## 5 Conclusions  
The results obtained through experimentation with the adopted mathematical model and the numerical approach form the basis for the correct configuration of the real-world model of the differential brake valve, which the authors assume will enable dual-range operation while maintaining vehicle stability and a high level of vehicle combination safety. From a scientific standpoint, this research contributes to the broader field of fluid dynamics and its applications in automotive engineering. It demonstrates the validity of using CFDs for analyzing complex flow scenarios in brake valve components and provides a foundation for future studies. The comparison of the results from different CFD software packages (SolidWorks Flow Simulation and Ansys Fluent) also offers valuable insights into the reliability and consistency of these tools for such applications. 1. The discrepancies between the numerical and experimental results range from 5.79 to 6.31%, with an average of 6.05% for both methods, which, given the effort and financial input for the construction and software of the bench, allows the use of numerical environments (CFDs) to assess the flow parameters. 2. The experimentally determined regression equation, MFR = 0.0017 \({d_{n}}^{2}-0.0010\)\({d_{n}}\), provides the basis for estimating the remaining values of the mass flow rate in front of a nozzle of the assumed length for other bore diameters in the range of (0.75\(\ldots\)5.00) mm. 3. From the determined flow characteristics using SW-FS, a significant effect of the numerical mesh used on the determined MFR value was noted, with the differences separable into two key ranges. In the first interval of (0.75\(\ldots\)3.50) mm, the value of the difference between the results obtained from the global mesh in size four and the global mesh in size seven with local compaction in the nozzle channel ranges from 53 to 67%, and in the interval of (3.75\(\ldots\)5.00) mm it ranges from 5 to 15%, which excludes the use of only global meshes to find a solution to issues with small flow channels. 4. The use of different configurations of locally compacting mesh tools in SW-FS in the geometry considered did not result in visible changes in the results obtained, so a size seven mesh with local compacting in a narrow channel, was used as a comparison option. Ansys Fluent, with its extensive finite element mesh modeling, yielded an average discrepancy value of 5.79% for the polyhexcore mesh with respect to the experimental studies, making it a tool that offers better capabilities in simulating the flow and determining its parameters, with the mere definition of simulation conditions, residuals, and the maximum number of solver iterations requiring more effort than is the case in SW-FS. The other numerical meshes used in A-F gave discrepancies of 11.22% for the polyhedral and 8.48% for the tetrahedral mesh. Considering the speed of the solver with the polyhedral mesh, the further optimization of the solver should be considered; as for the maximum edge length of individual cells of 0.3899 mm, the solver running time was approximately 40 to 60 s. For a polyhexcore mesh with an edge length in the range of (0.0566...0.2266) mm, the simulation time with a number of iterations equal to 200 and residuals 1 \(\times\) 10\({}^{-4}\) was almost 2400 s for all the geometry variants. Experimental tests on a conceptual bench using the direct MFR measurement method, together with the methodology presented in the article and the mathematical model developed, confirmed the possibility of using this method to determine even small throughput values, which has not yet been verified by other researchers. During the experimental tests, special attention must be paid to maintaining the tightness of the measuring system, as even small defects in the continuity of the compressed air nozzle flow may lead to the falsification of the results obtained.