| Summary: | An analysis of the cause-effect relationship of a free water table aquifer that changes laterally to an artesian aquifer was made for regions bounded internally by a circular cylinder. For a hydrologic system with a large pressure-head energy, development of the water resource by a single well is not the most practical approach and thus the study was extended to solve the problem of a line array of wells. The flow characteristic of the hydrologic system was divided into a regime of flow near the line array of wells which is titled the conduit regime, and a regime of flow distant from the line array, which is called the reservoir regime. This classification of flow type is based on the fact that the storage coefficient is not constant and accordingly the hydraulic diffusivity of the aquifer in the conduit region is much smaller than that in the reservoir region. Therefore, the mathematical continuity, which was assumed in previous analyses by other authors becomes discontinuous because linearity does not prevail throughout the flow system. The superposition principle, which is based on linearity and homogeneity, can not be applied to this non-linear system.
By subdividing the flow system into the two regimes of conduit and reservoir, Carslaw's solution for the circular cylinder may be amplified by two integrations to achieve mathematical continuity of the whole system. The range that Goldenberg solved analytically for a similar problem was extended to meet practical requirements in the field of ground-water hydrology. A new approach was developed for the solution of the mutual interference problem of an infinite line array of wells. The interference is expressed in terms of what is called the discharge efficiency factor. The findings were applied to a hydrologic analysis of the ground-water resources of the Western Desert, U. A. R. (Egypt) in or der to describe its significance and importance in the design of systems for water resources development in extensive aquifers. The results aid also in defining the applicability limits of the theory of images, which has been used by several authors to solve for the interference problem of an infinite line array of wells.
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