## 1 Introduction  
Implementation of novel technologies in production processes often requires optimising water supply systems, which range from simple open channels for the gravity-fed water supply to complex and sophisticated systems comprising a water treatment station, pumping technology, a reservoir and water distribution pipelines with a length of as many as several kilometres. Newly constructed and complex water distribution systems represent only a small portion of the total number of operated water supply systems. The majority of industrial hydraulic installations are sporadically innovated based on the current production process requirements or changes in the production portfolios of undertakings. A similar situation exists with regard to new installations, which often need adjustments, after only a few years, to the current requirements regarding the demand, operation cost-efficiency and effectivity, as well as the environmental impact [1; 2; 3; 4; 5; 6]. Just like any other systems, water distribution networks are exposed to various internal and external factors, associated with their operation and atmospheric phenomena, which may change the characteristics of the network that controls the system. Pressure losses in a pipeline network largely depend on the quality of the surface of inner pipe walls, which deteriorates over the distribution system utilisation period. The surface degradation is caused by the corrosive effect of transported fluids and incrustation [7; 8]. In long hydraulic pipelines, pressure losses are mainly caused by the pipeline length. In order to ensure that a pipeline network exhibits the required pressure or flow rate parameters, it is necessary to correctly identify the losses. Interventions performed in connection with the replacement of certain functional parts, repairs and accidents represent another source of contamination of hydraulic networks. Major changes and extensions of installations, primarily the extensions of the pipeline networks of the operated facilities and the attachment of new systems to the existing networks, may also contaminate water distribution networks. The accumulation of sediments on the walls reduces the flow rate profile of water pipelines, increases the pressure loss, and over time causes a disruption of the characteristics of the distribution networks, which is also facilitated by the corrosive effect. A similar case is the installation of new, remotely controlled regulating components, the replacement of which requires that the distribution system settings comply with the operational requirements of production. At present, it is a priority to regulate a hydraulic network based on the monitoring of its operational parameters in the steady-state fluid flow. This facilitates analysing the changes in the flow-rate characteristics that are caused by the gradual, prolonged incrustation and clogging of pipes [7; 8; 9]. Economically and environmentally efficient optimisation of the operation and the regulating components of water distribution systems, or the water management system of a particular enterprise from the global point of view, requires thorough monitoring of operational parameters with the aim of better understanding the behaviour of water or any other fluid flowing in the analysed system. A tool that is beneficial in the process of increasing operation efficiency is an analysis of the related laws of physics while applying mathematical and numerical models. Predicting the behaviour of a water distribution network with the use of mathematical models will increase the efficiency of a search for critical points in the system that are associated with higher risk; in terms of ensuring a faultless operation, it will facilitate identifying the behaviour of the hydraulic network in case of a deviation from the standard conditions and simplifying the process of assessing the risks associated with the network extension, since that usually results in elevated water consumption [10; 11; 12; 13; 14; 15; 16].