Fluid flow and charge transport in fine structures can be driven both by pressure gradients and by electric fields if electrochemical double layers are present on the surfaces. The interrelated electrohydrodynamic effects may be used to drive liquids without moving parts, for example, in dewatering or in electroosmotic chromatography, or to generate small electric currents. While the electrohydrodynamic transport is well understood for simple geometries, models for porous structures are complex. Furthermore, the interconnected porous structure of a packed bed itself strongly depends on the electrochemical double layers. In this study, the electrohydrodynamic transport in packed beds consisting of boehmite particles with an average diameter of 38 nm is investigated. We describe a new approach to the electrokinetic effects by treating the packed beds as theoretical sets of cylindrical capillaries. The charge transport and the electrically driven fluid flow predicted with this model agree well with experimental results. Furthermore, the hydraulic permeability was found to be a nonlinear function of the porosity, independent of whether the porosity change is caused by changing the compression or the electrochemical double layer.