# A Study on a Modified Model for the Hold Time of a Clean Extinguishing Agent
## 4 Results
This result is consistent with existing studies. The predicted outflow volumetric flow at different heights based on these experimental results can be seen in Figure 7. This figure shows the outflow volumetric flow value for each height predicted based on the concentration data for each height measured in Figure 6. These values show the same trend as the theoretical outflow volumetric flow shown in Figure 5. The outflow volumetric flow increases as the number of leakage holes increases and decreases gradually as the neutral plane \(\dot{H}_{np}\) decreases. _HFC-125_, with a high density of agent-air mixture, has a larger outflow volumetric flow value than _IG-01_. Figure 6: Concentration change according to time and enclosure height for each condition. Lighter shade indicates a decrease in the height, at which point the concentration was measured (\(c_{mix}=1,\ c_{air}=0\)): (**a**) _IG-01_, 4 holes; (**b**) _IG-01_, 8 holes; (**c**) _IG-01_, 12 holes; (**d**) _IG-01_, 16 holes; (**e**) _HFC-125_, 4 holes; (**f**) _HFC-125_, 8 holes; (**g**) _HFC-125_, 12 holes; and (**h**) _HFC-125_, 16 holes. Figure 8 shows a comparison between the theoretical hold time predicted by \(\dot{V}_{vo}\) and \(\dot{V}_{mo}\) and the hold time observed in the enclosure. The theoretical hold times \(t_{th}\) and \(t_{mth}\) predicted by \(\dot{V}_{vo}\) and \(\dot{V}_{mo}\) in Figure 8 have the same trends as the results of the outflow volumetric flow in Figure 5. The smaller the leakage exponent \(n\) is, the smaller the difference is between the existing \(t_{th}\) and the modified \(t_{mh}\). The larger the leakage exponent \(n\) is, the larger the difference is between \(t_{th}\) and \(t_{mh}\). Also, this result is more pronounced in the HFC series with large \(\rho_{mix}\). The hold time observed in the test enclosure was larger than the theoretically predicted hold time values. These results were measured equally for both IG and HFC series, and the same was applied to the change in the number of leakage holes. The validation of the proposed theory is summarized in Figures 9 and 10 and Table 3. Figures 9 and 10 show a comparison of experimentally observed and theoretically predicted results in a test enclosure. These figures demonstrate how well the theoretically predicted values can represent the experimentally observed values. The fact that the observed values are close to the dotted line means that the theoretically predicted values are highly accurate. A quantitative comparison of the observed and predicted values is shown in Table 3.  
Figure 5:0 Change of hold time according to enclosure height for each condition. The theoretical hold time was predicted based on _the wide model_. The threshold concentration \(c_{th}\) at which the hold time was determined was set to 85% of the initial concentration \(c_{mix}\): (\(c_{th}=0.85c_{mix}\): (**a**) _IG-01_, 4 holes; (**b**) _IG-01_, 8 holes; (**c**) _IG-01_, 12 holes; (**d**) _IG-01_, 16 holes; (**e**) _HFC-125_, 4 holes; (**f**) _HFC-125_, 8 holes; (**g**) _HFC-125_, 12 holes; and (**h**) _HFC-125_, 16 holes. Figure 5:1 Outflow volumetric flow at different enclosure heights according to the number of leakage holes predicted by the existing and proposed theoretical equations: (**a**) _IG-01_; (**b**) _HFC-125_. Figure 5:2 Comparison of theoretical and observed hold time (\(c_{th}=0.85c_{mix}\)): (**a**) _IG-01_, \(t_{\text{th}}\) vs. \(t_{h}\); (**b**) _IG-01_, \(t_{\text{th}}\) vs. \(t_{h}\); (**c**) _HFC-125_, \(t_{\text{th}}\) vs. \(t_{h}\); and (**d**) _HFC-125_, \(t_{\text{th}}\) vs. \(t_{h}\). In Figure 9, it can be seen that the outflow volumetric flow measured in the test enclosure is located below the dotted line as a whole. This means that the measurements are lower than the theoretically predicted values. These results become more pronounced as the number of leakage holes increases.