Page 127 - Advanced Mine Ventilation

108 Advanced Mine Ventilation

Hence,

2
2r ðr r Þ
air
v S ¼ g$T ¼ g$ (8.5)
9h
Table 8.1 shows the values of T for particle radii in the range 0.001e10 mm.

8.1.2 Settling Velocity When r [

In this case, the resistance of the medium, Fm, is derived as [3]:

2
6ph r v
Fm ¼ (8.6)
ðA þ QÞ[
The value of [ is given in Table 8.1.(A þ Q) has a value of 1.175, 1.091, or 1.131
2
depending on the type of reflection of particle (s ) [2].
Settling velocities can be derived in the same manner as shown in Article 8.1.1.

8.1.3 Settling Velocity When r z [
For a more rigorous analysis of Fm in Article 8.1.1, Cunningham [4] provided a better
estimate of resistance due to the medium as:
6phrv
(8.7)
Fm ¼
[
1 þ A
r
and the settling velocity is calculated as:

mg [
v S ¼ 1 þ A (8.8)
6ph r r
A has a value of 0.864 [5].
Eq. (8.7) was further modified to allow for cases where r z [. There is no theoret-
ical solution, but the experimental data fit Eq. (8.9) well [5].
6phrv
(8.9)
l l b r
Fm ¼
1 þ A þ Q e [
r r
This is the most generalized estimate for Fm, and both estimates of Fm (r[[ and
r [) can be derived from it. For r[[; / 0, and for r [;e b r l/[.
[
r