Abstarct: With the growth of the population in urban areas, the need to use public transportation becomes necessary, so the need to investigate the behavior of pedestrians is more expanded. In this study, the best speed-density model available for the flow of pedestrians in the subway, that has the lowest error rate and the highest accuracy with the fundamental equation q=kv is investigated. In this research, the density obtained from the two-parameter equation and the density from the fundamental equation were compared. it was observed that among the two-parameter relationships, the Underwood relationship has a better exxpression of the pedestrian flow behavior and is closer to the experimental data. In the next part of the research, in the fundamental relationship, the adaptation of speed to density is instantaneous, it means, in the equation v=q⁄k, as soon as the density changes, the speed changes instantly and zero time is considered for changing the speed of people. The discretion factor in the behavior of traffic is another reason for the lack of compatibility of experimental data with the data obtained from the fundamental relationship. In order to consider the effect of these parameters, we calculate the experimental density and compared it with the density obtained from the fundamental relation of the pedestrian flow. The results of this investigation show that in free flow and congested flow, the fundamental relationship does not provide an accurate descxription of the flow and requires a time lag between density and velocity parameters so we use the similarity between the pedestrian flow and the fluid flow, using the Fluids equations and the dimensional analysis, we modify the fundamental equation q=kv with the Reynolds number. By examining the statistical errors, it is clear that by considering the viscosity parameter and the reaction time of people, which are present in the definition of the Reynolds number, the density obtained from the fundamental equation is modified and becomes closer to the empirical density. baxsed on the MSE, it was observed that the amount of error in the relationship decreases from 0.366 to 0.058 after correction factor.