Three‐Dimensional Streamlines in Dupuit‐Forchheimer Models

An approximate method is presented for determining streamlines in three dimensions using two‐dimensional Dupuit‐Forchheimer models. The latter models of horizontal flow, which may comprise several aquifers, are based on the assumption that the resistance to flow in the vertical direction is neglected. This assumption does not preclude the occurrence of flow in the vertical direction; vertical components of flow are determined in an approximate fashion by requiring continuity of flow. The problem of leakage from a shallow pond above an unconfined aquifer is discussed as an example of determining streamlines in three dimensions. The errors induced by the approximation are determined for a few idealized flow problems that can be solved exactly.