The sewer network design problem consists of determining both the layout and the hydraulic design of the system. This paper aims to find an optimal hydraulic design for a specific layout consisting of a series of pipes. An optimal hydraulic design of a series of pipes is that which satisfies all the hydraulic, commercial, and construction constraints, while minimizing the construction costs. The present paper proposes a graph modeling framework in which the result of a shortest path problem coincides with the hydraulic design, and the underlying graph models the diameter and slope of each pipe in the series. To assess the performance of the methodology, several numerical examples are presented varying the pipe material, the topography, and the number of pipes in the series.