Biomedical Engineering Reference
In-Depth Information
FIGURE 9-13
Airway resistance
distribution in the
tracheobronchial
tree [Adapted from
(Fenn and Rahn
1965).]
WORKED EXAMPLE
Turbulent Flow
If the diameter of each of the eight bronchi after the third branching is 7.5 mm and the tidal
volume breathed is 0.6 L inhaled over 0.8 s, will the flow be laminar or turbulent? Using the
same breathing parameters, determine whether flow through the trachea with a diameter of
20 mm is laminar or turbulent.
The flow rate in both cases is the same:
0
.
6
Q
=
0
.
8
10
5
mm
3
/s
=
0
.
75 L
/
s
(
7
.
5
×
)
The total cross sectional area of the eight bronchi, assuming that they are perfectly circular, is
d
2
4
8
π
A
=
5
2
=
2
×
π
×
7
.
353 mm
2
=
Assuming an equal distribution of flow into each bronchus, the air flow velocity will be
Q
A
v
=
10
5
353
7
.
5
×
=
=
2125 mm/s
(
2
.
1 m/s
)
The density of air is 1.2 kg/m
3
, and the dynamic viscosity is 1
10
−
5
kg/(m
.
78
×
·
s); therefore,
the Reynolds number is
ρv
d
R
e
=
η
10
−
3
1
.
2
×
2
.
1
×
7
.
5
×
=
10
−
5
1
.
78
×
=
1061
This is smaller than 2300; therefore, the flow will almost certainly be laminar.
