  For a fissured medium, we analyze the impact that the geometry of the cracks,
has in the phenomenon of preferential fluid flow. Using finite volume meshes we
analyze the mechanical energy dissipation due to gravity, curvature of the
surface and friction against its walls. We construct parameters depending on
the \emph{Geometry} of the surface which are not valid for direct quantitative
purposes, but are reliable for relative comparison of mechanical energy
dissipation. Such analysis yields \emph{Information} about the preferential
flow directions of the medium which, in most of the cases is not deterministic,
therefore the respective \emph{Probability Spaces} are introduced. Finally, we
present the concept of \emph{Entropy} linked to the geometry of the surface.
This notion follows naturally from the random nature of the \emph{Preferential
Flow Information.
