Steady periodic flow through a rectangular dam

For unsteady free surface flow in a rectangular dam a simple integral relation which connects the pressure integral with the movement of the free surface is derived. In the case of steady periodic movement driven by oscillating reservoir levels the time average of the pressure integral can be found, which leads to an average discharge formula which is a generalization of the Dupuit‐Forchheimer discharge formula. For periodic fluctuations of groundwater in a coastal aquifer in response to tidal oscillations a corollary is that the equilibrium water level far from the sea is equal to the root mean square of the sea level, independent of the validity of the Dupuit‐Forchheimer assumptions.