Fractal Geometry in Designing and Operating Water Networks
Małgorzata Iwanek 1  
,   Dariusz Kowalski 1  
,   Beata Kowalska 1  
,   Paweł Suchorab 1  
 
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Lublin University of Technology, ul. Nadbystrzycka 40B, 20-618 Lublin, Poland
CORRESPONDING AUTHOR
Małgorzata Iwanek   

Lublin University of Technology, ul. Nadbystrzycka 40B, 20-618 Lublin, Poland
Publication date: 2020-08-01
 
J. Ecol. Eng. 2020; 21(6):229–236
 
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ABSTRACT
Fractals are self-similar sets that can not be easily described by classical geometry. Fractals sets have been implemented in almost all areas of human activity since they were introduced to science by Mandelbrot in 1982. For the last 10 years, an interest in fractal geometry has increased by issues connected with water distribution networks (WDNs). The aim of this paper is to review applying fractal geometry in designing and operating WDNs. Treating a WDN as a fractal pattern enables its description and classification, simplifies assessment of a network reliability, helps to solve problems of routing and dimensioning WDN, as well as enables to select places to locate measurement points in a network to control water quality, pressure in pipes and water flow rate. Moreover, applying tree-shaped fractal patterns to reflect WDNs helps to solve problems of their optimization. Fractal geometry can be also applied to investigate results of WDNs failures connected with leakage of water to the ground. Using fractal dimension of a pattern created by points reflecting places of water outflow on the soil surface after a prospective pipe breakage enables to determine the zone near a pipe, where outflow of water on the soil surface is possible. It is an important approach for the security of humans and existing infrastructure. Using fractal geometry in description, optimisation and operation analysis of WDNs is still continued, which confirms efficiency of fractal geometry as a research tool. On the other hand it can be supposed that fractal geometry possibilities have still not been fully used.