Ps @ Low Flow
Ps @ Design Flow
Pmax
Pr @ Low Flow
Pr @ Design Flow
P min Supply
Pmin Return
Distance from Plant
Figure 8. Hypothetical pressure distribution under high and low flow
conditions and absolute pressure constraints.
All the calculations made to check for absolute pressure constraint satisfaction
should use the maximum (design) mass flow rate. This will assure that constraint
satisfaction will be possible at all flow rate conditions. Since the pressure losses in
the piping and the consumer's heat exchanger will be greatest under this load
condition, the difference between supply and return pressure at the heating plant
will also be greatest under this load condition. Thus, under this condition the least
flexibility exists to adjust the supply or return pressure at the plant without violating
either the maximum pressure constraint in the supply, eq 4-11, or one of the
minimum return line pressure constraints at the plant, eq 4-24 and 4-25. If the
various maximum and minimum pressure constraints are satisfied for all points in
the network at the higher flow rate condition, it will always be possible to satisfy
them at the lower flow rates. This is easily shown graphically by considering the
pressures in the system along the piping route out to a consumer and back, as shown
for a hypothetical consumer in Figure 8.
In Figure 8 the horizontal lines are the constraints on the absolute pressures that
must be satisfied at all points along the route to the consumer. The solid lines that
have both positive and negative slopes are the supply and return pressures under
maximum load conditions. The magnitude and the sign of the slope of these lines are
determined by the sum of the hydrodynamic and hydrostatic pressure gradients as
given by eq 4-14. The dotted lines that behave in a similar fashion are the supply and
return pressures under some mass flow condition that is lower than the maximum.
In the extreme case where there is no flow, the pressure losses in the piping and
consumer equipment all vanish and the absolute pressure level is identical in the
supply and return lines for any point along the route. Also notice that we have
shown the pressure drop at the consumer as being lower at the reduced flow
condition. This results from lower pressure losses in the consumer's heat exchanger
at the reduced flow rate (see eq 4-6) as well as lower losses in the consumer's control
valve. If the network were ideally balanced and this consumer were the critical
consumer, his control valve would be completely open at all levels of load (i.e., flow
rate) and the pressure losses would always be the minimum possible.
By studying Figure 8, we can see that if we are able to "fit" the supply and return
absolute pressure lines within the constraints at the maximum flow condition, then
we can always do so for any lower flow condition simply by adjusting the absolute
pressure of either the supply or return at the heating plant. This results from the
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