From the earliest days of hydraulic engineering, various formulas have been used to relate the velocity. of flow with the dimensions and slope of a channel, those at present in most general use probably being the formulas of Kutter and Manning. In this article the physical basis is discussed and the application of slope formulas to rigid channels with clear flow, rigid channels with sediment transport, and erodible channels with sediment transport, is reviewed. It is shown that finality has not been reached in any of these three cases, particularly the last mentioned and that much research is still needed.
