Generally, the hydrodynamic description of a fluid-flow problem requires knowledge of the momentum equation, the law expressing the conservation of mass (continuity equation), and a state relationship among density, stress, and temperature. Mathematically the flow problem therefore is defined by a more or less complicated system of partial differential equations whose solution requires specification of boundary conditions and, if the flow is unsteady, initial conditions describing the specific flow situation.
From a merely conceptual point of view, the flow of water within the soil should be analyzed on the microscopic scale by viewing the soil as a disperse system and applying the Navier-Stokes equations. Such a detailed description of flow pattern at every point in the domain is practically impossible because actual flow velocities vary greatly in both magnitude and direction due to the complexity of the paths followed by individual fluid particles when they move through the interconnected pores. On the other hand, in many applications, greater interest is attached to the knowledge of flux density. Therefore, flow and transport processes in soils typically are described on a macroscopic scale by defining a REV and an averaged set of quantities and balance equations.
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