A variety of numerical simulations based on continuum medium models have been carried out in unsteady flows to explore the physical characteristics qualitatively. However, there still lack quantitative valid scales for these models, in which scale the solutions by simulation can be treated as physically credible. In this work, Euler and Navier-Stokes models are implemented on the typical unsteady flow with discontinuities: Sod shock tube problem. Firstly, based on the Boltzmann model whose valid scale is molecule kinetic scale, we compare the values of different moments of Euler and Navier-Stokes to Boltzmann with the evolution of flow. The results provide the valid scales of Euler and Navier-Stokes models quantitatively. Secondly, following the real conditions and parameters in real air, the physical characteristics of waves’ generation and evolution in Sod shock tube are observed and analyzed numerically at the microscopic level for the first time. Our results present the reference scales for the choice of minimal simulation scale in which the continuum medium models are used, and for the criteria whether the flow characteristics obtained by simulations can be treated as real physical characteristics.