(∆Pcv,i ) .
∆Pc m,i - ∆Pc+ ,i < 0
The assessment of which consumer will be the "critical" consumer having his ∆Pcv,i
bounded below by eq 5-6 was found above to be determined by finding the
consumer who has the maximum value of the sum of the non-control-valve pressure
losses ∆Pncv,i and the minimum control valve pressure loss ∆Pcvm,i. The non-control-
valve pressure losses ∆Pncv,i are given by
∆Pncv,i = ∑ (∆Ps + ∆Pr )j + ∆Phe
where the non-control-valve pressure losses (N/m2) are easily computed once the
pipe sizes are determined using the procedure discussed below.
Initial pipe size determination
As noted earlier, our objective function is separable in each pipe diameter. The
pipe diameter function for each pipe segment j is increasing in some terms while
decreasing in others. Thus, we should be able to find a minimum cost for each
diameter by proceeding exactly as we did in Chapter 2 if we at first ignore the
constraints. Therefore, we first find the optimal "independent" discrete diameters
using the methods developed in Chapter 2.
System constraint satisfaction
Once our pipe sizes are determined, we need to ensure that the constraints are
satisfied and, if not, determine a methodology for achieving this. Below is listed the
various constraints that were developed in Chapters 3 and 4, categorized by the
portion of the system in which they originate.
At each consumer
∆Php = ∑ (∆Ps + ∆Pr )j + ∆Pcv + ∆Phe
∆Pcv,i ≥ ∆Pcvm,i .
In the supply pipe
Pmax ≥ Php,s - ∑ ∆Ps, j - ρs gz
Php,s - ∑ ∆Ps, j - ρs gz ≥ Px,sat + Psaf .
In the return pipe
∆Php,s - ∑ ∆Ps, j - ρs gz - ∆Phe,i - ∆Pcv,i -∑ ∆Pr, j ≥ Px,sat + Psaf .
In the return pipe at the heating plant
Php,r ≥ PNPSH
Php,r ≥ Pa + Pasa .
All of these constraints deal with pressure levels at various points within the
system. Note that in eq 4-2 we have expressed the total piping pressure loss as its
supply and return components because it will be necessary to compute these