Page 130 - Advanced Mine Ventilation

Characteristics of Respirable Coal Dust Particles 111

Hence, for upper limit for nonsettling particle size,

1

4D 2
Fm B ¼ v S ¼ mg B ¼
p
(8.15)
1

4 3 4 KTB 2
or p r r gB ¼
3 p
Rearranging,
1
3 3 ðKTÞ 2
r ¼ (8.16)
3 1
2 p 2r gB 2
Assuming r[[:
1
Eq. (8.10) for B, reduces to B ¼
6phr
Substituting the value of B and squaring both sides in Eq. (8.16):
9 KT 6ph r
6
r ¼ $ 2 2 3
4 g r p
or

13:5KT h
5
r ¼ 2 2 2 (8.17)
p g r
An example:
Using Eq. (8.17), calculate the nonsettling size of a coal particle with a density of

1.3: assume T ¼ 300 Kelvin
h for air ¼ 181 10 6 P
K ¼ 1.3708 10 16 erg. Deg 1
g ¼ 981 cm/s 2
Hence,

13:5 1:3708 10 16 181 10 6 300
5
r ¼
2 2 2
p ð981Þ ð1:3Þ
¼ 66:3 10 25
r r ¼ 2:31 10 5 cm ¼ 0:23 mm

or non settling particle diameter ¼ 0:46 mm

Aerodynamic equivalent diameter ¼ 0:52 mm