<p>CHAPTER 4
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PIPE NETWORK ANALYSIS
4.1 INTRODUCTION
This chapter describes the analysis of steady flow in pipe systems. In any analysis
problem all of the physical features of the network are known, and the solution process
endeavors to determine the discharge in every pipe and the pressure, etc. at every node of the
network. Therefore in this chapter the diameters of all pipes, their lengths and their
roughnesses are known, as well as where reservoirs, pumps, pressure reduction valves, and
other fittings are located. The ways in which these devices influence the hydraulics of the
system will be specified. Design problems, on the other hand, try to select (wisely!) the
diameters of pipes, the capacities of pumps, the water surfaces elevations of reservoirs, and
so on. Thus, a design problem is distinguished from an analysis problem by the choice of
the variables that are regarded as unknown. At some risk we dare to generalize by saying
that design problems are usually more challenging to solve than are analysis problems, and
design problems usually require the simultaneous solution of a larger system of equations
than do analysis problems. A thorough understanding of the techniques of analysis for
large networks that are composed of known physical features is a prerequisite to the
understanding of the design of networks. The design of pipe networks is the focus of
Chapter 5 and is not discussed directly in this chapter.
The analysis of a pipe network can be one of the more complex mathematical problems
that engineers are called upon to solve, particularly if the network is large, as occurs in the
water distribution systems of even quite small cities. A significant fraction of the entire
set of equations consists of nonlinear equations, and a large number of these equations must
be solved simultaneously. Before digital computers were widely used in engineering
practice, it simply was not practical to solve such network problems, a