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Full Equations (FEQ) Model for the Solution of the Full, Dynamic Equations of Motion for One-Dimensional Unsteady Flow in Open Channels and Through Control Structures

U.S. GEOLOGICAL SURVEY WATER-RESOURCES INVESTIGATIONS REPORT 96-4240

1.5 Examples of Unsteady-Flow Analysis


Examples of unsteady-flow analysis are easily found, only a few are mentioned here.

  1. Passage of a Flood Wave. Flood-wave movement is unsteady, but in flood-insurance studies an approximate maximum-elevation envelope resulting from a flood wave is computed under the assumption of steady flow. Little work has been done to evaluate the accuracy of this approximation. In addition, the effect of flood-plain filling and obstruction is often analyzed by means of steady-flow analysis. Changes in the ability of the stream to convey water are evaluated in steady-flow analysis, whereas changes in the capability of the stream to store water are not considered in steady-flow analysis. The changes resulting from storage may be large in some cases. Therefore, application of unsteady-flow analysis may substantially improve flood-insurance studies.

  2. Operation of Irrigation and Power Canals. Unsteady-flow analysis is required to design these canals properly because the flow variations can often be abrupt. Allowance must be made for the wave heights that might result. Furthermore, the traveltime of transients becomes important in the design and operation of structures intended to reduce or control transients.

  3. Tidal Effects. Analysis of the effects of tides on streams requires consideration of unsteady flow. Steady-flow analysis is often used to approximate the envelope of maximum elevations; but again, little work has been done to evaluate the accuracy of this approximation.

  4. Junctions. The complex interactions at stream junctions often require unsteady-flow analysis. For example, a large flood or failure of a dam on a tributary to a second, larger stream can sometimes result in upstream flow at the junction in the receiving stream. This, in turn, can lead to a very rapid rise in water-surface elevation because the influx of water serves not only as a temporary dam but also as another source of inflow.

  5. Measures to Control Floods. Evaluation of the effects of proposed measures to control floods in a stream must involve unsteady-flow analysis. Simplified methods often fail to give adequate solutions where stream-bottom slopes are flat enough to make flow reversals possible or where flow is strongly affected by water-surface elevations downstream.


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