Civil Engineering Reference
In-Depth Information
theory method has several advantages over the Newton-Raphson or the Hardy-Cross
methods, because it does not require an initialization and it converges in relatively few
iterations. Linear theory transforms the nonlinear loop equations into linear equations
by approximating the head in each pipe. A system of linear equations is developed
that can be solved by linear algebra.
An excellent discussion of hydraulic analysis of pipe networks is presented by
Jeppson.
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In this reference, the reader may find detailed discussion of several methods,
the mathematics and examples of which are beyond the scope of this chapter.
Skeletonizing the Water Distribution System
Water systems may be large networks consisting of hundreds or thousands of pipes
and many different sources of water supply. To analyze such systems, it may be im-
portant to achieve a representation of the network consistent with computational ca-
pabilities. This representation must also be detailed enough so that the system can be
accurately analyzed to meet the desired objectives of the study. Distribution systems
are also skeletonized to make the analysis of the system more easily understood.
The above goals are accomplished by first skeletonizing the system, which reduces
the number of pipes analyzed by the modeling software using the equivalent pipe
method. An equivalent pipe is one in which the loss of head for a specified flow is
the same as the loss in head of the pipes that it replaces. This skeletonizing may
involve the total dismissal of an unimportant or minor pipe, the replacement of a series
of pipes of varying diameter with one equivalent pipe, or replacing a system of parallel
pipes with an equivalent pipe.
When skeletonizing the system, it must be recognized that the backbone of the
water distribution system is the transmission mains. Large water systems may contain
transmission mains that are 16 inches (41 mm) and larger. Connections to transmission
mains are typically held to a minimum; so it is typical to utilize all of the existing
transmission piping with no skeletonization. Connections from the transmission mains
to the distribution system can then be considered the demand, or load points, on the
system. Water distribution piping is interconnecting pipes, which are the principal
components of the distribution system.
The decision on how various pipes are included in the model is based largely on
the experience of the individual conducting the analysis. If the water system being
evaluated is small, it may be desirable to include all of the system piping. If the system
is very large, it may be desirable that pipes under a specific size—12 inches (30 mm),
for example—not be considered, unless they are necessary to complete a loop. For
medium-size systems, one must consider the effect of ignoring an existing pipe. If
problems become apparent in areas of the system where pipes have been ignored, then
the decision to ignore those pipes must be reevaluated.
Another factor affecting the amount of system skeletonizing is the intent of the
simulation analysis. When the purpose is to examine the impacts of fire flow in large
residential areas, it is necessary to include a significant portion of smaller-diameter
piping. However, if the intent is to evaluate the impact of a large development on the
transmission system, the majority of the small-diameter piping can be ignored.
Minor Losses
In the early analysis techniques, minor losses were included in the analysis. Water
flowing in a straight pipe under pressure at a constant velocity experiences a constant
