## 4 Observation Results
### Water Surface Change
On the contrary, when \(\frac{h_{t}-c}{H_{10}}>\) 0.45, it is submerged flow, where \(h_{t}\) is the downstream water depth, \(c\) is the height of the continuous ridge, \(H_{10}=\left[Q/(0.42B\sqrt{2g})\right]^{2/3}\), \(Q\) is flow rate, \(B\) is the width of the continuous ridge, and \(g\) is the acceleration of gravity. For example, in FDC No.1, \(H_{10}\) is 2.577 m according to the abovementioned formula, \(h_{t}\) = 996.58-982.00 = 14.58 m, and \(c\) = 8.0 m. We then have \(\frac{h_{t}-c}{H_{10}}=\frac{14.58-8}{2.577}=2.55>\) 0.45. Therefore, the flow pattern across the continuous ridge is a submerged flow. In the same way, it can be judged that flow patterns across the continuous ridge in FDC No.9 and No.16 are also submerged flows. The contracted water depth (\(hc\)) before the hydraulic jump can be obtained [16; 17]:  
\[E_{0}=h_{c}+\frac{Q^{2}}{2g\varphi^{2}b^{2}h_{c}^{2}} \tag{1}\]  
where \(E_{0}\) is the total upstream water head above the base level of the downstream riverbed; \(\varphi\) is the coefficient of flow velocity, here \(\varphi\) = 0.85; and \(b\) is the width of the single gate chamber, here \(b\) = 9.0 m.  
There are three sluice gates at the head of the open channel, and not all of them need to be opened evenly when the flood discharge is low. In some cases, only a single gate is \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \begin{tabular}{c} **FDC** \\ **No.** \\ \end{tabular} & \begin{tabular}{c} **Q** \\ **(m\({}^{2}\)/s)** \\ \end{tabular} & \begin{tabular}{c} **\(E_{0}\)** \\ **(m)** \\ \end{tabular} & \begin{tabular}{c} **\(v_{c}\)** \\ **(m/s)** \\ \end{tabular} & \begin{tabular}{c} **\(v_{2}\)** \\ **(m/s)** \\ \end{tabular} & \begin{tabular}{c} **\(b\)** \\ **(m)** \\ \end{tabular} & \begin{tabular}{c} **\(h_{c}\)** \\ **(m)** \\ \end{tabular} & \begin{tabular}{c} **\(h_{2}\)** \\ **(m)** \\ \end{tabular} & \begin{tabular}{c} **\(Fr_{c}\)** \\ **(m)** \\ \end{tabular} & \
\begin{tabular}{c} **\(Re\)** \\ **(m)** \\ \end{tabular} &
\begin{tabular}{c} **\(h_{2}\)** \\ **(\%)** \\ \end{tabular} \\ \hline
1 & 500 & 30.35 & 19.75 & 1.29 & 9.0 & 2.813 & 3.878 & 3.76 & \(5.5\times 10^{7}\) & \(-1.99\) & 80.4 \\
9 & 3000 & 31.27 & 18.97 & 5.09 & 9.0 & 5.857 & 8.752 & 2.50 & \(1.1\times 10^{8}\) & \(-0.18\) & 67.2 \\
16 & 250 & 32.04 & 20.85 & 2.16 & 9.0 & 1.332 & 2.448 & 5.77 & \(2.75\times 10^{7}\) & 0.70 & 93.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Hydraulic indexes for three FDCs. Figure 7: Schematic diagram for a hydraulic jump calculation. opened, and the water flow could then be diffused at the outlet of the gate chamber, forming a jet flow or transverse expansion flow. The jet flow becomes weaker as it moves farther away from the gate chamber exit. Therefore, it could be considered that the water depth after the hydraulic jump is approximately equal to the position of the continuous ridge. Water depth (\(h_{2}\)) after the hydraulic jump at the continuous ridge can be gained [23; 24]:  
\[bh_{c}^{2}+\frac{Q^{2}}{gbh_{c}}=Bh_{2}^{2}+\frac{Q^{2}}{gBh_{2}}+\beta\frac{v_ {2}^{2}S}{g} \tag{2}\]  
where \(B\) is the width of the open channel; \(S\) is the vertical area of the continuous ridge; and \(\beta\) is the momentum correction factor. In the current case, we have approximatively \(B=65\) m, \(S=520\) m\({}^{2}\), and \(\beta=1.0\). Flow velocity \(v_{c}\) before the hydraulic jump can be written by \(v_{c}=\frac{Q}{bh_{c}}\). The rate of energy dissipation (\(K\)) after the hydraulic jump at the continuous ridge can be written as [23; 24]:  
\[K=\frac{E_{0}-E_{2}}{E_{0}} \tag{3}\]  
where \(E_{2}\) is the total water head above the base level of the downstream riverbed at the continuous ridge. The hydraulic indexes for the three FDCs are provided in Table 2. From Table 2, it can be observed that the error of \(h_{2}\) is relatively large in FDC No.1 and No.16. At the same time, it is small in FDC No.9. The reason for this is that in FDC No.1 and No.16, only sluice gate No.6# is open.