# Sutherland's law

In 1893 William Sutherland, an Australian physicist, published a relationship between the dynamic viscosity, $\mu$, and the absolute temperature, $T$, of an ideal gas. This formula, often called Sutherland's law, is based on kinetic theory of ideal gases and an idealized intermolecular-force potential. Sutherland's law is still commonly used and most often gives fairly accurate results with an error less than a few percent over a wide range of temperatures. Sutherland's law can be expressed as: $\mu = \mu_{ref} \left( \frac{T}{T_{ref}} \right)^{3/2}\frac{T_{ref} + S}{T + S}$ $T_{ref}$ is a reference temperature. $\mu_{ref}$ is the viscosity at the $T_{ref}$ reference temperature
S is the Sutherland temperature

Some authors instead express Sutherland's law in the following form: $\mu = \frac{C_1 T^{3/2}}{T + S}$

Comparing the formulas above the $C_1$ constant can be written as: $C_1 = \frac{\mu_{ref}}{T_{ref}^{3/2}}(T_{ref} + S)$
Sutherland's law coefficients:
Gas $\mu_0 [\frac{kg}{m s}]$ $T_0 [K]$ $S [K]$ $C_1 [\frac{kg}{m s \sqrt{K}}]$
Air $1.716 \times 10^{-5}$ $273.15$ $110.4$ $1.458 \times 10^{-6}$