Table 1. Pressure drops and costs for discrete pipe sizes
under maximum flow conditions (pipe data from Marks
1978).
Nominal
Inside diameter
∆Pd
pipe size
schedule 40
Ct
($ 106)
(in.)
(in.) (m)
(Pa/m)
--
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.
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