## 4 Discussion  
The determination of the throughput values enabled the calculation of the MFR mass flow rate, based on experimental studies. By comparing the values obtained from the two numerical methods and the experimental studies (Figure 13), a discussion of the results obtained was carried out. The adoption of the numerical results presented in Figure 13 was preceded by an analysis of all the numerical variants used, based on Figures 11 and 12, and on this basis, the variants that were closest to the values obtained experimentally and were, at the same time, optimal in terms of the simulation time for SW-FS were selected.  
Figure 13 shows little discrepancy between the individual results. When considering the use of SolidWorks Flow Simulation software, the value of the average error for the mesh size seven with local compaction in the key flow channel was 6.31% over the entire measurement range, relative to the values obtained experimentally. Further compaction of the numerical mesh and the definition of additional wall layers in the key area did  
Figure 12: Static flow characteristics determined using experimental and empirical studies on concept test bench.  
Figure 13: Comparison view of static flow characteristics determined using experimental and numerical studies.  
not produce significant changes in the results obtained, so the variant shown in Figure 13 using the channels tool alone was used for comparison purposes. In the case of the Ansys Fluent environment, the average relative error to the experimental study was 8.48% for the tetrahedral mesh, 11.22% for the polyhedral mesh, and 5.79% for the polyhexcore mesh, which is a combination of the two previous meshes, with the solution time for this variant being significantly longer than for the other variants.  
Comparing the results obtained with SW-FS and A-F, it should be noted that the value of the average error between the methods was 4.66%. In the case of brake systems, this can be a key aspect in correctly configuring a further simulation model using multiphysics and achieving results close to the built real model. This will form the basis for the authors' further work on the introduction of a new technical solution in pneumatic braking systems, changing the nature and functional parameters of the basic relay valve. The mean value of the error of both the numerical methods on the basis of the determined static characteristics was 6.05%. In the course of further numerical research on the issue of the differential brake valve, due to the availability of extensive simulation tools, the Ansys Fluent software will be used, which, in addition to static simulations, allows dynamic issues, the results of which will again be evaluated in the course of experimental tests.  
By adopting an experimental methodology for determining the throughput of inter-chamber nozzles, the authors verified the computational flow and methodology used in the area of pneumatic braking systems, and the implementation of a control and measurement program created by the authors in Python and further identification in the MATLAB environment using the presented methodology confirmed the feasibility of using this approach in the course of further work.