(eq 3-17) into eq 3-21, we have

} .

2/*n*1

2

˙ ˙

(3-22)

represents the actual load on the system. The quantity *q*0 represents the maximum

load for which the consumers' radiators were designed, while the quantity *q*d

represents the maximum load for which the piping network was designed. These

two "design" loads will in most cases not be equal, as discussed earlier. They will,

however, be related by some "over-design factor," which will be a constant

(*q/q*d) = *A*13 (*q/q*0)

(3-23)

where *A*13 is the over-design factor for the consumer's radiators (dimensionless).

In the example of Chapter 2, we assumed a sinusoidal form for the variation of the

load over the yearly cycle. In general terms this can be written as

(3-24)

where *A*14 is the midpoint of the load curve (dimensionless) and *A*15 is the amplitude

of the load curve (dimensionless). The midpoint of the load curve *A*14 is simply the

average of the maximum and minimum loads. The amplitude of the load curve *A*15

is the maximum load minus the minimum load divided by two.

Now if we combine eq 3-223-24, we have the following expression for the

normalized mass flow rate over the yearly cycle

(*T*s - *T*r )d (A14 + *A*15 cos(2π*t */ 8760))

.

˙ ˙

2/*n*1

(

)

2

(3-25)

If we select the same values for *A*14 and *A*15 as we used in the Chapter 2 example

(0.575 and 0.425 respectively), we can compare the resulting mass flow rate function

of eq 3-25 to the mass flow rate function without the consumer model (eq 2-28). We

1.0

0.8

m/m d

0.6

w/o Consumer Model

0.4

0.2

m/m d

w/Consumer Model

0

2,000

4,000

6,000

8,000

Time (hr)

28