Abstract
Pipeline water conveyance systems have two fundamental characteristics: firstly, the head loss distribution to each pipeline section can be controlled as desired; and secondly the flow capacities affect considerably its construction costs. Therefore, it is a very important design problem to allocate suitable head loss to each section and to determine the optimum capacity (pipe diameter).
The problem to determine the optimum pipe diameter can be stated as follows: under a given total head loss finding the head loss allocation or pipe diameter of the each section so as to minimize the sum of the construction cost of each section.
Generally, either Dynamic Programing Method or Differential-Calculus Method is applied as searchtechniquc of optimum solution to a nonlinear optimizing problem of this type. Here, latter method alone is considered. Let Cost Potential corresponding to the Lagrange multiplier be defined for each section as,
φi=hi/yi
where yi and hi are the cost and head loss at ith-section respectively.
Then the optimum conditions require the following equations to hold at each node.
Σφi=0
Thus by using φi, the optimum conditions are expressed by the very simple form. Furthermore, we can easily derive optimum conditions in terms of Cost Potentials to other problems of similar structure.
