## 1 Introduction
Historically, it was relatively costly, time-consuming and labour-intensive to design and create mathematical models. Today, the model-building process is much easier, also thanks to the possibility of sharing data with other systems and applications, such as geographic information systems, SCADA (Supervisory Control and Data Acquisition) systems and CAD (Computer-Aided Design) systems [17]. The expertise of 1D fluid flow simulation was applied by [PERSON] et al. (2012). In their paper, a comparison of the 1D and the 2D approaches to simulating combined flows at open-channel junctions was presented. Channel junctions are found in nature; for example, in blood or hydrographic networks. Typical examples of such systems include municipal water distribution systems, irrigation and drainage systems, etc. They consist of the main channel and tributaries. In the 1D simulation, the Saint-Venant equations were coupled with the characteristic equations and junction models to find the solution in the network system. In the 2D simulation, the whole system was discretised into triangular cells forming an unstructured computational mesh. Therefore, the 2D Saint-Venant equations were applied without using empirical equations. The results of the numerical simulation indicated that the 1D approach is acceptable for small junction angles and subcritical and transitional flows. The 2D approach to simulating the junction flow is essential especially for a rectangular network, such as the branches in urban areas [12]. [PERSON] et al. (2023) addressed linear stability and numerical analysis with the use of a model for the momentum flux parameters of the 1D two-fluid model in vertical annular flows. The authors claimed that the models improved the prediction of the 1D two-fluid model and proved consistency in the accuracy of the analysed databases [18]. Other examples of mathematical models were applied by [PERSON] and [PERSON] (2016). The authors investigated solutions for a one-dimensional compressible viscous micropolar fluid flow with different boundary conditions. The mathematical model consisted of four partial differential equations, transformed from the Eulerian to the Lagrangian description. The equations were also associated with various boundary conditions. In their study, they worked with numerical approximations of the one-dimensional viscous heat conducting and micropolar fluid flow problems while using two different numerical schemes--the finite difference scheme and the Faedo-Galerkin method. Both approaches exhibited good concordance between the results. The authors also found out that the finite difference scheme exhibited a lower computational complexity [19]. 2D and 3D numerical models facilitate describing multidimensional relationships; however, their computational complexity is high, and the solutions are significantly time-consuming. In order to achieve optimal computation times, some authors use one-dimensional averaged models. The focus of this article is the prediction of pressures and flow rates in an open distribution system that supplies water to a production company with the use of an analytical dynamic model for fluid flow simulation and by applying the finite-difference time-domain method [19; 20; 21; 22]. In this paper, a dynamic model of main distribution pipelines is analysed with the aim of stabilising the discharge pressure in the industrial facility while maintaining a constant flow rate of water from the selected sources of industrial water.