Civil Engineering Reference
In-Depth Information
Figure 4.13
Measurement of tortuosity. The material is saturated with a conducting
fluid and the resistivity of the material is measured between the two electrodes.
method of measuring the tortuosity uses the time of flight of an ultrasound pulse across
the material. This method will be discussed in Chapter 5. The concept of tortuosity is
generalized in Section 5.3 for the case of materials having non-cylindrical pores.
4.10
Impedance at normal incidence and sound
propagation in oblique pores
4.10.1 Effective density
The material represented in Figure 4.14 is placed on an impervious rigid wall. The
acoustic field in the air above the material is plane and normal to the surface.
As shown in Figure 4.14, there are two microscopic directions of propagation parallel
to the two symmetrical directions of the pores. The macroscopic direction of propagation
is
x
and only the
x
components
υ(x)
of the microscopic velocities
υ
1
and
υ
2
must be
taken into consideration at the macroscopic level:
υ(x)
=
υ
1
(x)
cos
ϕ
=
υ
2
(x)
cos
ϕ
(4.148)
The flux of air
V
through a unit surface area perpendicular to the
x
axis is given by
υ(x)nπR
2
/
cos
ϕ
V(x)
=
(4.149)
M
1
M
2
u
2
u
1
l
d
j
X
2
X
1
X
Figure 4.14
Porous material with oblique pores in a normal plane acoustic field and
set upon an impervious rigid wall.
