piping code. In the case where all points in the distribution system are at or above

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

(4-10)

where *P*s = absolute pressure in supply pipe at point in question (N/m2)

∆*P*s,j = pressure loss in supply pipe *j *(N/m2)

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 *P*max is the maximum absolute pressure

for the piping system being used (N/m2), our constraint arising from it is then

(4-11)

where *P*max 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

(d*P*/d*x*)h = ρ*g*( *z*/ *x*)

(4-12)

where (d*P*/d*x*)h = hydrostatic pressure gradient (N/m3)

( *z*/ *x*) = partial derivative of the elevation of the pipe with respect to

its position (dimensionless)

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

(d*P */ d*x*)d = (*a */ 2)(4 / π)2+*c *εbρ-1 -*c*m2+*c *d-(5+*b*+*c*)

˙

(4-13)

35