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We also need to define an expression for dynamic viscosity, μ, which depends on temperature. The most significant impact of viscosity is in the definition of Reynolds number,

(2.11)

which is an expression of the ratio of inertial to viscous forces (here, U_∞ is the freestream velocity or airspeed, and c is the mean aerodynamic chord of the wing). Reynolds number has a significant impact on boundary layer development and aerodynamic stall, as we will see in Chapter 12.

The viscosity of air is related to the rate of molecular diffusion, which is a function of temperature (Sutherland 1893). This relationship has been distilled down to Sutherland's Law,

(2.12)

where T is the temperature in absolute units, and β and S_visc are empirical constants, provided in Table 2.2 for both English and SI units (NOAA et al. 1976). Based on Eq. (2.12), the viscosity of a gas increases with increasing temperature. Thus, the dynamic viscosity decreases gradually through the troposphere, starting with the standard sea level value of μ_SL = 1.7894 × 10⁻⁵ kg/(s m) = 3.7372 × 10⁻⁷ slug/(s ft) at a temperature of T_SL = 288.15 K = 518.67 ° R. If kinematic viscosity (ν) is desired instead of dynamic viscosity, it can be found based on its definition,

(2.13)

Table 2.2 Constants used in Sutherland's Law.

Source: Based on NOAA et al. 1976.

	SI	English
β	1.458 × 10−6 kg/(s m K1/2)	2.2697 × 10−8 slug/(s ft ° R1/2)
S visc	110.4 K	198.72 ° R