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Calculate Reynolds number for pipe flow, flow over flat plates, and open channel flow to determine whether flow is laminar or turbulent. Supports water, air, oil, and custom fluids with dynamic and kinematic viscosity.
The Reynolds number is the most important dimensionless parameter in fluid mechanics. It represents the ratio of inertial forces to viscous forces. Below Re=2300 in a pipe, flow is always laminar (smooth and predictable). Above Re=4000, flow is turbulent (chaotic mixing with higher friction losses but better heat and mass transfer).
The Reynolds number (Re) was introduced by Osborne Reynolds in 1883 through elegant experiments with dyed water injected into pipe flow. He observed that at low velocities, the dye filament remained straight and parallel (laminar flow), but above a critical velocity, the dye dispersed into chaotic mixing (turbulent flow). This simple observation led to one of the most fundamental dimensionless parameters in all of fluid mechanics.
| Application | Formula | Length Scale | Regime Criteria |
|---|---|---|---|
| Pipe/Duct flow | Re = ρvD/μ | D = pipe diameter | Laminar <2300, turbulent >4000 |
| Flat plate | Re = ρvL/μ | L = plate length | Transition at Re ≈ 500,000 |
| Sphere | Re = ρvD/μ | D = sphere diameter | Stokes law valid Re<1 |
| Open channel | Re = ρvRh/μ | Rh = hydraulic radius | Laminar <500, turbulent >2000 |
| Stirred tank | Re = ρND²/μ | N=rotation speed, D=impeller | Laminar <10, turbulent >10,000 |
| Boundary layer | Re = ρvx/μ | x = distance from leading edge | Transition at Rex ≈ 500,000 |
| Fluid | Density ρ | Dynamic Viscosity μ | Kinematic ν |
|---|---|---|---|
| Water (20°C) | 998 kg/m³ | 0.001001 Pa·s | 1.003×10⁻⁶ m²/s |
| Water (60°C) | 983 kg/m³ | 0.000467 Pa·s | 4.75×10⁻⁷ m²/s |
| Air (20°C) | 1.204 kg/m³ | 1.81×10⁻⁵ Pa·s | 1.50×10⁻⁵ m²/s |
| SAE 30 Oil (40°C) | 885 kg/m³ | 0.1 Pa·s | 1.13×10⁻⁴ m²/s |
| Glycerin (20°C) | 1260 kg/m³ | 1.412 Pa·s | 1.12×10⁻³ m²/s |
| Honey | 1360 kg/m³ | 10 Pa·s | 7.35×10⁻³ m²/s |
Laminar flow: Friction factor f = 64/Re (exactly). Pressure drop proportional to velocity. No lateral mixing between fluid layers. Excellent for precision flow metering. Turbulent flow: Friction factor from Moody chart (depends on roughness). Pressure drop proportional to velocity squared. Intense lateral mixing — excellent for heat and mass transfer. Most industrial pipe flow is turbulent because the high velocities needed for practical flow rates produce Re well above 4000. Laminar flow occurs in microfluidics, lubrication oil films, blood flow in small vessels, and very viscous fluid flows.
Engineering design always includes safety factors to account for material variability, load uncertainty, construction tolerances, and progressive deterioration. Typical safety factors: structural steel bending 1.67 (ASD), concrete compression 1.5-2.0, bolts in tension 2.0-3.0, pressure vessels 3.5-4.0. Always verify that your design complies with applicable local codes, national standards, and industry regulations before construction or installation.