Analysis of Fractality in Water Distribution Networks Using Hydraulic Criteria

Abstract

The fractal dimension in water distribution networks (WDN) can be seen as an indicator or a scaling factor of how much the network changes topologically, according to the scale in which it is analyzed. The fractal dimension of a considerable number of networks with different characteristics was calculated in order to study its behavior and have a better understanding of this feature. Three different criteria were used to calculate the weight of each node in the box covering algorithm used to determine the fractal dimension: topology, SumQ, and HGL*SumQ. All of the studied networks resulted to be fractal networks since the coefficient of determination (R2) of the linear fit after applying the box covering algorithm was always above 0.95. The largest values for the fractal dimension were obtained with the topology weight criterion. There was not a clear tendency in the variation of fractal dimension when modifying the networks’ demands and calculating the weights with the proposed hydraulic criteria (SumQ and HGL*SumQ).