Viscosity is a fluid’s resistance to shearing deformation. A high-viscosity fluid (honey) resists flowing; a low-viscosity fluid (air) flows easily. Viscosity is the reason boundary layers exist, the reason drag is not zero even on perfectly streamlined bodies, and — through its role in the Reynolds number — the property that determines whether flow is laminar or turbulent.
Two forms
Dynamic viscosity (μ) — the shear stress required to maintain a unit velocity gradient in the fluid. Measured in Pa·s (pascal-seconds). Air at sea level has μ ≈ 1.81 × 10⁻⁵ Pa·s. Dynamic viscosity appears in the Navier-Stokes equations.
Kinematic viscosity (ν) — dynamic viscosity divided by fluid density:
ν = μ / ρ
Measured in m²/s. Air at sea level has ν ≈ 1.48 × 10⁻⁵ m²/s. Kinematic viscosity is what appears in the Reynolds number:
Re = V × L / ν
Kinematic viscosity is the more operationally useful quantity because aerodynamic similarity depends on it, not on dynamic viscosity alone.
Viscosity and altitude
As altitude increases, air temperature drops and density decreases. Dynamic viscosity changes modestly with temperature (decreasing about 10% from sea level to the tropopause), but kinematic viscosity increases substantially because density drops faster than dynamic viscosity. At 10 km altitude, ν ≈ 3.5 × 10⁻⁵ m²/s — more than double the sea-level value. This means the same aircraft at the same speed has a lower Reynolds number at altitude, potentially changing boundary layer behavior and airfoil performance.
| Altitude (km) | Temperature (°C) | Density (kg/m³) | ν (m²/s) | Re at V=15 m/s, c=200 mm |
|---|---|---|---|---|
| 0 | 15 | 1.225 | 1.48 × 10⁻⁵ | 203,000 |
| 2 | 2 | 1.007 | 1.71 × 10⁻⁵ | 175,000 |
| 5 | -18 | 0.736 | 2.21 × 10⁻⁵ | 136,000 |
| 10 | -50 | 0.414 | 3.53 × 10⁻⁵ | 85,000 |
For small UAVs already operating in the low-Reynolds-number regime, altitude effects can push the Reynolds number below critical thresholds where airfoil performance deteriorates sharply.
Viscosity as the source of drag
An inviscid (zero-viscosity) fluid produces zero drag on a body moving through it — this is d’Alembert’s paradox, proven mathematically in 1752 and obviously contradicted by experience. All drag on subsonic aircraft ultimately originates from viscosity: skin friction drag from the viscous boundary layer, pressure drag from viscosity-induced flow separation, and induced drag from the trailing vortex system that exists because viscosity prevents the flow from slipping freely around the wing tip.
Related terms
- Reynolds Number — the ratio of inertial to viscous forces, with viscosity in the denominator
- Boundary Layer — the thin layer where viscous effects are concentrated
- Atmosphere — the medium whose viscosity varies with altitude and temperature
- Navier-Stokes Equations — the equations of viscous fluid motion