A new method of calculation of non-uniform groundwater movement at a sloping water table

Abstract

There are different methods of hydraulic calculation of groundwater flow in a homogeneous medium with a flat sloping water table. These methods are characterized by different degree of approximation. Thus, the formulas of G. N. Kamensky do not have a strict theoretical justification. The method of Acad. N. N. Pavlovsky's method is also approximate to a certain extent, since according to this method of calculation the surfaces of equal heads in the conditions of a flat problem are considered as vertical planes. The method of N.N. Pavlovsky can be considered as the most accurate at present, because it is based on a strict mathematical conclusion and its main provisions are very close to the true picture of motion when the slope of the water table and the slope of the depression surface are small. The new method proposed in this paper is also an approximation, but it is based on a fairly rigorous mathematical derivation. Determination of flow rate and construction of depression curve by this method is simpler and more convenient than by the method of N. N. Pavlovsky.