Library / Aerospace / AER-04
Aerospace
Reynolds number
Ratio of inertial to viscous forces in a flow.
- Ref
- AER-04
- Rev
- v1
- Field
- Aerospace
- Result
- Re
ρ in kg/m³, V in m/s, ℓ the characteristic length in m, μ dynamic viscosity in Pa·s and ν = μ/ρ kinematic viscosity in m²/s. Dimensionless.
Reynolds number tells you whether a flow is smooth (laminar) or chaotic (turbulent). A large value means the fluid’s momentum overwhelms its internal friction.
Calculator
- Kinematic viscosity ν = μ/ρ14.6 mm²/s
- Re in millions6.163 million
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- Pipe flow becomes turbulent at Re of about 2300. Wing boundary layers become turbulent from Re of about 500 000.
- Wind tunnel models must match the Reynolds number as well as shape, or the results will not scale to the full-size aircraft.
- All four inputs enter as simple powers, so the sweep chart is a straight line on log axes.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing () | Local step | Change in result |
|---|---|---|---|---|---|---|
| ρ Density | 0.1 to 1,100 kg/m³ | 503,100 | 5.534e9 | 5.533e9 | +10% | +10 % |
| ℓ Characteristic length | 0.01 to 20 m | 41,080 | 8.217e7 | 8.213e7 | +10% | +10 % |
| V Speed | 1 to 400 m/s | 102,700 | 4.108e7 | 4.098e7 | +10% | +10 % |
| μ Dynamic viscosity | 10 to 1,100 µPa·s | 100,200 | 1.103e7 | 1.092e7 | +10% | −9.09 % |
Sweep of Speed
| Speed (m/s) | Reynolds number |
|---|---|
| 1 | 102,700 |
| 2.115 | 217,200 |
| 4.472 | 459,300 |
| 9.457 | 971,400 |
| 20 | 2,054,000 |
| 42.29 | 4,344,000 |
| 89.44 | 9,187,000 |
| 189.1 | 1.943e7 |
| 400 | 4.108e7 |
Sweep one variable
Variables and how each one contributes
Reynolds number
What the equation gives you. Everything else feeds it.
Density
Fluid density. Directly proportional.
Speed
Flow speed relative to the body. Directly proportional.
Characteristic length
Often the wing chord or body length. Directly proportional.
Dynamic viscosity
Air about 18 µPa·s, water about 1000 µPa·s at 20 °C. Inversely proportional.
Worked example with the values above
- Convert viscosity: 17.89 µPa·s = 1.789×10−5 Pa·s.
- Numerator: ρVℓ = 1.225 × 60 × 1.5 = 110.3.
- Re = 110.3 / 1.789×10−5 = 6,163,000.
Assumptions and limits
- Length chosen consistently with the data or correlation being used.
- Constant fluid properties.
- Steady flow.
Common mistakes
- Using kinematic and dynamic viscosity interchangeably.
- Mixing µPa·s with Pa·s.
- Taking the wrong characteristic length (diameter vs radius, chord vs span).
Statistics and uncertainty
The four inputs multiply and divide, so the relative errors add in quadrature. Viscosity of air varies with temperature (about 0.7% per kelvin near 15 °C), which can be a larger error than the length or speed measurement.
Where it is used
- Predicting laminar-to-turbulent transition.
- Scaling wind tunnel and water tunnel tests.
- Friction drag estimates.
Maths you need
- Viscosity: a fluid’s internal friction
- Density: mass per unit volume