On the account of inertial forces on unsteady fluid filtration in nonuniform anisotropic porous media

On the base of continual description of effective inertial properties of heterogeneous media formed by fluid and fluidixed in it non deformable inclusions, from Lagrange equations for a fluid element unsteady filtration equations of ideal fluid in porous medium are obtaiined. It is shown that the porous medium structure in this case is described by two characterisitcs - porosity and tensor of coefficients of attached masses of inclusions or skeleton of porous material. Considered is the flow in anisotropic porous media the macroscopic non uniformity of which may be caused by non uniformity of scalar porosity field as well as by non uniformity of tensor field of coefficients of attached masses. Considered are two types of porous media having different topologic structure; it is shown that the flow in them is described by the same filtration equations which are analogous to Eiles equations for continuous medium but with effective density expressed by the second rank tensor. For macroscopically non uniform porous media motion equations comprise additional terms having a substantial significance for problems of unsteady filtration in deformable porous media. The evaluations of effective density for flows in rod assemblies and granular media with spherical particles are given