## 4 Results and Discussion
### Effects of Applied Pressures on Gas Chamber Pressure and PDR  
Figure 5 shows the time dependence of gas chamber pressure and PDR of different applied pressures (40 kPa, 60 kPa, 80 kPa, 100 kPa, and 120 kPa). The equivalent diameters of different defect sizes were evaluated to be 0.346 mm, 0.358 mm, 0.352 mm, 0.345 mm, and 0.350 mm, respectively. The measured pressure followed a decreasing tendency with time. Taking 120 kPa pressure as an example, the measured pressure decreased from 117.57 kPa to 1.48 kPa after 54.8 s. The measured PDR also decreased from 5.47 kPa/s to 0.02 kPa/s after 55.5 s. The pressure can be described as a quadratic function of time and may be presented by the following relationship:  
\[P=113.1908-4.0960t+0.0378t^{2},\ R^{2}=0.9992 \tag{17}\]  
In addition, it was found that the measured PDR had the highest value at the beginning and then decreased continuously. Moreover, along with the applied pressures increasing from 40 to 120 kPa, the required time for the measured pressure to decrease to zero became increasingly longer: 25.6 s, 34.0 s, 43.3 s, 50.7 s and 54.8 s, respectively. Similarly, the required time for the measured PDR to decrease to zero also became increasingly longer: 26.5 s, 34.5 s, 43.5 s, 51.5 s, and 55.5 s, respectively. The PDR values in the initial stages got larger: 2.74 kPa/s, 3.82 kPa/s, 4.22 kPa/s, 4.79 kPa/s, and 5.47 kPa/s, respectively. The longer required time and larger initial PDR value may have been caused by the change in gas mass or the number of moles due to the increasing applied pressure.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \(D_{0}\) (mm) & 0.185 & 0.189 & 0.276 & 0.352 \\ \hline \multirow{2}{*}{\(r\)} & Pressure & 0.993 & 0.987 & 0.990 & 0.999 \\  & PDR & 0.982 & 0.981 & 0.966 & 0.981 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Correlation between measured data and predicted values with different defect sizes. PDR: pressure decay rate.  
Similarly, for each applied pressure, the simulated curves had the same trend as that of the measured pressure and measured PDR. A fairly good agreement was observed between the experimental values and the numerical data, even though the measured data diverged a little from the simulated pressure. Unlike the results in Section 4.2, the measured pressure values were not always more than the simulated pressure values; instead, the measured pressures were higher than the simulated pressures when the applied pressure was less than 80 kPa. As for the PDR, the difference between the measured PDR and the calculated PDR changed with time, and it was relatively small in the middle of the pressure decay time. This correlation is demonstrated in Table 2. Values of Pearson's correlation coefficient \(r\) (more than 0.980) indicated a high consistency between the two curves. The significance (less than 0.001) showed the calculation model was valid for this study.  
Figure 5: The effect of applied pressure on the pressure and the PDR. (**a**) \(P_{g}\) = 40 kPa; (**b**) \(P_{g}\) = 60 kPa; (**c**) \(P_{g}\) = 80 kPa; (**d**) \(P_{g}\) = 100 kPa; (**e**) \(P_{g}\) = 120 kPa. Reaction conditions: water depth = 10 mm, gas chamber volume = 365.59 mL, and defect size = 0.35 mm.