The partial differential equations are deduced for unsteady radial flow to a well that is tapping an unconfined aquifer of infinite extent and discharging at a constant rate. Complete penetration of the aquifer by the well is assumed. Consideration is given to the average head, which is the observational head in a well that is screened throughout the unconfined aquifer, as well as to the head that corresponds to the free surface value. A relationship between the average head and the free surface head is assumed to be in the form of a vertical transfer linear equation.
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Tatiana D. Streltsova (1972) studied this question.
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