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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*

A classification scheme for steady and unsteady flow is useful in describing the flows of interest. The simplest steady flow is uniform flow, in which no flow variable changes with distance. In a uniform steady flow, every flow variable is a constant with respect to distance and time. If the flow is not uniform, then it is classified as nonuniform and can be further divided into gradually varied and rapidly varied flow. In gradually varied steady flow, the flow variables may change with distance, but all variables are constant in time. Furthermore, the variations with distance are gradual, so vertical accelerations are small. The series of backwater profiles discussed in the typical openchannel hydraulics course or textbook (for example, Chow, 1959, p. 227-237) are all gradually varied flows. In rapidly varied flow, substantial variations are present in vertical and/or transverse flow. An extreme example is a hydraulic jump below a dam. This flow can still be analyzed as 1-D flow, but the rapidly varied zone of the flow must be recognized and isolated in the analysis. Additional examples of rapidly varied flow are flows through culverts and bridges and over weirs and spillways.

Unsteady uniform flow is impossible, so only nonuniform unsteady flow is of interest in hydraulic analysis. Both gradually varied and rapidly varied unsteady flows are possible, and the same general rules for analysis apply as for steady flow. The zones of rapidly varied flow must be isolated before analysis under the 1-D flow assumption; thus, the method of analysis for steady and unsteady flow is the same in this respect.

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