## 5 Results and Discussion
The behavior of the trend lines for both types of profiles can be described by means of the second order parabolic equations that can be observed in the insets of the figure. Figure 6: Numerical result of the variation of the flow velocity along the duct as a function of the position and the input face velocity in splitter silencers with (**a**) rectangular and (**b**) semihexadecagonal profiles. Figure 7: Pressure loss in splitter silencers with (**a**) rectangular and (**b**) semihexadecagonal profiles as a function of the input face velocity, \(U_{0}\). The dashed black lines show the trend lines followed by the experimental results, used to obtain the fitting equation. The coefficient of determination \(R^{2}\) between the results of the pressure loss obtained by using the ISO standard and numerical methods, as a function of those obtained by means of experimental measurements, are shown in both configurations in Figures 8 and 9. For the system of splitter silencers with rectangular profiles, the coefficient of determination is found to be slightly higher in numerical simulations, meaning that this model can reproduce experimental results with a slightly higher quality. On the contrary, the coefficients of determination for the system of splitter silencers with semihexadecagonal profiles are very close when the ISO standard and numerical simulations are used (a difference of 0.0001 is found). In general, when only the \(R^{2}\) coefficient is analyzed, it is possible to observe that both models can reproduce experimental results with a similar quality. Nevertheless, the difference between the results obtained with the used methods can be also studied. The difference between the predicted pressure loss obtained with ISO 14163, VDI 2081-1 and FEM with that of experimental measurements with rectangular and semihexadecagonal profiles is shown in Tables 5 and 6. On the one hand, for the configuration in which the silencers have a rectangular profile, both ISO and FEM predict relatively similar values for the pressure loss, while the VDI clearly differs for velocities greater than 10 m/s. On the other hand, when semihexadecagonal profiles are considered, the use of numerical  
Figure 8: Coefficient of determination \(R^{2}\) between (**a**) analytical (ISO) and experimental results and (**b**) numerical and experimental results for the configuration of splitter silencers with rectangular profiles. Figure 9: Coefficient of determination \(R^{2}\) between (**a**) analytical (ISO) and experimental results and (**b**) numerical and experimental results for the configuration of splitter silencers with semihexadecagonal profiles. simulations provides results that are clearly in better agreement with the experimental results (average error of 8 %) than both standards (with average errors of 20 % and 18 % for ISO and VDI, respectively). Consequently, it is possible to observe that the standards can accurately predict the value of the pressure loss in the cases for which they are developed, but their accuracy is reduced when slight variations of the proposed geometries are implemented. Negative (positive) values in these tables indicate an underestimation (overestimation) of the pressure loss by a given method (ISO, VDI or FEM), compared to the experimental results. It is important to note that in many industrial sectors, the machinery is not always working in the same regime and, consequently, a buffer in these predictions is necessary. Additionally, given that some machines have technical requirements for a proper working regime, a slight overestimation of the values of the pressure loss reduces the risk in the design of the silencers to be applied. An underestimation of the pressure loss can reduce the efficiency of the machine and, consequently, affect its proper working.