consumers. Both absolute and differential pressure constraints are derived and
where possible strategies are given to allow for constraint satisfaction at all points
implicitly without considering every point in the system.
After a brief review of general methods for constrained nonlinear optimization
techniques at the beginning of Chapter 5, our general solution strategy is developed
for systems with multiple pipes and consumers. The method makes use of the
solution to the problem, unconfined by the network constraint requirements.
Monotonicity analysis is used to prove activity of some of the constraints and thus
simplify the problem somewhat. The result is used as a starting point for two
methods proposed to find a solution to the constrained problem with continuous
values for some of the pipe diameters. Finally, the branch-and-bound technique is
used to find a design with discrete values for all the pipe diameters.
In Chapter 6 we work a simple example with only four consumers and seven pipe
segments. The example illustrates the use of our method and also shows how the
branch-and-bound technique can be used to quickly eliminate candidate designs.
In Chapter 7 is a summary of our results and offers some conclusions and
suggestions for further study.
Because of the inordinate number of variables and parameters involved in the
analysis that follows, in choosing symbols for them, an attempt has been made to
make their meaning as intuitive as possible. Where accepted symbols exist they have
been used to the maximum extent possible. Where it has been mathematically
convenient to represent quantities that may have no particular physical significance
by a symbol, subscripted A's have been used for sums, products and quotients and
I's have been used for integrals.