Reynolds Number Calculator

The Reynolds number is defined as the ratio of inertial forces to viscous forces:

$$Re = \frac{\rho v D}{\mu} = \frac{v D}{\nu}$$

where:

• ρ — fluid density (kg/m³)
• v — characteristic flow velocity (m/s)
• D — characteristic length, typically pipe diameter (m)
• μ — dynamic viscosity (Pa·s)
• ν — kinematic viscosity = μ/ρ (m²/s)

The flow regime classification for internal pipe flow:

• Re < 2,300 — Laminar flow: smooth, orderly layers. Velocity profile is parabolic (Hagen-Poiseuille flow). Friction factor f = 64/Re.
• 2,300 ≤ Re < 4,000 — Transitional flow: intermittent switching between laminar and turbulent behavior. Unpredictable and generally avoided in design.
• Re ≥ 4,000 — Turbulent flow: chaotic, random fluctuations. Higher mixing, higher friction losses. Friction factor depends on Re and surface roughness (Moody chart).

The physical interpretation is straightforward: when inertial forces dominate (high Re), the flow cannot remain orderly and becomes turbulent. When viscous forces dominate (low Re), they damp disturbances and maintain laminar flow.

Different geometries have different critical Reynolds numbers. For flow over a flat plate, transition occurs around Re ≈ 500,000. For flow around a sphere, the drag crisis occurs near Re ≈ 200,000. The values 2,300 and 4,000 apply specifically to pipe flow.

A high Reynolds number means the flow is dominated by inertia and likely turbulent — expect higher friction losses but better mixing. A low Reynolds number indicates viscous-dominated laminar flow — lower friction but poor mixing. For engineering design, knowing the flow regime is essential for selecting the correct friction factor, heat transfer correlations, and mixing models.