## 5 Discussion
### Factor Analysis  
The standard gives the lift force formula: \(P_{t}=\rho g\beta_{t}H_{s}D_{1}B_{zs}\) (where \(\rho\) is the fluid density; \(\beta_{t}\) is the lift force coefficient; \(H_{s}\) is the upstream water depth; \(D_{1}\) is the upstream side rake face width; and \(B_{zs}\) is the seal width) and suction force formula: \(P_{X}=p_{X}D_{2}B_{zs}\) (where \(p_{X}\) is the average intensity specified as 20 kN/m\({}^{2}\); and \(D_{2}\) is the downstream side rake face width) [20]. Figure 12 depicts the lift force coefficient at the gate bottom with the opening rate. It can be seen from Figure 12 that the lift force coefficient is related to the upstream water depth, opening rate and service gate height. When the upstream water depth increases, the lift coefficient increases gradually. Nevertheless, it is different from the value 1.0 specified by the standard [20]. At a service gate height of 1.0 m, the coefficient remains almost constant at a large opening rate and decreases rapidly at opening rates below 0.3, as shown in Figure 12a. While the service gate height is 4.0 m, the coefficient decreases gradually with the decrease in opening rate (Figure 12b). However, an increase in the the upstream water depth only changes the value of the coefficient. It does not change the variation characteristics. Moreover, during the transition stage from the full-flow to open-flow, the flow pattern behind the gate is drastic turbulent. Afterwards, the air flows into the gate bottom and the negative pressure occurs at the gate bottom. The gate bottom pressure changes between the lift force and the suction force, which prompts the gate's vertical vibration. Meanwhile, the suction force at the gate bottom does not often happen as it is related to this transition. Thus, it seems to be unreasonable to regard the suction force as a constant. The suction force should be determined based on the actual situation. Combined with the above model test results, the main influence factor of the gate bottom hydrodynamic loads is the flow pattern behind the gate, and this is determined by the service gate height.  
Furthermore, the holding force is related to the gate opening rate, upstream water depth and service gate height, and its maximum might not always occur at the opening rate \(e=1.0\). Thus, the reasonable and accurate calculation of the holding force is of great significance to the selection of the hoist capacity. Based on the standard formula (4), the maximum holding force is 3246.45 kN under the upstream water depth of 100 m and service gate height of 1.0 m. The experimental result is 2943.53 kN and the relative error between the experiment and standard is over 10.36%. The standard calculation result might not meet the practical precision. Meanwhile, the simulation result is consistent with the experiment result. Thus, the fluid-structure interaction numerical simulation method can be used to predict the gate holding force in the closing process. If the gate counterweight is insufficient, the gate-closing speed would slow down gradually until  
Figure 12: Lift force coefficient: (**a**) service gate height 1 m; and (**b**) service gate height 4 m.  
it stops, suggesting that the method adopted in this study can also be utilized to check whether the counterweight meets the requirements and to predict the failure of gate-closing.  
The variation of friction coefficient between the gate and track was weakened in this study, and the friction coefficient was viewed as a constant in the numerical model. In fact, the relationship between the friction coefficient and the relative velocity in the closing process should be taken into account, which involves the study of the friction mechanism [30,31]. Thus, the relationship and distinction of the friction-induced vibration and flow-induced vibration in the closing process need to be given more attention in subsequent research.