Approximate discharge for constant head test with recharging boundary

The calculation of the discharge to a constant drawdown well or tunnel in the presence of an infinite linear constant head boundary in an ideal confined aquifer usually relies on the numerical inversion of a Laplace transform solution. Such a solution is used to interpret constant head tests in wells or to roughly estimate ground water inflow into tunnels. In this paper, a simple approximate solution is proposed. Its maximum relative error is on the order of 2% as compared to the exact analytical solution. The approximation is a weighted mean between the early-time and late-time asymptotes