Plane potential flow of ground water with linear leakage

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Abstract
Potential distributions are found for steady wells idealized as sinks, and tapping uniform confined aquifers into which there is leakage in proportion to the drawdown. Several plane regions are treated, along whose boundaries the potential, flux, or both are specified. The ratio of the conductivity of the aquifer to that of the confining bed is assumed very large so that the refraction of flow lines may be assumed complete as they cross the contact. The leakage, thus considered vertical through the confining bed, is assumedly distributed throughout the thickness of the aquifer as it thus aguments or diminishes the horizontal flow, which is then treated as two dimensional.Starting with the fundamental solution for an infinite plane region, the solutions for other plane regions are built up by the method of images. The Green's functions for leaky systems are thus obtained for infinite half‐planes (two cases), infinite quadrants (three cases), infinite strips (three cases), infinite half‐strips (six cases). and rectangles (six cases). Several graphs are given showing potential distributions in special cases and showing the magnitude of drawdown at the well face for various values of the parameters.The result obtained in Part I of this paper for the infinite plane is extended by the method of images to find solutions for infinite strips, infinite half‐strips and for rectangles, in Part II. These solutions are put in forms of series which are convenient for computations. These series are uniformly convergent for all values of x and y except when both are simultaneously taken at the center of the well in which case the series diverges logarithmically to negative infinity. Each of these solutions satisfies the properties of one of the three different types of Green's functions—the first, the second, or the mixed type, but instead of being a harmonic function it satisfies the equation of motion of ground water with linear leakage. Accordingly these solutions may be considered as the Green's functions for systems with linear leakage.

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