## 5 Results and Discussion  
Table 2 provides the information about the Reynolds number, Darcy friction factor and major friction loss in the duct as a function of different input face velocities. With this information, it is possible to show the Moody diagram, plotted in Figure 5.  
The results obtained by using the four methods described above (ISO, VDI, FEM and experimental measurements) are shown in Tables 3 and 4, in which it is possible to see at a glance the differences in the values of the pressure loss induced by the two types of profiles. When low input face velocities are considered (around 5 m/s), there are no significant differences in the pressure loss experimentally obtained with both shapes. This is due to the fact that, even though the flow is propagating in a turbulent regime (\(Re>2100\)), its interaction with the silencers has a similar effect  
Nevertheless, for input face velocities equal to or greater than 10 m/s, the pressure loss obtained by using rectangular profiles is approximately 1.5 times that obtained with semihexadecagonal profiles. This indicates, as it was mentioned in Section 3, that the fact of inserting a rigid wall (rectangular profile) in the duct perpendicular to the direction of the propagation of the flow leads to an increase in the turbulence and loss in kinetic energy of the flow. It is important to note that the VDI standard, unlike the ISO standard, does not include references to the shape of the silencer profile. Therefore, the same pressure loss values are predicted for both rectangular and semihexadecagonal profiles (third column in Table 3 and Table 4, respectively) when this standard is used. Tables 3 and 4 also show that, even if all the methods follow the same overall tendency in the prediction of the pressure loss, the differences between them increase with the considered input face velocity. This is because the behavior of the system becomes more complex as the flow velocity increases, due to the presence of turbulence and other associated phenomena that are difficult to predict. The increase in the turbulence in the system is associated, among other factors, both to the profile shape and to the input face velocity. Figure 6 shows the numerical result of the variation of the flow velocity in the duct as a function of the position and the input face \begin{table}
\begin{tabular}{r r r r r} \hline \hline
**U\({}_{0}\) [m/s]** & **ISO 14163** & **VDI 2081-1** & **FEM** & **Experimental** \\ \hline
5 & 77 & 114 & 110 & 98 \\
10 & 308 & 455 & 411 & 386 \\
15 & 692 & 1023 & 914 & 859 \\
20 & 1230 & 1818 & 1640 & 1517 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Pressure loss (in Pascals) obtained with ISO 14163, VDI 2081-1, FEM and experimental measurements for the system of splitters with semihexadecagonal profiles. Figure 5: Moody diagram of the duct used for experimental measurements. velocity. The flow velocity highly increases in the slit between both silencers, as the cross section in this region is reduced to 1/3 of the original cross section of the duct. This leads to a near tripling of the flow velocity in this section. It is also remarkable the fact that the flow velocity in the case of semihexadecagonal profiles progressively increases until in reaches its maximum and, from that point on, it stays relatively flat until the flow leaves the section of the duct occupied by the splitters. In contrast to this case, when rectangular profiles are considered, a higher peak is produced in the first interaction of the flow with the silencer, which explains the greater pressure loss in this configuration. Figure 7 depicts the results presented in Tables 3 and 4. The experimental values of the pressure loss are considered a reference for the validation of the results given by the standards and the numerical model; consequently, the trend line followed by the experimental results is also shown in this figure.