Mathematical expression

The mathematical definition of the static air flow resistivity given by Henry Darcy is:

\[ \sigma\phi\vec{v} = -\vec{\nabla} p \]

with

\[ \sigma=\frac{\eta}{k_{0}} \]

where $\phi$ is the open porosity of the material, $\eta$ the dynamic viscosity of air ($\sim$ 1.84 $\times$ $10^{-5}$ N.s.m$^{-2}$ at ambiant temperature and pressure conditions) and $k_0$ is the static permeability of the material.

Physical description

The static air flow resistivity characterizes, partly, the visco-inertial effects at low frequencies (when the viscous boundary layer is of the order of magnitude of the the characteritic size of the pores).
The models by Delany-Bazley [DB70] and Delany-Bazley-Miki [Mik90] use only this parameter to described the behavior of fibrous acoustical materials.

For acoustical materials, the range of values for the static air flow resistivity is approximately [$10^3$ $10^6$] N.s.m$^{-4}$.

The resistivity can be directly measured. [ISO 9053]