Simple, analytical approximations to the solution of the one-dimensional Boussinesq equation are obtained using a weighted residual method. The approach can be applied to both the recharging and the dewatering of an unconfined, homogeneous aquifer from a fully penetrating trench. Estimates for recharge, discharge, and the elevation of the water table are given by explicit algebraic expressions. Comparison with numerical solutions illustrates the accuracy of these new formulas.
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D. A. Lockington (1997) studied this question.
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