# Experimental Study on Dynamic Exhaust Law for Ventilation System of Gas Tunnel
## 4 Results and Discussion
### Ventilation Duration  
When the initial gas concentration in the model is 15%VOL and the equivalent diameter of the vent is 0.2 m, the ventilation duration under different exhaust velocities is as shown in Table 5. It can be seen that the exhaust velocity has an obvious impact on the ventilation duration. When the exhaust velocity is 1 m/s, the ventilation duration is 852 s. When the exhaust velocity increases to 9 m/s, the ventilation duration is only 45 s.  
When the initial gas concentration in the model is 15%VOL and the exhaust velocity is 5 m/s, the ventilation duration under different equivalent diameters of the vent is as shown in Table 6. It can be seen that the ventilation size also has a notable impact on the ventilation duration. When the equivalent diameter of the vent is 0.1 m, the ventilation duration is 756 s. When the equivalent diameter of the vent increases to 0.3 m, the ventilation duration is only 33.6 s.  
When the exhaust velocity is 5 m/s and the equivalent diameter of the vent is 0.2 m, the ventilation duration under different initial gas concentrations in the model is as shown in Table 7. It can be seen that the initial gas concentration has some influence on the ventilation duration. However, compared with the exhaust velocity and ventilation size, the impact is relatively small. When the initial gas concentration in the model is 5%VOL, the ventilation duration is 73.8 s. When the initial gas concentration in the model increases to 25%VOL, the ventilation duration is 115.2 s.  
In order to further study the relationships between ventilation duration and exhaust velocity, equivalent diameter of the vent and initial gas concentration, the data in Tables 5-7 are drawn into curves and fitted with formulas, as shown in Figures 9-11. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Equivalent Diameter of the Vent (m)** & **0.1** & **0.15** & **0.2** & **0.25** & **0.3** \\ \hline Ventilation duration (s) & 756 & 265.8 & 100.2 & 54 & 33.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Relationship between ventilation duration and equivalent diameter of the vent. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Initial Gas Concentration (\%VOL)** & **5** & **10** & **15** & **20** & **25** \\ \hline Ventilation duration (s) & 73.8 & 88.8 & 100.2 & 108 & 115.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Relationship between ventilation duration and initial gas concentration. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Initial Gas Concentration (\%VOL)** & **Linear Relationship** & \multicolumn{2}{c}{**Exponential Relationship**} \\ \cline{2-5}
**Concentration** & **Linear Curve** & **Goodness of Fit \(R^{2}\)** & **Exponential Curve** & **Goodness of Fit \(R^{2}\)** \\ \hline
5 & \(\varphi=-0.0805t+4.9088\) & 0.9998 & \(\varphi=63.045e^{-0.085t}\) & 0.994 \\  & \((0<t\leq 47.8)\) & & \((47.8<t\leq 73.8)\) & & \\
10 & \(\varphi=-0.1595t+9.8054\) & 0.9995 & \(\varphi=56.506e^{-0.065t}\) & 0.9857 \\  & \((0<t\leq 42.2)\) & & \((42.2<t\leq 88.8)\) & & \\
15 & \(\varphi=-0.2366t+14.67\) & 0.9995 & \(\varphi=62.684e^{-0.065t}\) & 0.982 \\  & \((0<t\leq 39)\) & & \((39<t<100.2)\) & & \\
20 & \(\varphi=-0.3144+19.518\) & 0.9996 & \(\varphi=75.698e^{-0.055t}\) & 0.9765 \\  & \((0<t\leq 36.6)\) & & \((36.6<t\leq 108)\) & & \\
25 & \(\varphi=-0.3925t+24.636\) & 0.9997 & \(\varphi=86.856e^{-0.065t}\) & 0.972 \\  & \((0<t\leq 35)\) & & \((35<t\leq 115.2)\) & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Relationship between concentration and time under different initial gas concentrations. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Exhaust Velocity (m/s)** & **1** & **3** & **5** & **7** & **9** \\ \hline Ventilation duration (s) & 852 & 205.8 & 100.2 & 63.6 & 45 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Relationship between ventilation duration and exhaust velocity. Figure 11: Variation of ventilation duration with initial gas concentration. Figure 10: Variation of ventilation duration with equivalent vent diameter.