# Hydraulic Performance of Wave-Type Flow at a Sill-Controlled Stilling Basin
## 3 Results and Discussion
### Pressure Head  
Figure 7 shows the maximum, mean, and minimum pressure head, \(H_{\text{p}}\), on the bottom along the silling basin starting at the weir toe (Station 0.0 m) at different unit discharges for Case M32 and a CHI (a classical hydraulic jump). It can be observed that the bottom pressure varied greatly along the silling basin for each unit discharge and reached a peak both at the location upstream and downstream of the sill (Figure 7a-e). Moreover, these peak values all increased with an increasing unit discharge due to the increase in water surface elevation. The maximum, mean, and minimum pressure head of a CHI is also shown in Figure 7f, where the depth of supercritical flow (\(y_{1}\)) and its subcritical conjugate depth (\(y_{2}\)) are 0.17 m and 0.92 m, respectively, when \(q_{\text{w}}=0.93\) m\({}^{2}\)/s [20]. For comparison purposes, the pressure profiles of a CHI increased monotonically along the stilling basin,  
Figure 6: Relative sill height \(S\) against the upstream Froude number \(F_{1}\)[7; 13]. except at its beginning. As observed in Figure 7a-e, for a small unit discharge (e.g., \(q_{\rm w}\) = 0.102 m\({}^{2}\)/s, and 0.154 m\({}^{2}\)/s), the values of the maximum, mean, and minimum pressure were nearly the same; i.e., the pressure fluctuation along the stilling basin bottom is small. However, as the unit discharge \(q_{\rm w}\) increased (\(q_{\rm w}\) = 0.188 m\({}^{2}\)/s, 0.205 m\({}^{2}\)/s and 0.230 m\({}^{2}\)/s, pressure fluctuations became greater in the vicinity of the sill, particularly at \(q_{\rm w}\) = 0.205 m\({}^{2}\)/s. This was attributed to the turbulent roller region of the jump, which was closer to the sill related to the transition from a submerged jump to a non-submerged jump. However, the pressure fluctuation of the classic hydraulic jump was more distinct at a near prototype scale. In order to prevent erosion below overflow spillways, chutes, and shuces, the pressure peak of wave-type flows should be carefully focused upon in this study. Figure 8 illustrates the normalized mean pressure heads (\(H_{\rm p}/y_{2}\)) along the stilling basin at different unit discharges (\(q_{\rm w}\)s) for each case and a CHJ. In this figure, the down  
Figure 7: Maximum, mean and minimum pressure head on the bottom along the stilling basin at different unit discharges for Case M32 and a CHJ: (**a**) \(q_{\rm w}\) = 0.102 m\({}^{2}\)/s; (**b**) \(q_{\rm w}\) = 0.154 m\({}^{2}\)/s; (**c**) \(q_{\rm w}\) = 0.188 m\({}^{2}\)/s; (**d**) \(q_{\rm w}\) = 0.205 m\({}^{2}\)/s; (**e**) \(q_{\rm w}\) = 0.230 m\({}^{2}\)/s; (**f**) \(q_{\rm w}\) = 0.93 m\({}^{2}\)/s for a classical hydraulic jump [16]. stream flow depth, \(y_{2}\), was used to normalize \(H_{\rm P}\). In general, the streamwise dimensionless mean pressure heads \(H_{\rm P}/y_{2}\)s for each case (Figure 8a-e) exhibited a similar trend at different unit discharges, with two distinct peak values observed along the stilling basin. For a CHI in Figure 8f, \(H_{\rm P}/y_{2}\) typically decreased initially and then increased along the stilling basin. A larger \(H_{\rm P}/y_{2}\) could be obtained for a smaller \(q_{\rm w}\) until the end of the jump, except for the beginning of the stilling basin. According to the existence of pressure peaks and the still position in Figures 7 and 8, the streamwise dimensionless mean pressure indicated the following flow zones: (1) deflection zone, (2) jump zone, and (3) wave impact zone. The defection zone was characterized by the pronounced mean pressures due to the impact and curvature of the flow. In this zone, the pressure head decreased, and the  
Figure 8: Normalized mean pressure head along the stilling basin for the range of \(q_{\rm w}\) tested for each case: (**a**) Case M12; (**b**) Case M22; (**c**) Case M32; (**d**) Case M31; (**e**) Case M33; (**f**) Classical hydraulic jump [16]. -dimensional impact pressure \(H_{\rm p}/y_{2}\)s was determined using the upstream weir flow. In the jump zone, the jump formation involved a strong pressure variation.