Flow of Liquids through Porous Media under the Action of Gravity

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Abstract
Recent published results of studies on the flow of liquids through porous media under the action of gravity have shown wide disagreement in both the formulation and interpretation of the problem. A new attack on the problem has been carried out and has led to unambiguous answers to the questions of interest. Experiments on a radial sector of sand show that the old Dupuit formula of 1863 stating that the fluid outflow is proportional to the square of the differences in the fluid heights in the sand is exact within experimental error provided the fluid heights are replaced by fluid heads as measured at the sand bottom. Both the pressure distribution formula and the integrated expression for the fluid outflow are verified in detail. The cases where an added pressure head is superposed upon the gravity flow, heretofore not mentioned in the literature, behaves both with regard to its pressure distribution and fluid outflow as a direct superposition of the simple gravity flow and pure radial flow systems. A semi-quantitative treatment is given for the flow in the capillary zone above the main fluid body. It is necessary under certain experimental conditions to correct for the added flow carried by the capillary layer in addition to that induced by the gravity drive. In most practical cases the capillary flow may be ignored. A theoretical discussion is given of the conditions at the free surface of a gravity flow system and it is shown that nowhere on it can the slope exceed 45°. The results on the radial flow experiments are also generalized to give a method for treating general drives.

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