ε = 5 105 m
a = 0.119 (dimensionless)
b = 0.152 (dimensionless)
c = 0.0568 (dimensionless)
Ts = 120C
Tr = determined by consumer model (eq 3-18) (C)
Ce = .0 105/Wh
Ch = .4 15/Wh
PVFe = PVFh = PVFm&r = 9.08 (dimensionless)
Load control by flow modulation with consumer model (eq 3-25).
There are a number of additional parameters that were introduced in developing
the multiconsumer constraints for which we have not yet assigned any typical
values. They are:
∆Pcvm,i = 5 104 N/m2
(for all consumers, i = 1,4)
∆Phe,i = 1.0 105 N/m2
(for all consumers, i = 1,4)
Pmax = 1.0 106 N/m2
Psaf = 1.0 105 N/m2
PNPSH = 2.0 105 N/m2
Pa = 1.0 105 N/m2
Pasa = 0.5 105 N/m2.
Before we can find the optimal independent diameters for the pipe segments, we
need to calculate the remaining parameters that are determined by the assumptions
above. Because the optimal pipe diameter for a single pipe segment is independent
of the pipe length and elevation (see eq 2-23), the optimal independent diameter will
be the same for pipe segments (6,1), (7,2), (7,3) and (5,4). Thus, we construct Table
7 with the parameter values needed and the resulting optimal independent diam-
eters. In each case, we have proceeded as before by solving the Lower Bounding
Problem (LBP) (eq 2-20), which neglects heat losses first and, subsequently, using
that as a starting point for finding the solution to the complete problem including
heat losses (eq 2-24). Also, as earlier, FORTRAN programs I1EQ3-26 and I2-C-GMT
were used to compute I1 and I3 respectively.
The optimal diameters found above do not necessarily correspond to actual
discrete pipe diameters available, so before we check this solution to see if it satisfies
the constraint set, we first need to determine what the optimal discrete diameters
would be. Table 8 contains pipe size data for standard metric pipe sizes in the range
needed for our example.
To find the optimal discrete diameters, we proceed as before in the example of
Chapter 2 by simply examining the total cost of the discrete pipe diameters that
Table 7. Parameter values and optimal independent diameters for ex-
ample of Figure 14.
Pipe
I1/L
I3/L
d by LBP
d by eq (2-24)
($ m4.095)
segment
($/m)
(m)
(m)
4.276 105
(6,1), (7,2),
73.3
0.0691
0.0666
(7,3), (5,4)
3.289 104
(6,7)
73.3
0.0966
0.0932
1.085 103
(5,6)
73.3
0.1175
0.1134
2.529 103
(8,5)
73.3
0.1350
0.1304
64
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