One of the greatest challenges of microfluid dynamics remains to describe the physical behavior in the transition region between the continuum and the free molecular regime. In this work, the non-dimensionalized relationship between mass flow and pressure drop in microchannels of different cross-sections is investigated. The flow resistance in microchannels is affected by increasing Knudsen numbers because the molecular wall collisions have an increasing influence. The reduced collision probabilities between the particles correspondingly reduce the influence of the effective viscosity of the fluid. In this work, approaches are investigated which have been able to predict the effective pressure difference specific permeation of a fluid as a function of the Knudsen number of an increasingly thinned gas flow. A further challenge is posed by the question of the origin of the local Knudsen minimum. This minimum of the non-dimensioned mass flow in the range Kn ≈ 1 is cancelled out in the range of free molecular flows by the increasing permeation. The model presented combines the effects of different scale ranges by superposition. The model data are compared with measured data and BGK simulation results in both the transient slip regime and the free molecular convection regime and show excellent agreement for both plane channel flows and pipe flows.