## 3 Results
### Response Surface  
The results of the numerical simulations for each treatment of the FFD are shown ordered according to their factors in Table 6 and for each treatment of the FCCD in Table 7.  
The results of the Fisher test \(F\) global allow one to conclude with full confidence that the analyzed data respond to a trend and, therefore, can be modeled (\(p\)-value = 1.332 \(\times\) 10\({}^{-8}\) for the FFD and \(p\)-value = 3.9 \(\times\) 10\({}^{-3}\) for the FCCD). A second-order multiple regression model with interactions is adjusted for each experimental design, with which the effect of the different factors is determined. The null hypothesis of the test establishes that the analyzed factor has no effect on the response variable. Therefore, the lower the \(p\)-value of each coefficient, the greater the evidence against the null hypothesis, suggesting a significant difference generated by the respective factor [42]. Table 8 summarizes the results of the variance analysis (ANOVA) for the adjustment of the regression models of the FFD and the FCCD. Table 9 shows the test statistics for each factor and experimental design results. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \(\mathbf{O}\) & \(\mathbf{P}\) & \(\mathbf{Q}\) & \(\mathbf{C_{P}}\) & \(\mathbf{O}\) & \(\mathbf{P}\) & \(\mathbf{Q}\) & \(\mathbf{C_{P}}\) & \(\mathbf{O}\) & \(\mathbf{P}\) & \(\mathbf{Q}\) & \(\mathbf{C_{P}}\) \\ \hline
96 & 12 & 6 & 0.4130 & 98 & 12 & 6 & 0.4243 & 100 & 12 & 6 & 0.4144 \\
96 & 12 & 8 & 0.4075 & 98 & 12 & 8 & 0.4003 & 100 & 12 & 8 & 0.3733 \\
96 & 12 & 10 & 0.3833 & 98 & 12 & 10 & 0.3824 & 100 & 12 & 10 & 0.3405 \\
96 & 16 & 6 & 0.3977 & 98 & 16 & 6 & 0.4219 & 100 & 16 & 6 & 0.3859 \\
96 & 16 & 8 & 0.4075 & 98 & 16 & 8 & 0.4279 & 100 & 16 & 8 & 0.3798 \\
96 & 16 & 10 & 0.4081 & 98 & 16 & 10 & 0.4070 & 100 & 16 & 10 & 0.3641 \\
96 & 20 & 6 & 0.3687 & 98 & 20 & 6 & 0.3576 & 100 & 20 & 6 & 0.3406 \\
96 & 20 & 8 & 0.3919 & 98 & 20 & 8 & 0.4115 & 100 & 20 & 8 & 0.3575 \\
96 & 20 & 10 & 0.4196 & 98 & 20 & 10 & 0.4015 & 100 & 20 & 10 & 0.3577 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Power coefficient (\(C_{P}\)) determined for each treatment of the FFD. \begin{table}
\begin{tabular}{l l l l l l l} \hline \hline \multirow{2}{*}{**Hypothesis**} & \multirow{2}{*}{**Term**} & \multirow{2}{*}{**Test Name**} & \multicolumn{3}{c}{\(\mathbf{p\)**-Value**}} & \multirow{2}{*}{**Decision**} \\  & & & & **FFD** & & **FCCD** & \\ \hline Nomality & Response variable (\(C_{P}\)) & Kolmogorov-Smirnov & 0.5722 & 0.4178 & \multirow{2}{*}{Cannot be rejected} \\ Nomality & Response variable (\(C_{P}\)) & Shapiro-Wilk & 0.1241 & 0.0579 & \multirow{2}{*}{Cannot be rejected} \\ Nomality & Residuals & Jarque-Bera & 0.9490 & 0.6770 & \multirow{2}{*}{Cannot be rejected} \\ Independence & Residuals & Wald-Wolfowitz (runs test) & 0.4233 & 0.2658 & \multirow{2}{*}{Cannot be rejected} \\ Homocadasticity & \(O\): Tip diameter & Levene & 0.6952 & 0.3829 & \multirow{2}{*}{Cannot be rejected} \\ Homocadasticity & \(P\): Inlet gap & Levene & 0.5690 & 0.5354 & \multirow{2}{*}{Cannot be rejected} \\ Homocadasticity & \(Q\): Outlet gap & Levene & 0.5569 & 0.5346 & \multirow{2}{*}{Cannot be rejected} \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results of the tests in the adjustment of the regression model for the FFD and the FCCD. The coefficients that correspond to each factor constitute the regression polynomial that determines the value of the response variable in each coordinate [43]. Equations (5) and (6) express the regression polynomials for the FFD and the FCCD, respectively. \[ \begin{split} C_{P}&=-49.703+1.232\cdot O+0.049454 \cdot P+0.1978\cdot Q\\ &-0.000442\cdot OP-0.0021635\cdot OQ+0.002614\cdot PQ\\ &-0.0050518\cdot O^{2}-0.0009056\cdot P^{2}-0.0018406\cdot Q^{2} \end{split}  \tag{5}\]  
\[ \begin{split} C_{P}&=-60.989+1.0068\cdot O+0.076752 \cdot P+0.20925\cdot Q\\ &-0.0007616\cdot OP-0.0024408\cdot OQ+0.0026814\cdot PQ\\ &-0.0014303\cdot O^{2}-0.0007783\cdot P^{2}-0.0009675\cdot Q^{2} \end{split}