Fire safety is one of the major design issues of tunnel engineers. Longitudinal ventilation is a common method for exhausting smoke and hot gases in tunnel fires. The minimum ventilation air velocity along the tunnel to prevent smoke back layering is called the critical velocity. This critical velocity is the key element in designing the longitudinal exhaust system. Several researchers have studied the impact of different parameters on critical velocity, including tunnel geometry, tunnel height, and fire magnitude, numerical and experimentally. In this study, an analytical solution was used to solve a third-order non-linear differential equation to determine the critical velocity of the tilted tunnel.

Dimensional analysis can significantly reduce the costs associated with the experimental study in the full-scale tunnels. The Froude number representing the power of the buoyancy force against the inertial force is widely used in the critical velocity studies. This study validated our analytical results with critical values obtained from an experimental and numerical simulation in a scaled model with a ratio of 1:8.

The results showed that the values calculated for the critical velocity employing an analytical solution were lower than the numerical and experimental studies' values.

Data from the latest international standard was used to enhance the precision of the critical velocity calculation. We showed that using a modified Froude number can significantly increase the accuracy of the analytical solution. The critical velocity values obtained using the modified Froude number were then compared with experimental results from full-scale tests.

This study emphasized that the analytical solution for the critical velocity saves a significant amount of time compared to the iterative solutions while keeping the accuracy in a reasonable range.

消防安全是隧道工程师的主要设计问题之一。纵向通风是在隧道火灾中排出烟雾和热气的常用方法。沿着隧道防止烟气分层的最小通风空气速度称为临界速度。这个临界速度是设计纵向排气系统的关键因素。几位研究人员研究了不同参数对临界速度的影响，包括隧道的几何形状，隧道的高度和火势，数值和实验结果。在这项研究中，使用解析解来求解三阶非线性微分方程，以确定倾斜隧道的临界速度。

尺寸分析可以显着降低与全尺寸隧道中的实验研究相关的成本。代表浮力相对于惯性力的力量的弗洛德数被广泛用于临界速度研究中。这项研究使用从比例为1：8的比例模型中的实验和数值模拟获得的临界值验证了我们的分析结果。

结果表明，使用分析溶液计算的临界速度值低于数值和实验研究的值。

最新国际标准的数据用于提高临界速度的计算精度。我们证明了使用修改后的Froude数可以显着提高分析解决方案的准确性。然后将使用修改后的弗洛德数获得的临界速度值与全尺寸试验的实验结果进行比较。

这项研究强调，与迭代解决方案相比，临界速度的解析解决方案可节省大量时间，同时将精度保持在合理范围内。