Solution for the upconing of an interface towards a drain

One of the problems encountered in groundwater flow involves an interface between two immiscible fluids. In this paper, the upconing of an interface between flowing fresh ground water and stationary salt water towards a drain will be discussed and solved. The interface flow problem is best solved by mapping the interface on to a hodograph plane so that the unkwon curves of the interface in the physical plane are mapped on to known curves in the hodograph plane. This enables the application of conformal transformation or mapping techniques. The relationship of the discharge to the depth of the drain will finally be obtained, along with the equation of the interface. From these relationships, the location of the drain and its limiting discharge, that is the maximum discharge that could be pumped before the salt water starts to intrude into the system, could be computed.

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