Recent work on carbon nanotubes (CNT) has focused on their potential application in water treatment as a result of their predicted and observed enhanced flow rates. Recent work on the lesser-known porous anodic alumina membranes (PAAMs) has also shown flow enhancement, albeit at only a fraction of what has been observed in CNTs. Despite their potential applications, little research has been conducted on PAAMs' hydrodynamic properties, and in this Article we present experimental results and theoretical models that explore the fluid flow behavior around and through these membranes. The experiments were conducted using an atomic force microscope (AFM) that pushed a solid silica particle against PAAMs that were characterized with different pore diameters. Furthermore, the PAAMs were classified as either closed or open, with the latter allowing fluid to pass through. The theoretical model developed to describe the experimental data incorporates Derjaguin-Landau-Verwey-Overbeek (DLVO) effects, cantilever drag, and hydrodynamic forces. By using the slip boundary condition for the hydrodynamic forces, we were able to fit the model to experimental findings and also demonstrate that the difference between closed and open PAAMs was negligible. The slip lengths did not correspond to any physical feature of the PAAMs, but our model does provide a simple yet effective means of describing the hydrodynamics for not only PAAMs but for membranes in general.