We used a mathematical model describing traveling-wave electroosmotic micropumps to explain their rather poor ability to work against pressure loads. The mathematical model is based upon the Poisson-Nernst-Planck-Navier-Stokes approach, that is, a direct numerical simulation, which allows a detail study of the energy transformations and the charging dynamics of the electric double layers. Using Matlab and COMSOL Multiphysics, we performed a set of extensive parametric studies to determine the dependence of generated electroosmotic flow on the geometric arrangement of the pump. The results suggest that the performance of AC electroosmotic pumps should improve with miniaturization. The AC electroosmosis is likely to be suitable only at submicrometer scale, as the pump's ability to work against pressure load diminishes rapidly when increasing the channel diameter.