In fluid mechanics, the Reynolds number is a critical dimensionless quantity that helps determine the nature of fluid flow. Named after the British engineer Osborne Reynolds, who introduced the concept in 1883, this number quantifies the ratio of inertial forces to viscous forces in a fluid. It plays a pivotal role in predicting whether a flow will be laminar or turbulent, influencing various practical applications in engineering, meteorology, and industrial processes.
Laminar vs. Turbulent Flow
The Reynolds number is instrumental in distinguishing between laminar and turbulent flow regimes (values are valid for pipe flow):
- Laminar Flow: Occurs at lower Reynolds numbers (typically Re<2,300). In laminar flow, the fluid flows smoothly in parallel layers with minimal mixing between them. This type of flow is predictable and stable, making it easier to model and analyze.
- Turbulent Flow: Characterized by higher Reynolds numbers (typically Re>4,000). In turbulent flow, the fluid exhibits chaotic and irregular fluctuations. This type of flow is more complex and can lead to increased drag and mixing. Turbulent flow is harder to predict and requires more advanced computational models.
To streamline the process of calculating the Reynolds number, several online calculators are available. These tools allow you to input fluid properties such as density, velocity, characteristic length, and dynamic viscosity, and quickly compute the Reynolds number. Using a Reynolds number calculator can save time and enhance accuracy, particularly when dealing with complex fluid systems or when conducting experiments.
Reference Values
Disclaimer: These reference values are just coarse estimations to help you quickly estimate the input. For more scientific projects, please use your own values!
| Fluid | Density (kg/m3) | Dynamic Viscosity (Pa.s) | Kinematic Viscosity (m2/s) |
| Air | 1.293 | 1.79e-5 | 1.48e-5 |
| Water | 997 | 8.9e-4 | 1e-6 |
Reynold Number Equation
The Reynolds number (Re) is defined by the following formula:
Re=ρUL/μ . . . . . . . . . . . . . . . . . . . . . (eq 1)
where:
- ρ is the fluid density,
- U is the velocity of the fluid,
- L is the characteristic length (such as the diameter of a pipe or the length of an airfoil),
- μ is the dynamic viscosity of the fluid.
If you have the data of kinematic viscosity (v) instead, you can relate to the equation v = μ/ρ, then the Reynold number equation becomes:
Re=UL/v . . . . . . . . . . . . . . . . . . . . . . (eq 2)
This dimensionless number essentially compares the relative importance of inertial forces, which promote flow, to viscous forces, which resist flow.
Some Unit conversions:
Density:
- 1 g/cm³ = 1,000 kg/m³
- 1 g/mL = 1,000 kg/m³
- 1 lb/ft³ ≈ 16.0185 kg/m³
- 1 lb/gal ≈ 8.3454 kg/m³
- 1 oz/in³ ≈ 27,679.9 kg/m³
- 1 kg/L = 1,000 kg/m³
Velocity:
- 1 mph≈0.44704 m/s
- 1 ft/s≈0.3048 m/s
- 1 in/s≈0.0254 m/s
- 1 knot (nautical miles/hr) ≈0.51444 m/s
- 1 Mach≈343 m/s
Length:
- 1 mm=0.001 m
- 1 cm=0.01 m
- 1 km=1,000 m
- 1 in≈0.0254 m
- 1 ft≈0.3048 m
- 1 yd≈0.9144 m
- 1 mi≈1,609.344 m
- 1 nmi≈1,852 m
Viscosity:
- 1 Poise = 0.1 Pa.s
- 1 cPoise = 0.001 Pa.s
- 1 Stokes = 0.0001 m^2/s
- 1 cSt=0.000001 m^2/s