Sutherland's law

In 1893 William Sutherland, an Australian physicist, published a relationship between the absolute temperature, $T$, of an ideal gas and its dynamic visocity, $\mu$, based on kinetic theory of ideal gases and an idealized intermolecular-force potential. This formula, often called 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:

$\mu = \mu_r \left( \frac{T}{T_r} \right)^{3/2}\frac{T_r + S}{T + S}$
$T_r$ is a reference temperature.
$\mu_r$ is the viscosity at the $T_r$ 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:

$C_1 = \frac{\mu_r}{T_r^{3/2}}(T_r + S)$

References

• Sutherland, W. (1893), "The viscosity of gases and molecular force", Philosophical Magazine, S. 5, 36, pp. 507-531 (1893).