# Hydraulic Performance of Wave-Type Flow at a Sill-Controlled Stilling Basin
## 2 Experimental Setup and Methodology  
The experiments were conducted in the High-Speed Flow Laboratory at Hohai University in Nanjing, China. The experimental setup consisted of a large feeding basin, a pump, an approach conduit, a rectangular flume, a stilling basin model, and a flow return system (Figure 2). The rectangular flume made of Perspex was 25.00 m in length, 0.50 m in width, and 0.60 m in height. The stilling basin model consisted of a weir and a sill. The height of the weir was 0.36 m. The weir was a standard Waterways Experiment Station (WES) weir with a crest profile of \(y=1.81x^{1.85}\) and a chute with an angle of 57\({}^{\circ}\) relative to the basin bottom. The sill in the stilling basin had a thickness and width of 0.01 m and 0.50 m. Wave-type flow was observed downstream of the weir by a sill with no tailwater conditions, and downstream flows were also supercritical. Figure 3 shows the experimental variables for submerged and non-submerged jumps, including the upstream flow depth, \(y_{0}\); the approaching supercritical flow depth, \(y_{1}\) upstream of the sill; the inflow discharge \(Q\); the sill height, \(s\), the length of the stilling basin, \(l_{\mathrm{s}}\) (i.e., the sill position), from the weir toe (Station 0.0 m) to the upstream face of the sill; and the downstream depth, \(y_{2}\). The inflow discharge, \(Q\), was measured using a 90\({}^{\circ}\) V-notch weir  
Figure 2: Experimental setup. with an accuracy of \(\pm 1\%\), and flow depths \(y_{0}\) and \(y_{2}\) were measured using point gauges with an accuracy of \(\pm 1\%\). Due to the effect of free-surface instability, \(y_{2}\) was measured 10 m downstream of the sill, where the free-surface undulations diminished. Since a submerged jump may occur under certain conditions, a different method was used to calculate the flow depth \(y_{1}\) and velocity \(v_{1}\). For non-submerged jumps (Figure 3b), flow depth \(y_{1}\) was calculated by means of an energy balance (i.e., \(y_{1}=E_{0}-\frac{Q^{2}}{2 gB^{2}\varphi^{3}y_{1}^{2}}\), where \(E_{0}\) is the total energy upstream of the weir, \(g\) is the acceleration of gravity, \(B\) = 0.50 m is the basin width, and \(\varphi\) = 0.95 is the coefficient of velocity), and velocity \(v_{1}\) was calculated by means of the continuity law. For submerged jumps (Figure 3a), \(v_{1}\) was calculated as \(\sqrt{2g(y_{0}-y_{4})}\), where \(y_{4}\) denotes the flow depth at the terminal section of the weir [16], and \(y_{1}\) was calculated by means of the continuity law. Figure 4 shows the layout of the air concentration and pressure measurement points. The pressure measurement points were placed at the centerline of the bottom (Figure 4b) corresponding to station 0 m, 0.05 m, 0.15 m,..., and 1.85 m (from the second to the last for every 0.1 m interval). The pressure on the bottom was measured with piezometric tubes with an error of \(\pm 0.5\) mm. The air concentration measurement points were placed both 0.1 m off the centerline on the bottom (Figure 4b) and 0.05 m above the bottom on the sidewall at the same station (Figure 4a), which corresponds to station 0.35 m, 0.45 m,..., and 1.05 m (from the first to the last for every 0.1 m interval). The air concentrations both on the bottom and the sidewall were measured by using a CQ6-2005 aeration apparatus with a sampling rate of 1020 Hz, a time period of 10 s, and an error of \(\pm 0.3\%\)[17]. For this study, the experiments were conducted for inflow unit discharges \(0.102\) m\({}^{2}/s\leq q_{\mathrm{w}}\leq 0.230\) m\({}^{2}/s\) (i.e., 0.102, 0.154, 0.188, 0.205 and 0.230), equaling Reynolds numbers of \(3.97\times 10^{5}\leq Re\leq 9.14\times 10^{5}\). Hence, the Reynolds numbers were large enough to avoid significant scale effects as identified in air-water flows in the stilling basin [18]. The experiments encompassed five sill-controlled stilling basins by altering the position (\(l_{\mathrm{s}}\)) and height (\(s\)) of the sill.