Page 197 - Advanced Mine Ventilation

Diesel Exhaust Control 177

Data required for solution of Eq. (11.29) are easily available. Values for c i and q are
obtained from test data on the engine, whereas values for leakage coefficient (a 0 ) and
interval between arrivals (Dt) are obtained from case studies. The velocity of air, u, and
velocity of engine, v, are already known. A computer program was written to solve Eq.
(11.29) in reference [8].

11.4.5 Diesel Engines Moving Continuously in a Cycle in a
Roadway With Little Leakage
In this case, the leakage coefficient, a 0 , is very small. Hence, the convective velocity
can be reasonably well estimated by the average velocity over the entire length, L,of
the roadway.
For exhaust type ventilation, the average velocity is given by

a 0 L
u ¼ u 0 1 (11.30)
2
Substituting U for U L in Eq. (11.30):

0:14 c i q
(11.31)
c ¼
B 1 U U
where,

u a 0 L
U ¼ ¼ U o 1 (11.32)
v 2

The differential equation in this case is

2
v c 1 U vc lU
þ c ¼ 0 (11.33)
vx 2 AvDt vx 8aAvDt
The solution of Eq. (11.33) is obtained by proper substitution in Eq. (11.28) and is
given below:

2 3
( ( 2 )1)
2
c ip q p 1 1 U 1 1 U l U
exp þ x
6 7
6 1 U U 2 AvDt 4 AvDt 8aAvDt 7
0:14 6 7
c ¼ 6 7
B 6 7
2
6 ( ( 2 )1) 7
4 c iq q q 1 1 þ U 1 1 þ U U 5
exp þ x
þ
1 þ U U 2 AvDt 4 AvDt 8aAvDt
(11.34)