A Mathematical Method of Designing Gravity Sewer Systems

Abstract

In Japan, a gravity sewer system is designed so that it satisfies the following conditions : the flow velocity is in the range from 0.6m/s to 3.0m/s and increases gradually to the downstream the slope becomes gradually gentle to the downstream.
This paper presents methods to find out the minimum-cost or a close to the minimum-cost design which satisfies the above conditions : If a design flow and a design velocity are given to a section, a commercially available diameter that minimizes the slope of the section is uniquely determined. Then, in case of a relatively flat region, by connecting such pipes and slopes chosen for each section, the total amount of the covering soil over the sewers, therefore the total cost, is minimized. In case of a region where steep downhills are included, the problem can be reduced to a one-dimensional nonlinear programming program, and the solution can be found by the golden section search.