Validity of Dupuit-Forchheimer Equation

The Dupuit-Forchheimer equation describing unconfined ground-water flow is limited by the underlying assumptions inherent in its derivation. A validity criterion is developed from an analysis of the exact equations of motion which shows that, in general, the Dupuit-Forchheimer equation describes a rising water table more accurately than a falling one. In the steady state the criterion reduces to a simple restriction on the free surface slope. For unsteady problems the criterion involves both the free surface slope and the rate of change of the free surface position. For the specific case of flow toward a well it is shown that the commonly used rule of thumb, r/h_o > 1.5, may not always be valid and a more general criterion is presented.