# Energy-Saving Network Ventilation Technology of Extra-Long Tunnel in Climate Separation Zone
## 2 Materials and Methods
### Calculation Methods of the Natural Wind Velocity in the Tunnel
#### 2.1.2 Calculation Methods of the Natural Wind Velocity in the Tunnel with Inclined Shafts
Calculation Method of Thermal-Potential Pressure Difference in the Tunnels with Shafts  
Suppose that the air temperature in the tunnel is \(T_{3}\), the temperature at the tunnel entrance, exit and (inclined) shaft exit are \(T_{1}\), \(T_{2}\) and \(T_{4}\), respectively. The corresponding air densities are \(\rho_{3}\), \(\rho_{1}\), \(\rho_{2}\) and \(\rho_{4}\). The elevation of the tunnel entrance, the exit, the shaft bottom and the shaft exit are \(H_{1}\), \(H_{2}\), \(H_{3}\) and \(H_{4}\), as shown in Figure 3.  
Assume that the average air density out of the tunnel is \(\rho_{avg}\), Equations (11) and (12) would find thermal-potential pressure difference:  
\[\Delta P_{t1}=\rho_{avg1}\cdot g\cdot H_{1-4}-\rho_{i}\cdot g\cdot H_{1-3}-\rho _{i}\cdot g\cdot H_{3-4} \tag{12}\]  
\[\Delta P_{t2}=\rho_{avg2}\cdot g\cdot H_{2-4}-\rho_{i}\cdot g\cdot H_{2-3}-\rho _{i}\cdot g\cdot H_{3-4} \tag{13}\]  
In the static atmosphere, the difference of barometric pressures between point \(m\) and point \(n\) is the static pressure difference. If the air density in the tunnel is equal to the air density out of the tunnel, the ultra-static pressure of point m relative to point n is zero, the air inside will not circulate. On the contrary, if air flows in the tunnel, the driving force of air in the tunnel is the thermo-potential difference only, whose effect is equal to ultra-static pressure. As a result, the thermo-potential pressure difference can be treated as the ultra-static pressure difference. The equivalence results are shown in \[\Delta P_{u1}\text{'}-\Delta P_{u4}\text{'}=(R_{1}+R_{1}\text{'})\cdot Q_{1} \cdot|Q_{1}| \tag{7}\]0  
According to the ultra-static pressure difference calculation method, we can obtain the air quantity (\(Q_{i}\)) of each section under the influence of thermo-potential pressure difference. The principle is the same for tunnels with many shafts, but multiple circulations are required, the circulation frequency is equal to the number of shafts. Generally speaking, an extra-long highway tunnel will be equipped with several shafts or inclined shafts. Therefore, the calculation method of the ultra-static pressure difference, the thermal-potential pressure difference and the ventilation-wall pressure difference of each tunnel section are obtained. Insert the wind pressure value calculated into Equation (6), and we can get the natural wind velocity of each section in the segmented longitudinal ventilation tunnel. .1.3 Additional Explanation about the Calculation Methods of the Natural Wind Velocity in the Tunnel  
What needs to be made clear is that the pressure induced by vehicles \(P_{t}\), the pressure induced by ventilation equipment \(P_{v}\) and the pressure loss due to wind resistance \(\Delta P\) (including local pressure loss \(\Delta P_{ei}\) and frictional pressure loss \(\Delta P_{r}\)) are all important pressure drivers in operating tunnels. The calculation methods of the three pressure drivers were introduced in many references such as _Chinese specification for design of ventilation and lighting of highway tunnel_[4]. The values of loss coefficients  
\[\Delta P_{u1}\text{'}-\Delta P_{u4}\text{'}=(R_{1}+R_{1}\text{'})\cdot Q_{1} \cdot|Q_{1}| \tag{7}\]1 Calculation method of thermal-potential pressure difference with shafts. \(\lambda_{r}\) and \(\xi_{e}\) were also set as the specification required. However, when calculating the natural wind velocity, the pressure resulted from cars and ventilation equipment is not within the research scope. The air temperature inside a road tunnel will be affected by the geothermal heat from the tunnel wall and the exhaust gas from the road vehicles. After the endothermic process of expansion, the air density declines and the airflow increases accordingly. As a result, the natural wind velocity in the tunnel will increase to a certain degree which improves natural ventilation. When considering the slope in a tunnel without (inclined) shaft, the heated air will tend to flow to the upper portal of the tunnel.