Reynolds Number Formula
Calculate the Reynolds number using Re = ρvL/μ.
Determine whether fluid flow is laminar or turbulent in pipes and channels.
The Formula
The Reynolds number is a dimensionless quantity that predicts the flow regime of a fluid.
Low Reynolds numbers indicate smooth, laminar flow.
High Reynolds numbers indicate chaotic, turbulent flow.
Variables
| Symbol | Meaning |
|---|---|
| Re | Reynolds number (dimensionless) |
| ρ | Fluid density (kg/m³) |
| v | Flow velocity (m/s) |
| L | Characteristic length — typically pipe diameter (metres, m) |
| μ | Dynamic viscosity of the fluid (Pa·s or kg/(m·s)) |
Flow Regime
- Re < 2,300 — Laminar flow (smooth, predictable)
- 2,300 < Re < 4,000 — Transitional flow (unstable, may switch between laminar and turbulent)
- Re > 4,000 — Turbulent flow (chaotic, with eddies and mixing)
Example 1
Water (ρ = 1000 kg/m³, μ = 0.001 Pa·s) flows at 0.5 m/s through a pipe with diameter 0.05 m. Find Re.
Re = ρvL / μ
Re = (1000 × 0.5 × 0.05) / 0.001
Re = 25 / 0.001
Re = 25,000 — Turbulent flow
Example 2
Oil (ρ = 900 kg/m³, μ = 0.1 Pa·s) flows at 0.2 m/s through a 0.03 m diameter tube. Find Re.
Re = ρvL / μ
Re = (900 × 0.2 × 0.03) / 0.1
Re = 5.4 / 0.1
Re = 54 — Laminar flow
When to Use It
Use the Reynolds number when you need to:
- Determine whether flow in a pipe or channel is laminar or turbulent
- Select appropriate friction factor equations for pressure drop calculations
- Scale up laboratory experiments to real-world systems
- Design piping systems, heat exchangers, and fluid transport systems
The characteristic length L depends on the geometry.
For pipes, use the internal diameter. For flat plates, use the plate length.