## 3 Results  
As a result of the experimental tests and calculations, three static characteristics were determined. Figure 10 shows the static characteristics obtained from numerical calculations in SolidWorks Flow Simulation for the different mesh variants. Analyzing the results shown in Figure 10, it should be noted that the use of a global finite volume mesh of size four significantly deviates from the others in the area of small nozzle bore diameters. This is a result of the mesh size, one node of which for diameters (0.75...3.50) mm is larger than the narrow flow channel. The situation improves for larger nozzle bore diameters, for which this mesh size results in the generation of two or three nodes in the flow section. When considering the value of the relative error for the global mesh and the simulation variant with global mesh seven and the local mesh tools channels, refinement, and advanced refinement, it should be noted that for nozzle diameter values (0.75...1.25) mm, the value of the difference varies between 53 and 67%, taking the value from the locally compacted mesh in the sensitive area as the reference value. For the other borehole diameters, the value of the relative error fluctuates between 5 and 15%, which is the basis for the validity of using local meshes and compaction tools to obtain better results  
Figure 9: Pressure waveforms: (**a**) experimental for nozzle diameter 3.00 mm; (**b**) experimental and model waveforms in a limited area of stable flow. while increasing the simulation time from 20 s for the variant with a global mesh of size four to approximately 540 s for the locally densified mesh. The static flow characteristics determined using the Ansys Fluent environment, for the different mesh types, are shown in Figure 11.  
When proceeding with the numerical calculations in A-F, it was assumed that all three mesh variants used would be pre-densified by specifying the minimum and maximum edge lengths of the nodes. In addition, the Ansys Meshing tool in the Ansys 2023 R1 release controls, in addition to the user control, the local mesh compaction in the key model volumes based on boundary criteria, giving the possibility of additional mesh compaction. The three types of meshes used for the case under consideration are the most commonly used for flow studies, yielding relative error values between individual meshes for the same flow diameters, ranging from 0.3 to 5.6%. In the case of inter-chamber flow through a small borehole, this represents an acceptable discrepancy. In the case of the tetrahedral and polyhedral meshes considered, assuming 200 solver iterations and residuals of \(1\mathrm{e}^{-4}\), it took a maximum of 200s to determine the MFR value, while for the polyhexcore mesh, which is a combination of the tetrahedral and polyhedral meshes, the search for a solution with the same solver settings took approximately 2400s for a single case. To compare the obtained results, experimental tests were carried out to finally validate the calculation results. As a result of the identification, according to the functional and mathematical description presented in Section 2.3, the throughputs (\(\mu A\))\({}_{\mathrm{nozzle}}\) were determined for all the selected nozzles. On this basis, \(Q\) values were calculated based on the relationship presented in Equation (7). From the five calculated mass flow rate values, the arithmetic mean was calculated, and a static flow characteristic was plotted, based on the experimental results (Figure 12). Figure 11: Static flow characteristics determined using A-F for different mesh types. Figure 10: Static flow characteristics determined using SW-FS for different mesh types. The experimentally determined MFR values are shown in Figure 12. The results were fitted using a regression, using the least squares method in a two-dimensional space, obtaining the equation MFR = 0.0017 \({d_{n}}^{2}-0.0010\)\({d_{n}}\).