Chemistry Reference
In-Depth Information
measurements are made with compression waves; at the pipe-fluid in-
terface shear waves can also be involved (Kishiro
et al.
, 2004).
3.4.2
Attenuation
Ultrasound transducers are phase sensitive; thus, a low measured signal
is not certainly due to attenuation but possibly scattering. This is one of
the reasons why the measurement of the attenuation is less reliable than
the sound velocity measurement. In addition, there are diffraction, losses
at interfaces and relaxation effects. The attenuation coefficient can be
calculated by fitting the data from a measurement of the amplitude as a
function of the distance from the transducer to following equation:
ξ
=
ξ
0
e
−
α
z
(3.2)
where
ξ
is the amplitude,
z
the distance in beam direction and
ξ
0
the
original amplitude at
z
=
0.
3.4.3
Sound velocity
The velocity of sound is a function of the density and the adiabatic
compressibility of the medium. For most materials, with the exception
of water, it decreases with increase in temperature. As the pressure
waves propagate through the medium, the volume and density fluctuate
locally about the normal values. This can be expressed as dilation:
=
V
V
0
D
(3.3)
and condensation:
s
=
ρ
ρ
0
(3.4)
The adiabatic compressibility
κ
is then defined as follows:
V
∂
1
V
D
p
∂
p
=
κ
=−
(3.5)
The bulk modulus of elasticity is then:
=−
p
D
=
1
κ
B
(3.6)
