Building Acoustics

198 Building acoustics

where μ is the coefficient of viscosity.

5.6.2 Porosity

By the porosity of a porous material, it is understood as the relative part of the volume of
the open pores in the material, which in our case is the relative volume part of air. This
applies to fibrous materials as well as granular ones. As is apparent from the models
described above, the parameter is important when it comes to sound propagation in
porous materials. In connection with geophysical characterization, it is common practice
to determine this parameter by filling up the pores with water or some other fluid. It goes
without saying that this will not be a practical procedure in the case of the porous
materials used as acoustic absorbers.

Piston

V

V = V + V

0

t fs

Figure 5.34 A principal set-up for determining porosity.

Champoux et al. (1991) have developed an accurate method based on using air. The
principle is not new but by using modern equipment they arrive at accuracy better than
1%. As shown in Figure 5.34, the material having a given total volume Vt = Vf + Vs is
placed in a closed compartment. Here Vf and Vs denote the volume of the pores and the
volume of the solid frame, respectively. By definition, the porosity σ is given by

f
t

.

V

V

σ= (5.69)

When we talk about the volume of the pores we shall infer that the pores in this volume
are interconnected, i.e. excluding the volume of closed pores. The rest of the air volume
in the chamber is denoted V 0. The procedure is now to give the piston a controlled
displacement resulting in a precise change ΔV in the volume and a resulting pressure
change ΔP. Assuming that the pressure in the chamber initially is equal to the barometric
pressure P 0 and, furthermore, that the change of state takes place isothermally we get

00

0

()(

or

().

PV P P V V

V

VPP

P

= +Δ +Δ)

Δ

=− +Δ

Δ

(5.70)