Flow through Soils and Rocks

Before any mathematical treatment of groundwater flow can be attempted, certain simplifying assumptions have to be made, namely, that the material is isotropic and homogeneous, that there is no capillary action and that a steady state of flow exists. Since rocks and soils are anisotropic and heterogeneous, as they may be subject to capillary action and flow through them is characteristically unsteady, any mathematical assessment of flow must be treated with cautton. 

The basic law concerned with flow is that enunciated by Darcy (1856), which states that the rate of flow, v, per unit area is proportional to the gradient of the potential head, /, measured in the direction of flow, k being the coefficient of permeability  

Darcy s law is valid as long as a laminar flow exists. Departures from Darcy s law therefore occur when the flow is turbulent, such as when the velocity of flow is high. Such conditions exist in very permeable media. Accordingly, it usually is accepted that this law can be applied to those soils that have finer textures than gravels. Furthermore, Darcy s law probably does not accurately represent the flow of water through a porous medium of extremely low permeability because of the influence of surface and ionic phenomena, and the presence of any gases. 

Apart from an increase in the mean velocity, the other factors that cause deviations from the linear laws of flow include the non-uniformity of pore spaces, since differing porosity gives rise to differences in the seepage rates through pore channels. A second factor is the absence of a running-ln section where the velocity profile can establish a steady state parabolic distribution. Lastly, such deviations may be developed by perturbations due to jet separation from wall irregularities. 

Darcy failed to recognize that permeability also depends on the density, p, and dynamic viscosity of the fluid involved, p, and the average size, D , and shape of the pores in a porous medium. In fact, permeability is directly proportional to the unit weight of the fluid concerned and is inversely proportional to its viscosity. The latter is influenced very much by temperature. The following expression attempts to take these factors into account  

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