Now the remaining branches yet to be explored are those with discrete pipe sizes
for pipe segment (6,7) more than one size below our original design. To explore these
branches, we neglect the pressure losses of the pipe segments (7,2) and (7,3) and then
calculate the minimum value of d(6,7) that will satisfy constraint h1 for both consum-
ers 2 and 3. We find that the minimum continuous diameter of d(6,7) is 0.0800. The
next largest discrete diameter is d(6,7) = 0.0825 and we see that this branch has already
been searched. Thus, there are no other feasible branches with discrete values of d(6,7)
less than that of our original design. We have now exhausted all the alternatives and
have found our original discrete design to be the optimal discrete design.
We still have several constraints remaining that must be checked for satisfaction.
The remaining constraints are eq 4-11, 4-22, 4-23, 4-24 and 4-25. These constraints all
deal with the absolute pressure level in the piping. Before we can compute the
absolute pressure at any point, we must first assign an absolute pressure in the
supply pipe at the heating plant. Since we suspect that this will be the place of highest
pressure in the network, we let the absolute pressure at that point be equal to the
maximum allowed, i.e.
Php,s = Pmax = 1 106 N/m2 .
We start with eq 4-11, which is a constraint on the maximum pressure in the
supply pipe. The right-hand side of eq 4-11 equals the pressure level in the supply
pipe. As we have shown earlier in this chapter (see eq 4-15), the maximum pressure
must occur at a pipe node and not at an intermediate point. In Table 14, we have
calculated the pressure in the supply pipe at each of the nodes. We see that the
constraint of eq 4-11 is satisfied, since the pressure level does not exceed the
maximum allowed at any point in the supply piping.
Equation 4-22 requires that the pressure at each point in the supply pipe (the left-
hand side of the equation) exceed the sum of the saturation pressure Psat and a
safety margin Psaf. For the supply pipe temperature of 120C, the saturation pressure
is 1.985 105 N/m2 (Reynolds and Perkins 1977). Thus, the sum of these two
becomes 2.985 105 N/m2. We see by examining Table 14 that this constraint is also
satisfied at all nodes.
We have a similar constraint for the return pipe, eq 4-23. The left-hand side of this
equation equals the pressure in the return pipe, which has also been computed and
is given in Table 14. The temperature and thus the saturation pressure in the return
pipe are different from those in the supply pipe, of course. The return temperature
will vary with load as per our consumer model, eq 3-25. The maximum temperature
will occur at the design condition of maximum load, as can be seen from Figure 5,
and its value is 55C as determined in Chapter 3 for our supply temperature of 120C
and our assumptions regarding the radiator design conditions. The saturation
pressure will be greatest at the highest temperature, so if our constraint is satisfied
Table 14. Pressure levels in the piping network.
∆Ps
∆Pr
Node
Ps
Pr
Ps Pr
(N/m2)
(N/m2)
(N/m2)
(N/m2)
(N/m2)
number
1
659,272
340,728
150,000
190,728
150,000
2
518,744
481,256
246,183
235,073
246,183
3
449,187
550,813
200,374
350,439
200,374
4
291,257
708,743
231,376
477,367
231,376
5
107,219
892,781
385,267
394,554
498,228
6
197,874
802,126
294,546
485,275
316,852
7
218,488
781,512
273,916
505,905
275,607
8
--
1,000,000
--
287,256
712,744
72
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