Navier-Stokes Equation and the Classical Permeability Theory

We assume that the fluid mixture is compressible (p / constant) and the intrinsic part of the solid is incompressible (p = constant). Then (5.18) reduces to 

By substituting (5.53) into (5.52), we obtain (5.54), which, when substituted into (5.62), gives the following seepage equations for a compressible fluid  

3 Navier-Stokes Equation and the Classical Permeability Theory 

The true velocity v of a fluid mixture flowing in a porous medium is a function not only of the porosity n but also of several other factors, including the particle size and surface conditions due to the viscous properties of the fluid. In this Section we assume that the problem has a simplified geometry in order to solve the problems of viscous flow and discuss the permeability characteristics. 

---