Analysis of Fractality in Water Distribution Networks Using Hydraulic Criteria

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. (R-2) 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).