The governing equations derived are in general applicable to all kinds of porous media
including soil, rock and concrete. A summary of the essential equations is given as follows.
We assume that the co-ordinate system moves with the solid phase and hence convective acceleration applies only to the fluid. For a unit volume of the porous media, the overall equilibrium is indicated in the first equation.
In the case of water passing through soil, the validity of Darcy law is assumed. For a unit volume of water, the Darcy law in its generalised form can written as the second equation.
The third equation is a general equation for the continuity of water flow through a partially saturated porous medium.