Design of Sewer Line

Sewerage involves the major portion of the cost of a wastewater system. In the design of a sewerage system the sewer line is the basic unit occurring repeatedly in the design process. Any savings during the design of this unit will affect the overall cost of the sewerage system. A survey of the literature showed that the present status of sewer line design algorithms use linear programming and dynamic programming. The linear programming, using piecewise linearization of the objective function and constraints in every cycle, requires substantial computer time. On the other hand, dynamic programming algorithms are subjected to the "curse of dimensionality," thus requiring large amounts of computer memory. In this paper, using a dimensionally consistent resistance equation, the sewer line design problem is formulated as a minimization of the cost function subjected to tight and loose constraints. The problem is solved by iterative application of the Lagrange-multiplier method.