End Depth under Zero-Inertia Conditions

by Theodor Strelkoff, (M.ASCE), Prof. of Water Sci. and Civ. Engrg.; Univ. of California, Davis, Calif.,
Nikolaos D. Katopodes, (A.M.ASCE), Asst. Development Engr.; Dept. of Land, Air and Water Resources, Univ. of California, Davis, Calif.,

Serial Information: Journal of the Hydraulics Division, 1977, Vol. 103, Issue 7, Pg. 699-711

Document Type: Journal Paper


The terminal depth and velocity conditions for flow in an open channel ending in a free overfall are investigated under the assumption that inertial effects are everywhere negligible. When inertial terms are retained, as in the Saint-Venant or varied-flow equations, these terminal conditions are both at critical. When not only the inertial terms but the depth-gradient term too is dropped, depth and velocity at the brink of the overfall are at normal. Under the zero-inertia assumption, end depth is found to be zero and the velocity correspondingly infinite. This notion is tested in a series of steady-flow comparisons with results obtained from the varied-flow equation. The results of the zero-inertia assumption lie close to those of the varied-flow equation, when the flow conditions are characterized by low Froude numbers. In application to the problem of discharge from a lake into a channel ending in an overfall, the traditional trial-and-error solution is replaced by a new direct solution read off from a graph.

Subject Headings: Inertia | Settling velocity | Open channel flow | Wave velocity | Open channels | Steady flow | Comparative studies | Froude number

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