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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
1.2 Classification of One-Dimensional Steady Flow and Unsteady Flow
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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