pressure is prudent. The resulting constraint is
Px ≥ Px,sat + Psaf
where Px,sat is the saturation pressure of the liquid at point x within the pipe segment
(N/m2) and Psaf is the minimum allowable safety margin on saturation pressure
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
Pr = Php,s - ∑ ∆Ps, j - ρs gz - ∆Pcv,i - ∆Phe,i - ∑ ∆Pr, j
where Pr,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.
The evaluation of pressures in the return pipes using this expression requires
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
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
Php,s - ∑ ∆Ps, j - ρs gz ≥ Px,sat + Psaf .