Application of Hankel transforms to boundary value problems of water flow due to a circular source

With the aid of Hankel transform technique, we obtain close-form solutions for discontinuous boundary-condition problems of water flow due to a circular source, which located on the upper surface of a confined aquifer. Owing to difficult evaluations of the original solutions that are in a form of an infinite range integral with a singular point and Bessel functions in integrands, we adopt two numerical algorisms to transform the original solutions as a series form for convenient practical applications. We apply the solutions in series form to numerical examples to analyze the characteristics of the flow in the confined aquifers subjected to pumping or recharge. By numerical examples, it indicates that: the drawdown will reduce with the increase of the layer thickness and the distance from the center of a circular source when pumping in a region with a finite thickness and a finite width; two algorisms for closed-form solutions of an infinite range integral have almost the same results, but the second algorism is superior for a faster convergence; in a semi-infinite confined aquifer, the drawdown due to a constant pumping rate Q and uplift due to recharge by a given hydraulic head s0 will both decrease with the increase of Kr/Kv; however, the radius r0 of the circular source has a reverse influence on the drawdown and the uplift, i.e., the drawdown decrease with the increase of r0, while the uplift increase with r0.