Table 10. Pressure losses for the pipe segments in the example.
Pipe
Discrete
Length
Elevation
Flow rate
Pd ,s
Pd ,r
(N/m2)
(N/m2)
segment
diam. (m)
(m)
diff. (m)
(kg/s)
6,1
0.0703
100
40
10
91,585
91,652
7,2
0.0703
25
30
10
22,896
22,913
7,3
0.0703
50
20
10
45,793
45,826
5,4
0.0703
100
10
10
91,585
91,652
6,7
0.1071
50
0
20
20,615
20,630
5,6
0.1071
100
0
30
90,655
90,721
8,5
0.1325
200
0
40
107,219
107,297
sum the pressure losses in the portions of the piping system servicing each con-
sumer. Recall that earlier we assigned values for the minimum pressure drop in the
consumer's control valve and the pressure drop in the consumer's heat exchanger,
∆Pcvm,i and ∆Phe,i, respectively, as follows:
∆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).
We will also assume initially that for each consumer ∆Pcv,i = ∆Pcvm,i. The process of
calculating the ∆Php for each of the consumers is summarized in Table 11.
have calculated is different for each consumer. As shown in Chapter 5, since ∆Php
can only assume one value, it must be the greatest value that results from consider-
ation of all the consumers, and for the other consumers ∆Pcv,i will be greater than
∆Pcvm,i. The consumer who requires the greatest ∆Php is called the critical consumer.
Referring to Table 11, we see that consumer 1 is our critical consumer and thus
∆Pcv,1 = Pcvm,1. This has been determined for the maximum load condition, but will
hold for all load conditions since we have assumed that all consumers have loads
varying in the same manner over the yearly cycle. For the other consumers, eq 4-2
will require that ∆Pcv,i > ∆Pcvm,i. By using the ∆Php calculated for consumer 1, our
critical consumer, we find the following values for the ∆Pcv,i of the other consumers
at the maximum load condition:
∆Pcv,2 = 146,183 N/m2
∆Pcv,3 = 100,374 N/m2
∆Pcv,4 = 231,376 N/m2.
Notice that the control valve pressure drops for all these consumers are high
compared to the minimum value of 5 104 N/m2. This situation sometimes makes
it difficult for the control valve to function properly. It also represents a wasteful
Table 11. Heating plant pressure increase required by eq 4-2 for each consumer.
∑ ∆Pr,j
∑ ∆Ps,j
∆Php
Consumer
Servicing
Pcvm,i + Phe,i
j
j
(N/m2)
(N/m2)
(N/m2)
(N/m2)
index, i
pipes, j
1
(6,1), (5,6), (8,5)
289,459
289,670
150,000
729,129
2
(7,2), (6,7), (5,6), (8,5)
241,385
241,561
150,000
632,946
3
(7,3), (6,7), (5,6), (8,5)
264,281
264,474
150,000
678,755
4
(5,4), (8,5)
198,804
198,949
150,000
547,753
66
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