FLOW TO A WELL IN A WATER-TABLE AQUIFER - AN IMPROVED LAPLACE TRANSFORM SOLUTION

An alternative Laplace transform solution for the problem, originally solved by Neuman, of constant discharge from a partially penetrating w ell in a water-table aquifer was obtained. The solution differs from e xisting solutions in that it is simpler in form and can be numerically inverted without the need for time-consuming numerical integration. T he derivation involves the use of the Laplace transform and a finite F ourier cosine series and avoids the Hankel transform used in prior der ivations. The solution allows for water in the overlying unsaturated z one eo be released either instantaneously in response to a declining w ater table as assumed by Neuman, or gradually as approximated by Boult on's convolution integral. Numerical evaluation yields results identic al with results obtained by previously published methods with the adva ntage, under most well-aquifer configurations, Of much reduced computa tion time.