## 3 Calibration and Verification
### Verification Based on the Prototype Data  
The data at three flow rates were measured in the spillway tunnel of the Jinping-I project: 3200 m\({}^{3}\)/s (labeled Q1), 2130 m\({}^{3}\)/s (labeled Q2) and 1462 m\({}^{3}\)/s (labeled Q3). To validate the established theoretical approach, the theoretical calculations were compared with the prototype data.  
Figure 6: The trial results of the constant term in the drag coefficient equation.  
The comparison of the actual and the theoretical air velocities of the air intake wells is shown in Figure 7a. The trend of the theoretical air velocity is consistent with that of the prototype data. In general, the theoretical calculations are approximately 74%\(\sim\)114% of the prototype data with an average relative error of 13%. Compared with the results calculated with the constant term proposed by [PERSON] [14], it is apparent that the air velocity calculated with the constant term proposed in this study is much closer to the prototype data.  
A comparison of the actual and the theoretical air velocities in the water-free space of the spillway tunnel is shown in Figure 7b. The actual air velocity refers to the average air velocity calculated according to the air velocity inside the air intake well and the cross-sectional area of the air intake well and the water-free space. In general, the air velocity in the water-free space is lower than the water velocity, except at the position of the air intake well, where the air velocity increases sharply due to the inflow of air. Although there are certain differences between the theoretical calculations and the prototype data, the values have the same magnitude and a consistent distribution trend.  
Figure 7: Comparison of the actual and the theoretical air velocities. (**a**) Air intake well and (**b**) spillway tunnel.  
The air pressure in the water-free space of the spillway tunnel calculated by the theoretical approach is shown in Figure 8. The corresponding piezometric head along the flow direction, divided with the specific weight of the water is also shown in Figure 8. The maximum sub-pressure appears at the beginning of the free flow tunnel, and along the flow direction, the sub-pressure decreases gradually, reaching up to the atmospheric pressure at the outlet of the spillway tunnel. Due to the inflow of air, a sudden drop in the air pressure occurs at the position of the air intake well. The sub-pressure at the outlet of the air intake well is always higher than that in the water-free space at the same horizontal position, which is related to the decrease in airflow caused by the change in the cross-sectional area. Overall, the distribution of the air pressure in the water-free space of the spillway tunnel is reasonable.  
Based on the above analysis results, with a reasonable drag coefficient, the theoretical approach established in this paper can be used to study the ventilation characteristics of multi-intake-well air supply systems in spillway tunnels. In view of the convenience of this approach, the method can be better applied in the design and layout optimization of the multi-intake-well air supply system.