Drawdowns for Constant‐Discharge One‐Dimensional Leaky Aquifer

Abstract

A new mathematical solution was developed for the constant-discharge boundary condition for one-dimensional horizontal flow under nonsteady conditions in a semi-infinite leaky aquifer. The solution can be used to calculate aquifer drawdowns due to discharge into a line sink as a function of the aquifer parameters transmissivity, leakance, storage coefficient, and distance from the line sink and time since the discharge began. The solution is in the form of exponential and complementary error functions, and the polynomial approximation to the solution is easier to use, computationally, than an existing integral-form solution that requires numerical integration. In the solution, the discharge into the line sink is derived from artesian storage in the aquifer and from vertical leakage through the confining bed from a source bed that is at constant hydraulic head. As an example of its use, the solution could be used to analyze the results of a canal pumping test. In this application, aquifer parameters could be determined by analyzing transient drawdowns that resulted from abruptly lowering the canal water level by means of a constant pumping rate in a canal that incised a confined leaky aquifer.