## 4 Results and Discussion
### ASD System with One Branch Pipe with Ten Holes
In Figure 7a, the correlation between slope and normalized length was investigated. In that, the normalized length is the location of the hole over the total length. When the smokebox is located at the hole near the ASD, the slope is largest. On the other hand, when the smokebox is located at the hole which is far away from the ASD, the slope is smallest. Similarly, the obscuration ratio in the ASD had the same trend as the slope in Figure 7b, the obscuration ratio is largest at the hole which is located nearby to the ASD. Besides, the correlation between the slope and obscuration ratio is shown in Figure 7c. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Hole**} & \multirow{2}{*}{**Slope**} & **ASD Obscuration** & **Chamber Obscuration** & **Obscuration Ratio** \\  & & **(\%/m)** & **(\%/m)** & **(\%/m)** \\ \hline
1 & 0.1952 & 1.74 & 10 & 0.174 \\
2 & 0.1707 & 1.54 & 10 & 0.154 \\
3 & 0.1387 & 1.38 & 10 & 0.138 \\
4 & 0.1124 & 1.24 & 10 & 0.124 \\
5 & 0.0994 & 1.1 & 10 & 0.11 \\
6 & 0.0754 & 0.983 & 10 & 0.098 \\
7 & 0.0645 & 0.91 & 10 & 0.091 \\
8 & 0.0444 & 0.853 & 10 & 0.085 \\
9 & 0.0315 & 0.8 & 10 & 0.08 \\
10 & 0.0241 & 0.76 & 10 & 0.076 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The slope and obscuration ratio at ASD 1 when chamber obscuration is 10%/m. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Hole**} & \multirow{2}{*}{**Slope**} & **ASD Obscuration** & **Chamber Obscuration** & **Obscuration Ratio** \\  & & **(\%/m)** & **(\%/m)** & **(\%/m)** \\ \hline
1 & 0.2796 & 2.523 & 15 & 0.168 \\
2 & 0.224 & 2.23 & 15 & 0.149 \\
3 & 0.1821 & 2.02 & 15 & 0.135 \\
4 & 0.1519 & 1.787 & 15 & 0.119 \\
5 & 0.1233 & 1.593 & 15 & 0.1061 \\
6 & 0.0976 & 1.483 & 15 & 0.098 \\
7 & 0.0845 & 1.363 & 15 & 0.0908 \\
8 & 0.0571 & 1.203 & 15 & 0.0802 \\
9 & 0.0426 & 1.17 & 15 & 0.078 \\
10 & 0.0321 & 1.073 & 15 & 0.0715 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The slope and obscuration ratio at ASD 1 when chamber obscuration is 15%/m. Figure 7: (a) The slope and normalized length correlation; (b) The obscuration ratio and normalized length correlation; (c) The slope and obscuration ratio correlation. The fitting correlation between normalized length and slope in Figure 7a were derived as the following Equations (23)-(25) for 5%/m, 10%/m, and 15%/m chamber obscuration cases, respectively. \[S =0.1425e^{(-\overline{L}/0.4305)}+0.002 \tag{23}\] \[S =0.2515e^{(-\overline{L}/0.4505)}+0.001\] (24) \[S =0.36801e^{(-\overline{L}/0.54565)}-0.02676 \tag{25}\]  
where \(S\) is the slope, \(\overline{L}\) is normalized length. Similarly, the fitting correlation between normalized length and obscuration ratio in Figure 7b was derived as the following Equations (26)-(28) for chamber obscuration 5%/m, 10%/m, 15%/m. \[R =0.17608\mathrm{e}^{(-\overline{L}/0.59593)}+0.04178 \tag{26}\] \[R =0.145438\mathrm{e}^{(-\overline{L}/0.54049)}+0.05314\] (27) \[R =0.14623\mathrm{e}^{(-\overline{L}/0.58791)}-0.04487 \tag{28}\]  
where \(R\) is obscuration ratio, \(\overline{L}\) is normalized length. From Figure 7a,b, the correlation between slope and obscuration ratio were shown as Figure 7c, and correlation equations were derived as Equations (29)-(31):  
\[S=-0.2866^{(-R/0.10141)}+0.14885 \tag{29}\] \[S=-0.6143\mathrm{e}^{(-R/0.18062)}+0.42904\] (30) Figure 7:0  
From the Equations (23)-(25), the fire source location can be determined as the following equations:  
Figure 7:1  
Figure 7:2  
Figure 7:3  
Based on Equations (32)-(34), the fire source location can be determined with chamber obscuration of 5, 10, 15%/m, respectively.