Table of Contents
What Is Reynolds Number?
The Reynolds number (Re) is a dimensionless quantity that predicts flow patterns in fluid dynamics. It represents the ratio of inertial forces to viscous forces within a fluid. Named after Osborne Reynolds, who demonstrated in 1883 that the transition from laminar to turbulent flow depends on this single parameter, it is one of the most important numbers in fluid mechanics.
Low Reynolds numbers indicate laminar flow where viscous forces dominate and the fluid moves in smooth, orderly layers. High Reynolds numbers indicate turbulent flow where inertial forces dominate and the fluid exhibits chaotic, irregular motion with eddies and vortices.
Reynolds Number Formula
Where ρ is fluid density, v is flow velocity, D is the characteristic length (pipe diameter for internal flow), μ is dynamic viscosity, and ν = μ/ρ is kinematic viscosity.
Flow Regimes
| Reynolds Number | Flow Regime | Characteristics |
|---|---|---|
| Re < 2,300 | Laminar | Smooth, parallel layers, predictable |
| 2,300 < Re < 4,000 | Transitional | Intermittent turbulence, unstable |
| Re > 4,000 | Turbulent | Chaotic, eddies, higher friction |
Common Fluid Properties
| Fluid (20°C) | Density (kg/m³) | Dynamic Viscosity (Pa·s) |
|---|---|---|
| Air | 1.204 | 1.81 × 10&sup5; |
| Water | 998 | 1.002 × 10³ |
| Motor oil (SAE 30) | 880 | 0.29 |
| Glycerin | 1260 | 1.5 |
Frequently Asked Questions
Why is the Reynolds number important in engineering?
Engineers use the Reynolds number to design piping systems, predict drag forces on vehicles, size pumps and compressors, and model heat transfer. The flow regime directly affects pressure drop, energy losses, and mixing efficiency in any fluid system.
What is the characteristic length for different geometries?
For pipe flow, use the internal diameter. For flow over a flat plate, use the distance from the leading edge. For non-circular ducts, use the hydraulic diameter: Dh = 4A/P, where A is the cross-sectional area and P is the wetted perimeter.
Can laminar flow exist at high Reynolds numbers?
In carefully controlled laboratory conditions, laminar flow has been maintained at Reynolds numbers up to 100,000. However, any disturbance in practical systems triggers the transition to turbulence above Re = 2,300 for pipe flow.