🔬 Reynolds Number Calculator

The Reynolds number (Re) is a dimensionless quantity in fluid mechanics that predicts flow patterns. Named after the Irish engineer Osborne Reynolds (1883), it is defined as Re = ρ × v × D / μ, where ρ is fluid density (kg/m³), v is flow velocity (m/s), D is the characteristic length or pipe diameter (m), and μ is dynamic viscosity (Pa·s). The Reynolds number represents the ratio of inertial forces to viscous forces.

The Reynolds number determines whether flow is laminar (smooth, parallel streamlines at Re < 2300), transitional (2300 < Re < 4000), or turbulent (chaotic, mixing eddies at Re > 4000). This classification is essential for pipe design, aircraft aerodynamics, heat exchangers, and chemical reactors.

The calculator computes Re = ρ × v × D / μ. For non-circular ducts, D is replaced by the hydraulic diameter Dₕ = 4A/P (A = cross-sectional area, P = wetted perimeter).

1. Enter the fluid density (ρ) in kg/m³.
2. Enter the flow velocity (v) in m/s.
3. Enter the pipe diameter or characteristic length (D) in metres.
4. Enter the dynamic viscosity (μ) in Pa·s.
5. Click Calculate to get the Reynolds number and flow regime classification.

What does the Reynolds number tell me?

It predicts the flow regime: Re < 2300 means laminar flow (smooth and predictable), Re > 4000 means turbulent flow (chaotic with mixing), and 2300-4000 is transitional. This determines pressure drop, heat transfer, and mixing behaviour.

Why is the Reynolds number dimensionless?

All units cancel: (kg/m³)(m/s)(m) / (kg/(m·s)) = 1. Being dimensionless means Re is the same regardless of the unit system used, as long as the units are consistent.

What is the critical Reynolds number?

For pipe flow, the commonly accepted critical value is Re ≈ 2300, below which flow is laminar. Above 4000, flow is fully turbulent. The exact transition depends on pipe roughness, entrance effects, and disturbances.

How does temperature affect the Reynolds number?

Temperature changes viscosity dramatically. For liquids, viscosity decreases with temperature (Re increases). For gases, viscosity increases slightly with temperature (Re decreases slightly). Always use viscosity at the operating temperature.

Can I use this for non-circular pipes?

Yes—replace diameter D with the hydraulic diameter Dₕ = 4A/P, where A is the cross-sectional area and P is the wetted perimeter. For a rectangular duct, Dₕ = 2ab/(a+b). For a full circular pipe, Dₕ = D.

What is kinematic viscosity and how does it relate?

Kinematic viscosity ν = μ/ρ (units: m²/s). Using ν, the formula simplifies to Re = vD/ν. Some references use ν directly instead of μ and ρ separately. They are equivalent: Re = ρvD/μ = vD/ν.

Use consistent SI units: density in kg/m³, velocity in m/s, diameter in m, viscosity in Pa·s (= kg/(m·s)). Common viscosity values at 20°C: water = 0.001 Pa·s, air = 0.000018 Pa·s, olive oil = 0.08 Pa·s, glycerin = 1.5 Pa·s. The transition between laminar and turbulent is not sharp—the range 2300-4000 is transitional, and surface roughness can trigger turbulence earlier. For open channel flow, the characteristic length is the hydraulic radius, not the diameter.