## 2 Laboratory Stand
The valve closing time was determined based on the closing course recorded in the data acquisition system. The uncertainty in determining this time is negligibly small and depends on the resolution of the potentiometer and the resolution of data recording. A 16-bit measurement card and an application based on the DASYLab software (v.2016) by DASYTEC System Daten Technik GmbH (Ludwigsburg, Germany) were used to record the measurement data. Measurement signals were recorded with a frequency of 20 kHz. Figure 1: Laboratory stand for testing water hammers in series-connected pipes of different diameters. The choice of such a high recording frequency opens the possibility of conducting future analyses of phenomena revealing themselves in the high frequency range (e.g., FSI). For the analysis, these signals were processed and the frequency was reduced to 1 kHz. This significantly facilitated the work related to data processing and therefore made it sufficient to conduct a reliable analysis of the phenomenon in terms of the set goals of the work being carried out. Before the tests, the stand was carefully sluiced and filled with fresh tap water and left idle for five days in order to minimize the influence of the air contained in the water on the tested phenomenon. During the standstill, the system was kept open--valves in the pipeline lines open, pressures between the upstream tank and downstream tank equalized. The measurement results for four selected test runs of a water hammer are shown in Figure 2. It presents pressure changes in the cross-section closest to the quick-closing valve (Figure 1). These pressure changes were recorded at different water pressures in the upstream tank (from 26.4 m wc to 119 m wc) and for different initial flows (from ca. 114 L/h to ca. 530 L/h). The compilation of these pressure waves allows the comparison of the influence of the initial conditions on the scope and nature of the recorded pressure changes during the water hammer. Figure 2: Examples of pressure changes measured at the valve for various initial conditions (pressure in the upstream tank, \(H_{0}\), and initial flow, \(Q_{0}\)). There is a phenomenon of interference of these waves, which can be observed in the irregular wave shape, manifested by an asymmetric course with numerous refractions, particularly at the beginning of the course, covering from a few to a dozen consecutive amplitudes (ca. the first 7 s for each analyzed pressure course). The influence of the particular geometry of the hydraulic pipeline system on the course of pressure changes is clearly visible at about halfway through the first pressure peak where a decrease in the mean pressure level is observed--Figure 3. This is mainly the result of the passage of the pressure wave from the pipe with a smaller diameter (pipe #2 with the quick-closing valve installed at its end) to the pipe with a larger diameter (pipe #1). In the cross-section of the diameter change, the pressure wave is reflected propagating simultaneously in both pipes. Pressure fluctuations, both high-frequency, accompanying mainly the first pressure increase, and low-frequency, observed e.g., between \(\sim\)0.6 s and \(\sim\)0.7 s, superimposed on the main water hammer pressure changes, may be related to various factors. Among the most important, apart from the geometric conditions of the pipeline (step change in diameter between two pipes), phenomena related to the impact of waves propagating in the liquid and in the material of the pipeline structure (FSI phenomenon [12]), as well as the impact of pipeline fastenings or the presence of air in the liquid, should be mentioned. The last two factors are manifested by relatively low frequency pressure changes (comparable to the main pressure changes related to the water hammer). The high-frequency pressure changes observed mainly at the beginning of the test runs are most likely related to the movement of the shut-off valve, which stops by hitting the bumper at high speed.