Biomedical Engineering Reference
In-Depth Information
WORKED EXAMPLE
The speed of sound in any gas mixture can be calculated by using the molecular weight to
determine the density. Air is made up of O
2
,N
2
, and CO
2
in proportions (21:78:1); therefore,
the molecular weights are 16
+
16
=
32
,
14
+
14
=
28, 12
+
16
+
16
=
44. The molecular
mass,
M
, of the mixture is therefore
21
32
100
×
78
28
100
×
1
44
100
×
M
=
+
+
=
29
Remembering that at atmospheric pressure and at 0
◦
C the volume of 1 mole of gas is 22.414
liters the density can be determined
10
−
3
29
×
29 kg/m
3
ρ
o
=
=
1
.
10
−
3
22
.
4
×
And, finally, the speed of sound through the air can be calculated
1
10
5
.
013
×
×
1
.
4
c
air
=
=
331
.
6 m/s
1
.
29
If about 50% of the oxygen has been used and no additional CO
2
has been added, then the
proportions become 11:88:1, and the molecular mass changes to
11
32
100
×
88
28
100
×
1
44
100
×
M
=
+
+
=
28
.
6
This results in a change in density
10
−
3
.
×
29
6
277 kg/m
3
ρ
o
=
=
.
1
10
−
3
22
.
4
×
which results in a change in the speed of sound of nearly 0.5% to
1
10
5
.
013
×
×
1
.
4
c
air
=
=
333
.
25 m/s
1
.
277
Figure 9-20 shows the theoretical change in the speed of sound for oxygen concentrations
varying from 0% up to about 25%. It is interesting to note that the relationship looks very linear.
Commercial instruments pass the dried gas intoa1mlong tube and determine the sound
velocity at 150 kHz by measuring the phase shift. Sensitivities of 0.004% for oxygen up to
21% concentration and 0.0008% for CO
2
up to 8% concentration are possible.
9.5.2 Pneumotachography
A pneumotachograph is a device for measuring airflow. It consists of a respiratory tube
with a small resistance to airflow. The two chambers on either side of the resistance are con-
nected to a differential pressure transducer by thin tubes, as shown in Figure 9-21. During
respiration through the pneumotachograph tube, a small pressure difference,
P
, is mea-
sured across the resistance. The laminar flow rate is directly proportional to the ratio of the
pressure difference,
P
, and resistance,
R
f
, according to the fluid version of Ohm's law.
Q
=
P
R
f
(9.12)
The resistance element consists either of a wire screen or a series of capillaries that main-
tains laminar airflow even at the maximum air speed.
