Reynolds Number
Will the flow in a pipe be smooth (laminar) or chaotic (turbulent)? Calculate the Reynolds number — or the speed, diameter, density or viscosity that gives a chosen value.
What is the Reynolds Number?
The Reynolds number compares the fluid’s inertia (its tendency to keep moving) with its viscosity (internal friction that smooths the flow). It has no units, so the same value means the same kind of flow in a garden hose or an oil pipeline.
At low Re, viscosity wins and the fluid slides in neat parallel layers: laminar flow. At high Re, small disturbances grow into swirling eddies: turbulent flow, which mixes well but needs much more pumping power.
Flow Regime
turbulentTypical Reynolds Numbers
order of magnitude| Situation | Re |
|---|---|
| Bacterium swimming | 10−5 |
| Blood in a capillary | 10−3 |
| Honey poured from a spoon | 10−2 |
| Blood in the aorta | ~4000 |
| Water in a household pipe | 104–105 |
| Swimming person | 106 |
| Airliner wing | 107–108 |
Key Relations
Tables often give ν instead of μ. Water at 20 °C has ν ≈ 1.0×10−6 m²/s, air about 15 times more.
Solve for the speed at Re = 2300 to find how fast a fluid can flow before turbulence sets in.
For a square or rectangular duct, use the hydraulic diameter: four times the area divided by the wetted perimeter.
Sources & Verification
- Y. A. Çengel & J. M. Cimbala, Fluid Mechanics: Fundamentals and Applications, 4th ed., McGraw-Hill, 2018 — Ch. 8 (Internal Flow).
- F. M. White, Fluid Mechanics, 8th ed., McGraw-Hill, 2016 — Ch. 6 (Viscous Flow in Ducts: Reynolds number regimes).