pressure is prudent. The resulting constraint is

(4-20)

where *P*x,sat is the saturation pressure of the liquid at point *x *within the pipe segment

(N/m2) and *P*saf is the minimum allowable safety margin on saturation pressure

requirements (N/m2).

The saturation pressure is a function of the fluid temperature, which will vary

between supply and return portions of the system, as well as within each portion.

Thus, it will be necessary to verify the satisfaction of this constraint at all points

within the system. Again, some simple rules will allow us to forgo the calculation at

many points, as with the maximum absolute pressure constraint described earlier.

As noted earlier, in some cases when the temperature is below 100C, the air infusion

constraint above (eq 4-19) will dominate. The concept of constraint dominance is

illustrated later in Chapter 5.

The pressure level at any point in the supply side can be calculated with eq 4-10.

For the return side, the absolute pressure is given by

(4-21)

where *P*r,j is the pressure loss in the servicing return line *j*. The *j *subscript on the

return line summation indicates only those return pipes servicing consumer *i*

between consumer *i *and the point in question.

some care and forethought to avoid errors and redundant calculations. Errors can

result if the summations include pipes other than the appropriate ones, which will

be different in the case of supply and return. Equation 4-20, as written, could be

evaluated for each consumer at all locations in the piping system. However, all that

is required is to find the pressure at each location once for any consumer served

through that point. The evaluation of the equation for all remaining consumers

served through that point would yield the same result and thus is not required. Some

simple rules will allow us to reduce the number of locations where calculation of the

pressure will be necessary. For example, consider the case where the entire system

is at or below the elevation of the heating plant. In this case, the minimum pressure

in the return line would be at the heating plant. In the supply line, however, the

lowest pressure could be at any location, dependent on the relative magnitude of the

hydrodynamic gradient from friction and the hydrostatic gradient from elevation

differences. If the entire system was at the elevation of the heating plant, then the

lowest pressure in the return line would be at the consumer, who is, in a hydraulic

sense, the most distant from the heating plant.

It is important to note that in the case of this absolute pressure constraint,

the supply and return piping must be considered separately, since the temperature,

and thus saturation pressure, will usually be quite different in each. Strictly

speaking, it would be necessary to determine the actual temperature at each

location in the system and compare the saturation pressure requirement with

the other applicable low pressure constraints to determine which one is dominant

there.

Once the pressure has been calculated at the locations where the minimum

pressure constraint could be active, these pressures would be compared to the

minimum allowed pressure for that location determined from the dominant con-

straint of the applicable ones given above. Thus, our minimum pressure constraint

for the supply pipe becomes

(4-22)

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