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
Flow Analysis
Formula: Re = ρuL/μ = uL/ν
Flow regime criteria: Re < 2100 (Laminar), 2100 < Re < 3000 (Transitional), Re > 3000 (Turbulent)
Flow Regime Interpretation
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
Typical Reynolds Numbers
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