▸ processconvert
Fluid Mechanics

Reynolds Number Explained

The Reynolds number is a dimensionless ratio that indicates whether flow is laminar, transitional, or turbulent. Learn the formula, flow regime thresholds, and common mistakes.

TypeEngineering guide — concept explainer

Definition

The Reynolds number (Re) is a dimensionless ratio of inertial forces to viscous forces in a flowing fluid. It indicates the flow regime: low Re means viscous forces dominate (laminar flow), high Re means inertial forces dominate (turbulent flow). For pipe flow, Re = ρvD/μ, where ρ is density, v is velocity, D is pipe internal diameter, and μ is dynamic viscosity.

Why it matters

The flow regime directly affects pressure drop, heat transfer, mixing, and mass transfer. Laminar flow has predictable, orderly streamlines. Turbulent flow has chaotic eddies that enhance mixing and heat transfer but increase pressure drop. Engineers check the Reynolds number early in any pipe flow calculation to determine which correlations and design methods apply.

Formula

Using dynamic viscosity
Re = ρ × v × D / μ
Using kinematic viscosity
Re = v × D / ν
Kinematic-dynamic relationship
ν = μ / ρ

Units involved

  • •Re — dimensionless (no units)
  • •ρ — density in kg/m³ or lb/ft³
  • •v — velocity in m/s or ft/s
  • •D — pipe internal diameter in m, mm, inches, or ft
  • •μ — dynamic viscosity in Pa·s, mPa·s, or cP
  • •ν — kinematic viscosity in m²/s, mm²/s, or cSt

Concept diagram

laminartransitionalturbulentRe ≈ 2,100Re ≈ 4,000Re = ρvD/μ = vD/ν

Worked example

Water flows through a 50 mm (0.05 m) internal diameter pipe at 2 m/s. Water density is 998 kg/m³ and dynamic viscosity is 1.002 × 10⁻³ Pa·s (approximately 1 cP). What is the Reynolds number?

  1. 01ρ = 998 kg/m³
  2. 02v = 2 m/s
  3. 03D = 0.05 m
  4. 04μ = 1.002 × 10⁻³ Pa·s
  5. 05Re = (998 × 2 × 0.05) / (1.002 × 10⁻³)
  6. 06Re = 99,800 / 0.001002
  7. 07Re ≈ 99,600
Result

Re ≈ 99,600 — turbulent flow (Re >> 4,000)

Common mistakes

  • •Mixing up diameter units — if D is in mm and other values are in SI base units (m, kg, Pa·s), divide D by 1000. A 50 mm pipe has D = 0.05 m.
  • •Confusing dynamic viscosity (μ, in Pa·s or cP) with kinematic viscosity (ν, in m²/s or cSt) — they are related by ν = μ/ρ but have different units and magnitudes.
  • •Forgetting that 1 cP = 1 mPa·s = 0.001 Pa·s — using cP directly in the SI formula without converting gives Re values 1000 times too large.
  • •Using pipe outer diameter instead of internal diameter — Re uses the internal flow diameter. Pipe schedule tables list both; use the ID.
  • •Applying pipe flow Re thresholds to non-circular geometries — for non-circular ducts, use hydraulic diameter. The standard Re = 2,100 threshold is for circular pipes.

When to use the calculator

Use the Reynolds Number calculator when you know the fluid velocity, pipe diameter, and either dynamic or kinematic viscosity. The calculator handles unit conversions and reports whether the flow is laminar, transitional, or turbulent.

Reynolds Number Calculator →Pipe Velocity Calculator →

FAQ

What Reynolds number values define laminar and turbulent flow?
For internal pipe flow: Re < ~2,100 is generally laminar, Re > ~4,000 is generally turbulent, and the range between is transitional. These thresholds are approximate and apply to smooth circular pipes. Surface roughness, vibration, and entrance conditions can shift the transition.
Can I use the Reynolds number for open-channel flow?
Yes, but the characteristic length is the hydraulic radius (not diameter), and the transition thresholds are different. Open-channel flow typically transitions at Re ≈ 500–2,000 based on hydraulic radius. The calculator on ProcessConvert is designed for internal pipe flow.
Why is the Reynolds number dimensionless?
All units cancel: (kg/m³)(m/s)(m) / (Pa·s) = (kg/m³)(m/s)(m) / (kg/(m·s)) = 1. This means Re is the same regardless of the unit system used, as long as units are consistent.
Where do I find viscosity values for my fluid?
Viscosity depends on the fluid and its temperature. Common references include Perry's Chemical Engineers' Handbook, the NIST webbook, and manufacturer data sheets. For water at 20 °C, dynamic viscosity is approximately 1.002 cP (1.002 × 10⁻³ Pa·s).