piping code. In the case where all points in the distribution system are at or above
the level of the heating plant, the maximum absolute pressure will occur in the
supply pipe at the heating plant. In the general case, however, this will not always
be true and it will be necessary to determine that this constraint is not violated at any
point within the system. However, several heuristics will allow us to forgo compu-
tation of the absolute pressure level at many of the points. At any point in the supply
side of the system the absolute pressure is given by
Ps = Php,s - ∑ ∆Ps, j - ρs g z
(4-10)
j
where Ps = absolute pressure in supply pipe at point in question (N/m2)
Php,s = absolute pressure in supply pipe at heating plant (N/m2)
∆Ps,j = pressure loss in supply pipe j (N/m2)
z = elevation at point in question relative to heating plant (m).
Again, we have assumed that no intermediate pumping is employed and that the
summation over j includes only those pipe segments between the heating plant and
the point in question along the supply line. If Pmax is the maximum absolute pressure
for the piping system being used (N/m2), our constraint arising from it is then
Pmax ≥ Php,s - ∑ ∆Ps, j - ρs gz
(4-11)
j
where Pmax is the maximum absolute pressure for the piping system being used
(N/m2).
We can easily eliminate the need to verify that the upper limit on absolute
pressure is not exceeded for the return side of the system. First, we assume that the
supply and return line are at the same elevation at any given point, certainly a
reasonable assumption. Since there will always be a finite pressure drop across the
consumer's heat exchanger and control valve, the absolute pressure in the return
line will always be less than that in the supply line at any point, with the difference
being the smallest at the consumer. Thus, we need not verify that the maximum
absolute pressure constraint (eq 4-11) is satisfied for the return system.
We can also easily show that eq 4-11 only needs to be satisfied at certain points
along the supply line. For pipelines that are laid at a constant slope between junction
points, the hydrostatic component of the pressure gradient along the pipe will be
constant as well. This gradient is given by the following equation
(dP/dx)h = ρg( z/ x)
(4-12)
where (dP/dx)h = hydrostatic pressure gradient (N/m3)
( z/ x) = partial derivative of the elevation of the pipe with respect to
its position (dimensionless)
x = position along the pipe in the direction of flow with x = 0
being defined as the inlet end to the pipe segment in question
(m).
Using our approximation for the friction factor previously determined (eq 2-12),
we can find the pressure gradient attributable to frictional losses in the flowing fluid
from the following equation
(dP / dx)d = (a / 2)(4 / π)2+c εbρ-1 -cm2+c d-(5+b+c)
˙
(4-13)
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