∆Pd

Ct

--

8.187

0.208

340

1.111

8

7.981

0.203

384

1.112

10

10.020

0.255

120

1.178

12

11.938

0.303

50

1.305

adequate in some cases, they lack the flexibility to account for varying conditions,

most notably economic. Because these rules of thumb are based on designs proven

only to be functional, they cannot profess to yield least life cycle cost designs. To see

how the results of the above example would compare with a rule of thumb based

design, we consider a very common design rule of thumb used in Europe for systems

in this temperature range: that the pressure loss in the piping not exceed 100 Pa/m.

For this example, standard schedule 40 pipe sizes are used.

To apply the above rule of thumb, we simply calculate the pressure loss that

would result at maximum flow conditions using increasing pipe size until we find

a size that satisfies the rule. This calculation is done using eq 2-15 given earlier. The

results are shown in Table 1. We see from Table 1 that a 12-in. (300-mm) pipe would

be necessary to satisfy the rule of thumb. The pressure loss for the 10-in. (250-mm)

pipe exceeds the 100-Pa/m level by over 20% and therefore would probably be

considered unacceptable.

Now we need to determine what discrete pipe diameter would be recommended

by the procedure outlined in the previous section. The optimal nondiscrete diameter

was found to be 0.208 m or 8.187 in. We see from Table 1 that this lies between the

inside diameters of the 8- and 10-in. (200- and 250-mm) nominal pipe sizes.

To determine which to use, we simply calculate the cost of each alternative using

eq 2-19. These results are also included in Table 1. We see from these figures that the

total life cycle cost of the 8-in. pipe is about 6% less than the 10-in. pipe and thus the

8-in. pipe should be selected. We also note that the life cycle cost of the 8-in. pipe is

only 0.1% greater than that of an optimal 8.187-in. inside diameter pipe, if such a pipe

were available.

If we compare the cost of the 8-in. pipe, which our method recommends, to the

12-in. pipe required by the maximum pressure drop rule of thumb, we find that the

life cycle cost of the rule based design is 17% greater. This great saving in life cycle

cost is also accompanied by an even greater 30% reduction in capital costs (sum of

eq 2-16 and 2-17). As the financing of a new district heating system is often a barrier

to implementation, such large reductions in capital costs could make a system

feasible where it might not be otherwise.

We have arrived at an optimal pipe size that promises to save 17% in life cycle cost

over a rule of thumb based design. This result is consistent with the results of others

(Bhm 1986, Koskelainen 1980) who have compared optimized designs with rule of

thumb based designs. In determining this pipe size, we have not considered any

constraints on the selection, other than it be a commercially available size. Of course,

in reality, other constraints exist. Before this method could be used to design an

entire system, the constraints that arise from interconnection of the pipes need to be

considered. Constraints also arise because of the consumer's equipment and mini-

mum temperature requirements. Other constraints are associated with the limita-

tions of the piping system and the plant that supplies the heat. These constraints will

be considered in the following chapters.

16

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