## 3 Results
### Maximum Disturbed Region Width  
Figure 10 illustrates the maximum disturbed region widths of \(\max(W_{f}/h_{c})\), \(\max(W_{m}/h_{c})\) and \(\max(W_{b}/h_{c})\) for free-surface, mainstream and bottom rotations. There is always \(\max(W_{b}/h_{c})>\max(W_{m}/h_{c})>\max(W_{f}/h_{c})\). With increasing convergence angle \(\Phi\), \(\max(W_{b}/h_{c})\), \(\max(W_{m}/h_{c})\) and \(\max(W_{f}/h_{c})\) all rise, with \(\max(W_{b}/h_{c})\) and \(\max(W_{f}/h_{c})\) having the biggest and smallest growing rates, respectively; \(\max(W_{b}/h_{c})\), \(\max(W_{m}/h_{c})\) and \(\max(W_{f}/h_{c})\) also increase with the decrease of \(\theta\) and the increase of \(h_{c}/B\).  
A basic form of regression equations for predicting the maximum dimensionless disturbed region widths for free-surface, mainstream and bottom rotations is proposed by  
Figure 10: Maximum disturbed region widths of \(\max(W_{f}/h_{c})\), \(\max(W_{m}/h_{c})\) and \(\max(W_{b}/h_{c})\) for (**a**) free-surface; (**b**) mainstream; and (**c**) bottom rotations.  
studying the influence of the dimensionless critical flow depth \(h_{c}/B\), the spillway slope \(\theta\), and the convergence angle \(\Phi\):  
\[\max\left(W_{f}/h_{c}\right),\max(W_{m}/h_{c}),\max(W_{b}/h_{c})=D\times\left( \tan\phi\right)^{E}\times\left(\frac{h_{c}}{B}\right)^{F}\times\left(\tan\theta \right)^{G} \tag{4}\]  
where \(D\), \(E\), \(F\) and \(G\) are coefficients to be determined.  
By substituting all the experimental data of Figure 10 into Equation (4), we can anticipate \(\max(W_{f}/h_{c})\), \(\max(W_{m}/h_{c})\) and \(\max(W_{b}/h_{c})\) by the following equations  
\[\max(W_{f}/h_{c})=2.974\times\left(\tan\phi\right)^{0.3}\times\left(\frac{h_{c }}{B}\right)^{-0.5}\times\left(\tan\theta\right)^{-0.5},\text{COD}\left(R^{2} \right)=0.948 \tag{5}\]  
\[\max(W_{m}/h_{c})=6.361\times\left(\tan\phi\right)^{0.3}\times\left(\frac{h_{c }}{B}\right)^{-0.5}\times\left(\tan\theta\right)^{-0.5},\text{COD}\left(R^{2} \right)=0.851 \tag{6}\]  
\[\max(W_{b}/h_{c})=10.867\times\left(\tan\phi\right)^{0.3}\times\left(\frac{h_{c }}{B}\right)^{-0.5}\times\left(\tan\theta\right)^{-0.5},\text{COD}\left(R^{2} \right)=0.878 \tag{7}\]  
For Equations (5)-(7), the coefficients of \(E\), \(F\) and \(G\) can be constant for free-surface, mainstream and bottom rotations; \(\max(W_{b}/h_{c})\) is almost 1.5 times as large as \(\max(W_{m}/h_{c})\) and 3 times as large as \(\max(W_{f}/h_{c})\) based on the variations in the coefficient \(D\) between Equations (5)-(7). Figure 11 compares the experimental data of \(\max(W_{f}/h_{c})\), \(\max(W_{m}/h_{c})\) and \(\max(W_{b}/h_{c})\) with their predicted value by Equations (5)-(7), and all the data plot within the error deviation boundaries of \(\pm 25\%\). The prediction performances of Equations (5)-(7) were evaluated by the mean relative deviation (MRD).  
\[\text{MRD}=\frac{1}{i}\sum_{i}\frac{|\text{predicted value}-\text{ experimental data}|}{\text{experimental data}} \tag{8}\]  
It is found that MRD are 9.6%, 11% and 13.1% for \(\max(W_{f}/h_{c})\), \(\max(W_{m}/h_{c})\) and \(\max(W_{b}/h_{c})\), respectively, demonstrating the predicting accuracy of Equations (5)-(7).  
Figure 11: Comparison of predicted \(\max(W_{f}/h_{c})\), \(\max(W_{m}/h_{c})\) and \(\max(W_{b}/h_{c})\) from Equations (5)–(7) with experimental data in Figure 10.