148
4 Mine Ventilation Networks
(continued)
Variable Q 14(3)
Q 12(3)
Q 24(3)
Q 34(3)
Q 23(3)
N 1
1
−1
0
0
0
=
−150
N 2
0
1
−1
0
−1
=
0
N 3
0
0
0
−1
1
=
150
M 1
27.7792
24.1656
5.3438
0
0
=
0
M 2
0
0
−5.3438
12.5537 8.7232
=
0
Inverse matrix
Solution
0.50585
0.07598
0.04483 0.01779
0.00357 Q 14(3) = −69.15
−0.49415
0.07598
0.04483 0.01779
0.00357 Q 12(3) =
80.85
−0.39496 −0.73854 −0.43575 0.01422 −0.03471 Q 24(3) =
−6.12
−0.09920 −0.18549 −0.51942 0.00357
0.03828 Q 34(3) = −63.03
−0.09920 −0.18549
0.48058 0.00357
0.03828 Q 23(3) =
86.97
…
Iteration 19
Branch 14
12
24
34
23
R ij
0.4
0.3
0.8
0.2
0.1
Q i(18)
−69.29
80.71
−6.39
−62.89
87.11
Q 11(19)
Q 12(19)
Q 13(19)
Q 21(19)
Q 22(19)
Independent term
N 1
1
−1
0
0
0
=
−150
N 2
0
1
−1
0
−1
=
0
N 3
0
0
0
−1
1
=
150
M 1
27.715424
24.213432
5.1149014
0
0
=
0
M 2
0
0
−5.114901
12.578987 8.7105066
=
0
Inverse matrix
Solution
0.5055491
0.0735746
0.0434719 0.0178403
0.0034559 Q 11(19) = −69.312
−0.494451
0.0735746
0.0434719 0.0178403
0.0034559 Q 12(19) =
80.688
−0.398669
−0.746964
−0.441347
0.0143844 −0.035086
Q 13(19) =
−6.402
−0.095782
−0.179462
−0.515181
0.0034559
0.0385419 Q 21(19) = −62.910
−0.095782
−0.179462
0.4848186 0.0034559
0.0385419 Q 22(19) =
87.090
Iteration 20:
Branch 14
12
24
34
23
R ij
0.4
0.3
0.8
0.2
0.1
Q i(19)
−69.32
80.68
−6.41
−62.91 87.09
Q 14(20)
Q 12(20)
Q 24(20)
Q 34(20)
Q 23(20)
Independent
term
N 1
1
−1
0
0
0
=
−150
(continued)