# Power-law viscosity law

A power-law can be used as an approximation of the viscosity of dilute gases. For dilute gases at moderate temperatures this formula is slightly less accurate than Sutherland's law. The power-law viscosity law can be written as:

$\mu = BT^n$

Where $\mu$ is the viscosity in kg/m-s, $T$ is the static temperature in K, and $B$ is a dimensional coefficient. For air at moderate temperatures and pressures $B = 4.093 \times 10^{-7}$, and $n = 2/3$.

The power-law viscosity law can also be written as:

$\mu = \mu_{ref} \left(\frac{T}{T_{ref}}\right)^n$

Where $\mu$ is the viscosity in kg/m-s, $T$ is the static temperature in K, $T_{ref}$ is a reference value in K, $\mu_{ref}$ is a reference value in kg/m-s. For air at moderate temperatures and pressures, $\mu_{ref} = 1.716\times 10^{-5} kg/m-s$, $T_{ref} = 273 K$, and $n = 2/3$.

Note that there exists a different power-law for non-Newtonian fluids!