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 *h*1 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.

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 *P*sat and a

safety margin *P*saf. 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

∆Ps

∆Pr

Ps

Pr

Ps Pr

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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