Page 274 - Fair, Geyer, and Okun's Water and wastewater engineering : water supply and wastewater removal

JWCL344_ch07_230-264.qxd 8/2/10 8:44 PM Page 234

234 Chapter 7 Water Distribution Systems: Modeling and Computer Applications
7.4 PIPE NETWORKS

In practice, pipe networks consist not only of pipes, but also of miscellaneous fittings,
services, storage tanks, reservoirs, meters, regulating valves, pumps, and electronic and
mechanical controls. For modeling purposes, these system elements can be organized into
four fundamental categories:

1. Junction nodes: Junctions are specific points (nodes) in the system where an event
of interest is occurring. Junctions include points where pipes intersect, points
where major demands on the system (such as a large industry, a cluster of houses,
or a fire hydrant) are located, or critical points in the system where pressures are
important for analysis purposes.
2. Boundary nodes: Boundaries are nodes in the system where the hydraulic grade is
known, and they define the initial hydraulic grades for any computational cycle.
They set the hydraulic grade line used to determine the condition of all other nodes
during system operation. Boundary nodes are elements such as tanks, reservoirs,
and pressure sources. A model must contain at least one boundary node for the hy-
draulic grade lines and pressures to be calculated.
3. Links: Links are system components such as pipes that connect to junctions or
boundaries and control the flow rates and energy losses (or gains) between nodes.
4. Pumps and valves: Pumps and valves are similar to nodes in that they occupy a sin-
gle point in space, but they also have link properties because head changes occur
across them.

An event or condition at one point in the system can affect all other locations in the
system. Although this fact complicates the approach that the engineer must take to find a
solution, there are some governing principles that drive the behavior of the network, such
as the conservation of mass and the conservation of energy.

7.4.1 Conservation of Mass
The conservation of mass principle is a simple one. At any node in the system under in-
compressible flow conditions, the total volumetric or mass flow entering must equal the
mass flow leaving (plus the change in storage).
Separating the total volumetric flow into flows from connecting pipes, demands, and
storage, we obtain the following equation:

a Q in ¢t = a Q out ¢t +¢s (7.2)
where
Q in total flow into the node
Q out total flow out of the node
s change in storage volume
t change in time.

7.4.2 Conservation of Energy

The principle of conservation of energy dictates that the head losses through the system
must balance at each point (Fig. 7.4). For pressure networks, this means that the total head
loss between any two nodes in the system must be the same regardless of the path taken
between the two points. The head loss must be “sign consistent” with the assumed flow