Environmental Engineering Reference
In-Depth Information
TABLE 3.3
Reynolds Numbers by Airway Generation (Calculated at 1 atm and 37°C)
Airway 
Generation
Airway Cross 
Section 76  (cm 2 )
Airway 
Diameter 76  (cm)
Velocity a
(cm/s)
Velocity b
(cm/s)
Re a
Re b
0
2.54
1.800
98.43
393.70
1077.42
4309.68
1
2.33
1.220
107.30
429.18
796.07
3184.27
2
2.13
0.830
117.37
469.48
592.44
2369.76
3
2.00
0.560
125.00
500.00
425.70
1702.80
4
2.48
0.450
100.81
403.23
275.87
1103.49
5
3.11
0.350
80.39
321.54
171.10
684.41
6
3.96
0.280
63.13
252.53
107.50
430.00
7
5.10
0.230
49.02
196.08
68.57
274.26
8
6.95
0.186
35.97
143.88
40.69
162.76
9
9.56
0.154
26.15
104.60
24.49
97.97
10
13.40
0.130
18.66
74.63
14.75
58.99
11
19.60
0.109
12.76
51.02
8.46
33.82
12
28.80
0.095
8.68
34.72
5.02
20.06
13
44.50
0.082
5.62
22.47
2.80
11.21
14
69.40
0.074
3.60
14.41
1.62
6.49
15
117.00
0.050
2.14
8.55
0.65
2.60
16
225.00
0.049
1.11
4.44
0.33
1.32
17
300.00
0.040
0.83
3.33
0.20
0.81
18
543.00
0.038
0.46
1.84
0.11
0.43
19
978.00
0.036
0.26
1.02
0.06
0.22
20
1743.00
0.034
0.14
0.57
0.03
0.12
21
2733.00
0.031
0.09
0.37
0.02
0.07
22
5070.00
0.029
0.05
0.20
0.01
0.04
23
7530.00
0.025
0.03
0.13
0.01
0.02
a 15 L /min.
b 60 L /min.
called the entrance length, L e , l . Under laminar conditions, the inal velocity proile is parabolic,
with the velocity increasing from zero at the tube walls to the free stream velocity V 0 at the center
of the tube. The actual shape of the inal parabolic proile is determined by both the absolute luid
viscosity and the pressure gradient driving the low. In turbulent low, the boundary layer grows
more rapidly, the entrance length ( L e , t ) is shorter, and the fully developed velocity proile is latter. 74
In turbulent low, a laminar sublayer will exist near the wall, and a transitional layer will lie between
this laminar layer and the entirely turbulent low that exists in the tube's center. These important
details are shown in Figure 3.2.
Since inhaled particles are transported via airstreams, knowledge of both low development
characteristics and velocity proiles are fundamental to predicting particle deposition patterns.
However, the airlow patterns in human lungs are much more complex than the idealized situation
described earlier. The human bronchial tree is a branching network of bifurcating, irregular tubes.
This network also contains morphological surface features that affect low patterns. A vast body of
work has been generated in attempting to characterize airlow in anatomically realistic human lung
models. In this chapter, the discussion will be limited to a short overview of low in curved tubes,
bifurcations, and branching networks.
 
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