(∆*P*cv,i ) .

∆*P*c m,i - ∆*P*c+ ,i < 0

(5-6)

v

v

The assessment of which consumer will be the "critical" consumer having his ∆*P*cv,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 ∆*P*ncv,i and the minimum control valve pressure loss ∆*P*cvm,i. The non-control-

valve pressure losses ∆*P*ncv,i are given by

∆*P*ncv,i = ∑ (∆*P*s + ∆*P*r )j + ∆*P*he

(5-7)

j

i

where the non-control-valve pressure losses (N/m2) are easily computed once the

pipe sizes are determined using the procedure discussed below.

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.

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

∆*P*hp = ∑ (∆*P*s + ∆*P*r )j + ∆*P*cv + ∆*P*he

(4-2)

∆*P*cv,i ≥ ∆*P*cvm,i .

(4-5)

In the supply pipe

(4-11)

(4-22)

In the return pipe

∆*P*hp,s - ∑ ∆*P*s, j - ρs gz - ∆*P*he,i - ∆*P*cv,i -∑ ∆*P*r, j ≥ *P*x,sat + *P*saf .

(4-23)

In the return pipe at the heating plant

(4-24)

(4-25)

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

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