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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
5. FULL, DYNAMIC EQUATIONS OF MOTION FOR ONE-DIMENSIONAL, UNSTEADY FLOW IN OPEN CHANNELS
The equations presented in section 5 include the major physical factors affecting shallow-water flows and are thus called full equations. Various forms of the equations are shown. All are mathematical restatements of the same physical principles, each having advantages and disadvantages as detailed in the subsections that follow. The integral form of the equations is basic to all forms, so it is presented first. The integral form is used as a basis for defining numerical approximations to shallow-water flows applied in the FEQ model and described in section 6, "Approximation of the Full Equations of Motion in a Branch."
Detailed derivations of the unsteady-flow equations are given in Cunge and others (1980, p. 7-24), Strelkoff (1969), and Yen (1973). Abbott and Basco (1989, p. 1-43) present a detailed mathematical and philosophical discussion of these equations. The major assumptions applied in the derivation of the full, dynamic equations of motion are listed in section 1.4.
- 5.1 Integral Form of the Equations
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- 5.2 Differential Form of the Equations
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- 5.3 Nature of Shallow-Water Waves
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- 5.4 Integral Form for Curvilinear Alignment
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- 5.5 Special Terms in the Equations of Motion
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- 5.6 Extended Motion Equation
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