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.
