Table 8. Standard metric steel pipe sizes
(data from DFF 1985).
Nominal
Outer
Wall
Inner
diameter
diameter
thickness
diameter
(mm)
(mm)
(mm)
(mm)
50
60.3
2.9
54.5
65
76.1
2.9
70.3
80
88.9
3.2
82.5
100
114.3
3.6
107.1
125
139.7
3.6
132.5
bound the optimal diameters we have found. The bounding diameter that has the
lowest total cost will become our optimal discrete diameter. Obviously, it is only
necessary for us to compute the portion of the total cost that is dependent on pipe
diameter in making this decision. Table 9 gives the cost data for the bounding
discrete diameter for each of the pipe segments of our example. The costs are
calculated on a unit length basis using eq 2-23 divided through by L, the pipe length.
The portions of the total variable cost ascribable to each of the major component costs
are also given in Table 9. The parameter values of I1/L and I3/L used for each pipe
segment are the same as those given in Table 7.
Now we need to consider the constraints on our multiconsumer system as
derived earlier in Chapters 3 and 4. These are summarized in Chapter 5 in the System
Constraint Satisfaction subsection. All of these constraints deal with pressure levels
at various points within the system. Since verification of satisfaction for these
constraints requires calculation of the pressure losses in the supply and return line,
we begin by doing so for each of the pipe segments. The pressure losses in the supply
or return pipes are calculated with eq 5-8 and 5-9 using the optimal discrete
diameters we have determined independently. The results are given in Table 10.
Satisfaction of the constraint of eq 4-2 at each of the consumers requires that we
Table 9. Discrete bounding diameters and variable costs for the example (optimal non
discrete diameters shown in boldface, optimal discrete diameters shown in italic).
Variable costs ($/m)
Pipe
d
Discrete cost
segment
(m)
Heat loss
Capital
Pumping
Total
premium (%)
0.0545
64.76
140.61
117.31
322.68
12.44
(6,1), (7,2),
0.0666
72.90
171.83
42.23
286.96
--
(7,3), (5,4)
0.0703
75.34
181.37
32.06
288.78
0.63
0.0825
83.24
212.85
109.11
405.20
4.14
(6,7)
0.0932
90.02
240.46
58.62
389.09
--
0.1071
98.65
276.32
28.87
403.84
3.79
0.1071
98.65
276.32
95.21
470.18
0.85
(5,6)
0.1134
102.51
292.57
71.16
466.24
--
0.1325
114.03
341.85
32.19
488.07
4.68
0.1071
98.65
276.32
222.03
597.00
12.51
(8,5)
0.1304
112.77
336.43
81.44
530.64
--
0.1325
114.03
341.85
75.07
530.95
0.058
65
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