A proposal for the application of fractal geometry in describing the geometrical structures of water supply networks

Abstract

The paper presents the problem of describing a water supply network as a complex geometrical structure. The authors suggest that many problems connected with the design and various aspects of exploitation of water supply networks may result from the lack of a universal language of their description. As a solution, the authors propose using the theory of fractal geometry. In the authors' opinion, it allows us to unify the description of branched as well as looped water networks, including their size and complexity degree. The practical application of that theory requires us to verify whether the geometrical structures of water supply networks meet the formal conditions of fractal sets. Such estimation has been done on the basis of three model networks with various geometrical structures. The considerations and analysis presented in the paper seem to give the affirmative answer to the question raised in the study. As a result of the work done the authors have elaborated the iterative formula which allows the description of the flat geometrical structures of branched and looped water networks. The formula is based on tree-like structures and several assumptions of their application. © 2014 WIT Press.