Pattern of Potential Flow in a Free Overfall

A theory is presented to describe the two-dimensional flow of liquid in an open channel which terminates abruptly at a sharp drop. A dimensionless diagram expressing constancy of total head on the upper free surface and similar to the conventional specific-head versus depth and discharge versus depth diagrams is used to trace the course of the flow in the overfall. Together with the fact that the ratio of free-surface-velocity magnitude to average horizontal component of velocity in the cross-section is a decreasing function of distance in the direction of flow, an observation drawn from a subsequent, detailed examination of the flow, the diagram is used to show that the limiting case of the free overfall is at a Froude number of approach of unity. A detailed description of the flow is given by an integral equation derived from conformal mapping and singularity distributions. Comparisons are made between the computed profiles and theoretical and experimental results of other investigators.