## 2 Materials and Methods
### Experimental Research  
Experimental tests of both supply tracts were carried out on the developed test stand (Figure 5) operating in accordance with the design assumptions of the tank method, which allows for determining, among others, the static flow characteristics of the tested pneumatic resistance. The possibility of using this approach was confirmed in previous publications by the authors mentioned in previous sections, as well as in other literature [28; 29], drawing attention to its high effectiveness in determining the flow parameters of compressed air, as well as other gases. The measurement principle involves recording the pressure courses in two tanks of known volume, between which a solenoid valve is mounted to start the measurement, and directly behind it is the tested brake valve 8 (Figure 5). The recording of pressure courses in the measuring tanks, the algorithm controlling the sequence of solenoid valves and the acquisition of results with a sampling time of 3 ms were implemented using the Python 3.11 language and the additional PyQT5 graphic library using the Raspberry Pi 3 microcomputer Raspberry Pi Foundation (Cambridge, UK). The current readings can be viewed and the station can be operated using a dedicated touch screen. The practical implementation of the station is shown in Figure 6. During the tests, a counter was declared, which automatically enabled the measurement to be repeated five times. Figure 4: Additional supply tract. The measurement sequence of one measurement is as follows:  
* Open the solenoid valve 3 supplying the measuring system from the compressed air preparation station and fill the supply tank 6 to the working pressure;
* Close the supply solenoid valve 3, stabilize the pressure in the supply tank 6 and start pressure recording to a *.csv file with the declared sampling time;
* Open the measuring solenoid valve 7 and flow of compressed air from the supply tank 6 to the measuring tank 9 through the brake valve. The flow is caused by the pressure gradient in both tanks;
* After equalizing the pressure in both tanks, end the recording, close the measuring solenoid valve 7, save the *.csv file, open the release solenoid valves 5 and 10, enabling the pressure in both tanks to equalize to the atmospheric pressure, and close it to ensure the re-sealing of the measuring system;
* Ending a measurement sequence after reaching the specified repetition counter causes the program to terminate or loop if the required number of repetitions has not been reached. The measurement file in *.csv format, in accordance with Figure 5 and the adopted methodology, contains input data for the MATLAB environment, which, after implementing the mathematical description of the station based on the lumped method [30], enables  
Figure 5: Construction diagram of the test bench: 1—air compressor, 2—pressure regulator, 3, 5, 7, 10—12 VDC electrovalve, 4—choke valve, 6, 9—40.23 \(\times\) 10\({}^{-3}\) [m\({}^{3}\)] tank, 8—tested brake valve regulated with screw, 11–13—voltage pressure transmitter, 14—Raspberry Pi measuring unit, 15—MATLAB 2023 software. Figure 6: Test rig view: 1, 4—40.23 \(\times\) 10\({}^{-3}\) [m\({}^{3}\)] tank, 2—24 VDC electrovalve, 3—tested brake valve with installed digital dial gauge, 5—Raspberry Pi measuring unit, 6—laptop with MATLAB preinstalled. the identification of flow parameters, in particular the effective flow field \((\mu A)_{truct}\), the value of which is mainly dependent on the geometry of the compressed air flow channels. Determining the \((\mu A)_{truct}\) value from the pressure curves in both tanks allows the determination of the mass flow rate MFR for each valve opening degree and the plotting of the static characteristics. Based on the schematic description of the research stand (Figure 7) and the lumped method, for each concentrated volume in the considered system, a description of the mass flow of the inflowing or outflowing gas can be presented according to the basic relationship in Equation (1).