ε = 5 105 m

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:

∆*P*cvm,i = 5 104 N/m2

(for all consumers, *i *= 1,4)

∆*P*he,i = 1.0 105 N/m2

(for all consumers, *i *= 1,4)

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 *I*1 and *I*3 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

I1/L

I3/L

d *by LBP*

d *by eq (2-24)*

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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