Page 198 - Advanced Mine Ventilation

178 Advanced Mine Ventilation

For the same reasons as before, the absorption terms can be dropped from Eq.
(11.34), which then reduces to

" #
0:14 c ip q p 1 U c iq q q 1 þ U
c ¼ exp x þ exp x (11.35)
B 1 U U AvDt 1 þ U U AvDt
If leakage is neglected, i.e., a 0 ¼ 0, then U m ¼ U L ¼ U ¼ U 0 and solution for both
cases is the same. In either case,

0:14 c ip q p 1 U 0 c ip q q 1 U 0
c ¼ exp x þ exp x
B ð1 U 0 ÞU 0 AvDt ð1 þ U 0 ÞU 0 AvDt
(11.36)

Solutions as obtained in Eqs. (11.29) and (11.35), of course, correspond to the high-
est concentration that can arise in a roadway.
Thus, these solutions constitute a limit. Data required to solve Eq. (11.35) are the
same as those for Eq. (11.29).

11.4.6 Diesel Engines Moving Randomly in a Roadway With
Uniform Air Velocity

When diesel engines move in a roadway without any definite pattern, they are defined
as performing randomly. This situation can be best analyzed by assuming that the
diesel exhaust source is uniformly distributed over the entire length of the roadway.
Assuming further that a steady-state concentration is developed very soon, the required
differential equation is

2
v c vc qc i
E x 2 þ u ¼ (11.37)
vx vx FL
Physical situations are best represented by the following boundary conditions:

vc
¼ 0at x ¼ 0 (11.38)
vx

i.e., there is no transfer of material at x ¼ 0.

vc qc i
ucj þ E x ¼ (11.39)
x¼L
vx F
x¼L
i.e., matter is conserved in the roadway.