For the transport in an inert pore the local species momentum balance is reconsidered. This leads to a Maxwell-Stefan type equation for a component rr in which the gradient in chemical potential, the interspecies friction and the cr-cr shear stress form the momentum balance. From the set of equations the component axial velocity profiles can be derived, and so we call this model the velocity profile model (VPM-1), in which I stands for the fact that we only consider here the flow in one direction. For binary systems the set of equations is solved, and pore-integrated velocities are derived. This is done both for liquids with a no-slip boundary condition and for gases with Maxwell-slip boundary condition. The pore-averaged velocities can be expressed in the same form as the binary friction model. The use of the difference in pore-averaged velocities instead of the pore-averaged differences requires a correction function, which is derived for both fluid types. For liquids the component-wall friction factors are equal to those in the binary friction model, for gases a slightly different form is obtained. Comparison of predictions for liquid ultrafiltration and gas transport through porous plugs shows in general very small differences between the present model and the BFM, and good agreement with experimental data. The VPM-1 predicts a second flow reversal point of (near-)equal mass isobaric diffusion of gases at different pressures, and a reversal with temperature, From the model follows a new expression for the velocity difference. Velocity profiles for various situations are explored such as liquid ultrafiltration and diffusion, counterdiffusion of gases and for the Stefan-tube. In the latter we find that for a zero average flux of inert gas there is a core of inert gas moving in the direction of the water vapor, and a reverse flow in the area near the wall. The model can be extended to more-dimensional flow problems such as in adsorption and heterogeneous catalysis.