Fractal-Based Approach to Simultaneous Layout Routing and Pipe Sizing of Water Supply Networks

The process of designing water distribution networks is divided into two main stages: network layout routing and pipe sizing. However, routing and sizing are not separate tasks—the shape of the network affects the diameters of the pipes, and vice versa. This paper presents an innovative fractal-based method, which enables the simultaneous layout routing and pipe sizing of water supply networks. The developed pipe routes and diameters selected according to the method are mathematically justified; the selection considers the total length of the pipes, the number of rotation angles of the base section, the cost of the water supply system construction and the priority of water supply to individual customers. The novelty of the method lies in the possibility of carrying out the processes of routing and sizing of the network in a recursive manner by the adoption of the principles of fractal geometry and Murray’s law. The method was tested under the conditions of a synthetic settlement. The obtained results enable us to conclude that the method is universal and suitable for shaping water supply networks, while determining the pipes’ diameters, both under the conditions of a single- and multi-sided water supply source.