
Notes
- High Re: Inertial forces dominate → Turbulent flow
- Low Re: Viscous forces dominate → Laminar flow
- Transition region: Mixed characteristics
Flow Regimes
Pipe Flow
- Re < 2300: Laminar flow
- 2300 < Re < 4000: Transition zone
- Re > 4000: Turbulent flow
Flow Over Flat Plate
- Re < 500,000: Laminar boundary layer
- Re > 500,000: Turbulent boundary layer
Flow Around Sphere
- Re < 1: Stokes flow (creeping flow)
- Re > 1000: Turbulent wake formation
Characteristic Lengths
Pipe Flow
- L = D (pipe diameter)
- Re = ρvD/μ
External Flow
- L = plate length or object diameter
- Context-dependent definition