Reynolds Number Calculator
Calculate the Reynolds number to determine if fluid flow is laminar or turbulent based on velocity, diameter, and viscosity.
Reynolds number (Re) is a dimensionless quantity used in fluid mechanics to predict whether fluid flow will be laminar (smooth and orderly) or turbulent (chaotic and mixing). It is one of the most important parameters in engineering design of pipes, aircraft, ships, pumps, and heat exchangers.
Reynolds number formula: Re = (ρ × v × L) ÷ μ
Or equivalently using kinematic viscosity: Re = (v × L) ÷ ν
Where:
- ρ (rho) = fluid density (kg/m³)
- v = flow velocity (m/s)
- L = characteristic length (m), pipe diameter for internal flow; chord length for airfoils
- μ (mu) = dynamic viscosity (Pa·s = kg/(m·s))
- ν (nu) = kinematic viscosity = μ ÷ ρ (m²/s)
Flow regime interpretation:
- Re < 2,300: Laminar flow, fluid moves in smooth parallel layers, low mixing, predictable
- 2,300 < Re < 4,000: Transition zone, unstable, can be either
- Re > 4,000: Turbulent flow, chaotic mixing, higher heat transfer, higher friction losses
Common fluid properties at 20°C:
- Water: ρ = 998 kg/m³, μ = 1.002×10⁻³ Pa·s, ν = 1.004×10⁻⁶ m²/s
- Air: ρ = 1.204 kg/m³, μ = 1.825×10⁻⁵ Pa·s, ν = 1.516×10⁻⁵ m²/s
- Honey: ρ ≈ 1,400 kg/m³, μ ≈ 10 Pa·s (very high viscosity)
Worked example: Water flowing through a 50 mm (0.05 m) diameter pipe at 2 m/s. At 20°C: ν = 1.004×10⁻⁶ m²/s.
Re = (v × D) ÷ ν = (2 × 0.05) ÷ 1.004×10⁻⁶ = 0.10 ÷ 0.000001004 = 99,602
Re » 4,000 → turbulent flow. The engineer must account for higher pressure drop (using the Darcy-Weisbach equation) and select a pump accordingly.