Reynolds Number Calculator

Calculate Reynolds number to predict laminar or turbulent flow regime

Flow Parameters

Velocity of fluid relative to object

Pipe diameter, sphere diameter, or chord length

Mass per unit volume of fluid

Resistance to deformation by shear stress

Reynolds Number Results

0
Reynolds Number (Re)
Laminar Flow

Flow Analysis

0.000
Kinematic Viscosity (mm²/s)
0.00
Velocity (m/s)
0.0
Length (mm)

Formula: Re = ρuL/μ = uL/ν

Flow regime criteria: Re < 2100 (Laminar), 2100 < Re < 3000 (Transitional), Re > 3000 (Turbulent)

Flow Regime Interpretation

Laminar (Re < 2100): Smooth, predictable flow with minimal mixing
Transitional (2100 < Re < 3000): Flow alternates between laminar and turbulent
Turbulent (Re > 3000): Chaotic flow with eddies and vortices

Example Calculation

Water Flow in Pipe

Problem: Water flowing at 1.7 m/s through a 2.5 cm diameter pipe

• Velocity: u = 1.7 m/s

• Pipe diameter: L = 0.025 m

• Water density: ρ = 999.7 kg/m³ (10°C)

• Dynamic viscosity: μ = 0.001308 Pa·s

Solution

Re = ρuL/μ = (999.7 × 1.7 × 0.025) / 0.001308

Re = 42.488 / 0.001308 = 32,483

Result: Re = 32,483 (Turbulent flow)

Since Re > 3000, the flow is turbulent with chaotic mixing.

Flow Regime Boundaries

LaminarRe < 2100
Transitional2100 - 3000
TurbulentRe > 3000

Pipe Critical≈ 2300
Sphere Critical≈ 200,000

Typical Reynolds Numbers

Blood in capillary0.1
Water in straw1,000
Water in pipe10,000
Swimming4×10⁶
Aircraft wing10⁷
Large ship10⁹

Understanding Reynolds Number

What is Reynolds Number?

The Reynolds number is a dimensionless quantity that predicts flow patterns in different fluid flow situations. It represents the ratio of inertial forces to viscous forces and helps determine whether flow will be laminar or turbulent.

Physical Significance

  • Low Re: Viscous forces dominate → Laminar flow
  • High Re: Inertial forces dominate → Turbulent flow
  • Critical for heat transfer and pressure drop predictions
  • Essential for scaling model experiments

Reynolds Number Formulas

Re = ρuL/μ

Re = uL/ν

  • ρ: Fluid density (kg/m³)
  • u: Flow velocity (m/s)
  • L: Characteristic length (m)
  • μ: Dynamic viscosity (Pa·s)
  • ν: Kinematic viscosity (m²/s)

Note: The characteristic length depends on geometry - pipe diameter for internal flow, chord length for airfoils, etc.

Applications

Pipe Flow

  • • Water distribution systems
  • • Oil and gas pipelines
  • • HVAC ductwork
  • • Blood flow in arteries

External Flow

  • • Aircraft and vehicle design
  • • Wind loads on structures
  • • Sports ball aerodynamics
  • • Marine vessel hulls

Process Engineering

  • • Chemical reactor design
  • • Heat exchanger analysis
  • • Mixing and separation
  • • Microfluidics