Flow Depletion Induced by Pumping Well from Stream Perpendicularly Intersecting Impermeable/Recharge Boundary

Abstract

Analytical solutions for rate and volume of flow depletion induced by pumping a well from a stream that intersects an impermeable or a recharge boundary at right angles are derived using the basic flow depletion factor defined earlier by the author. A new concept of directly obtaining stream flow depletion using the method of images is proposed. The solutions are derived for five different management cases of a stream and boundary intersecting at right-angles, assuming the aquifer to be confined with semi-infinite areal extent. A computationally simple function is proposed for accurately approximating the error function. The existing analytical solution in the case of a right-angle bend of stream given by Hantush was obtained for unconfined aquifers using a linearization of the governing partial differential equation. The solution for this case obtained using the proposed method for confined aquifer is the same as obtained by Hantush for unconfined aquifers, which shows that the linearization adopted by Hantush does not actually solve this problem for unconfined aquifers.