## 3 Results
### Simulation, Hydraulic Model Calibration, and Performance  
The simulation starts from the city's reservoir, which consists of two identical reinforced concrete cisterns at an altitude of 196 m, connected to a pump that draws water from the reservoir, and through the existing conveying pipe, water is sent to the main balancing tank (MBT) located at an altitude of 231 m at the foothills of the mountain, which was designed with a cumulative capacity of 800 m\({}^{3}\). From the modeled MBT, through a gravity pipe, the water ends up in the city's internal aqueduct, where it is distributed to consumers. The simulation presents the operation of the entire water distribution network of the city for 24 h, with data on the level of the MBT from the telemetry, as well as the corresponding supply for 24 h.  
The daily demand remained constant at 5500 m\({}^{3}\)/day for the whole city, but the distribution patterns of water demand were calibrated by trial and error, using the observed data. Peak demand variations are a critical factor in urban water distribution systems. Figure 5 illustrates the fluctuation of the hourly commercial water demand and main supply of the main balancing tank throughout the day. This process went through several stages, with the most important steps being creating appropriate patterns for the total demand throughout the day and specifically approaching the hourly demand. The demand spikes correspond to periods of heightened commercial water use, whereas lower demand is recorded during late-night hours, reflecting minimal network activity, which is typical in densely populated areas. Figure 4: District metered areas (DMAs). Figure 5: Hourly patterns of **(a)** the commercial water demand; **(b)** main supply of the tank. The graph in Figure 6 presents the performance curve of the city's reservoir pump. In fact, it illustrates the relationship between the flow rate, the head, and the pump efficiency. As the flow rate increases from 0 to 97.2 L/s, the head (blue line) gradually decreases, indicating a typical pump performance curve. Conversely, pump efficiency (orange line) rises with the flow, reaching a peak ca. 69.4 L/s before declining. This behavior highlights the optimal operating range of the pump, where both head and efficiency are balanced for maximum performance. Table 4 of Hazen-Williams roughness coefficients provides a detailed comparison between the initial values and those adjusted through calibration. The PVC roughness coefficient was significantly reduced from 150 to 100-120, reflecting the aging effects of the pipes and the simulation-confirmed adjustments. This reduction aligns with expected deterioration patterns, where older PVC pipes exhibit increased internal resistance due to material wear, scaling, or minor deformations. The HDPE coefficient remains relatively high (150-155), indicating that its hydraulic performance has not degraded significantly. Ductile iron pipes maintain their expected calibration ranges, ensuring consistency with industry standards and observed network behavior. Figure 7 illustrates the comparison between the observed and simulated elevation of the MBT. In this 24 h graph, with \"continuous red squares\", the real level that emerged from the telemetry system can be distinguished, while the values of the level that emerged from the simulation of the network are marked with the \"blue continuous line\". The hydraulic model was validated using real-time SCADA data and field measurements. The Nash-Sutcliffe efficiency (NSE) of 0.841 demonstrates strong agreement between the observed (\(x_{i}\)) and simulated values (\(y_{i}\)), confirming the model's reliability for predicting network behavior. According to the established NSE classification ranges [41], values above 0.75 are considered good, above 0.85--very good, which aligns with results from similar studies [4; 7; 8; 12; 18], reinforcing the effectiveness of this methodological approach.