## 3 Results and Discussion
### Derivation of Mean Velocity using GMDH
In the training mode of the model at 0.6 width ratio, the maximum relative error is related to \(\theta=60\) which is equal to 6.8% although similar results could also be seen for the other two angles. Therefore, the presented model shows good results for different angles at 0.6 width ratio. As the width ratio increases and at \(\mathrm{W_{r}}=0.8\) the prediction accuracy decreases in such a manner that the maximum relative error is approximately 8% which occurs at \(\theta=30\) while it presents almost similar results to that of the existing width ratio at the two other \(\theta\)s. Greater increase in the width ratio value decreases the prediction accuracy but the outstanding point is that the total mean of all the predictions made in this research in the training mode of the model is as \(\mathrm{R^{2}}=0.86\), \(\mathrm{MAPE}=10.44\), \(\mathrm{RMSE}=0.03\), and \(\mathrm{SI}=0.12\), which shows that the model is fairly accurate for all the training data. Figure 6:1 Performance of outcomes for testing phase of the GMDH model at different angles. The results of the statistical indexes in the testing mode of the model are almost similar to those of the training mode of the model. In such a manner that at 6% width ratio the relevant maximum relative error is approximately 6% which also follows an almost similar process at 0.8 width ratio. Like the training mode, as the width ratio increases the prediction accuracy decreases in this mode as well, however, what stands up in this table is that the velocity prediction results at the test mode of the model (R\({}^{2}\) = 0.88, MAPE = 9.72, RMSE = 0.03, and SI = 0.11) also follow an almost similar process to that of the training mode of the model which indicates the flexibility of the presented model under different hydraulic conditions. Figure 9 shows the error distribution of the presented model for different width ratios (Figure 9b) and different angles (Figure 9a). In statistics, a frequency distribution is a graph that displays the frequency of various outcomes in a sample. Each entry in the table contains the frequency or count of the occurrences of values within a particular group or interval. It could be seen that the relative error distribution is almost constant in all three models at different angles. The point to be considered in this Figure 9 is that almost 80% of the data used in this study have a relative error less than 15% which indicates that the model presented in the present study through using GMDH performs well when determining the mean velocity. It could also be seen at different width ratios that the predictions made have a relative error less than 10% at the width ratio of approximately 90%. The maximum error values are related to 1.4 width ratio but as seen almost 70% of the predictions have a relative error less than 15% in this state as well which reveals that the model suggested in the current research performs well. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Train** & **Wr** & \(\theta\) & **R\({}^{2}\)** & **MAPE** & **RMSE** & **SI** \\ \hline \multirow{8}{*}{} & 0.6 & 30 & 0.50 & 4.35 & 0.01 & 0.05 \\  & & 60 & 0.60 & 6.80 & 0.02 & 0.08 \\  & & 90 & 0.48 & 5.72 & 0.02 & 0.07 \\  & 0.8 & 3  
It could be stated in general and with regard to Figures 8 and 9 which show the differences between the estimated values and the real values and the relative error distribution respectively and also the values of the statistical indexes presented in Table 2, which have presented relatively good results for different angles and width ratios, that using the equation which has been presented in this study can perform well in predicting the mean velocity in an intake (Equation (23)) and it could decrease the problems stemming from experimental researches which are usually time- consuming and costly, with a relatively fair level of accuracy.