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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

4.1 The One-Dimensional Assumption


Because 1-D analysis ignores accelerations and velocities other than those in the longitudinal direction, 1-D analysis in even its most complex form in unsteady flow is approximate: no flow is really one dimensional. Nevertheless, analysts frequently lose sight of the approximate nature of 1-D methods, and focus too much analytical energy on what may prove to be trivial parts of the method. There are no easy answers in defining triviality. The only ultimate answer is comparison to experimental measurements and for some questions that may be difficult and expensive. In this report, judgment is used in defining what is important and in making general recommendations on approximations. The FEQ user should weigh these recommendations on the basis of new information either from the literature of hydraulics or measurements in the field or laboratory. Engineering judgment is a necessary part of all analysis because problems must be solved with the information at hand and with current tools.

Whitaker (1968, p. 212) makes a comment about this issue in a chapter on macroscopic balances (his term for 1-D analysis):

The student should be forewarned that the methods to be studied in this chapter, and subsequent ones, are approximate; in general, there will be no "right" answers. There will often, however, be a "best" answer, and as often as possible we shall try to determine the best answer by comparing our results with experiments. In attacking this chapter, we should remember the macroscopic balances are perhaps the most powerful tool the engineer possesses for solving the often ill-defined problems of everyday practice. Judicious application of these equations comes only with experience and practice. At best, the student can hope to understand the development of the equations and gain some insight regarding the difficulties that may be encountered in their application.

In the methods used in FEQ and in applications of FEQ, 1-D analysis is pushed to its limits; therefore, simplifications involved in 1-D analysis need to be thoroughly understood. Consideration also must be given to the requirements on the hydraulic geometry to meet the assumptions of 1-D analysis and to development of a description of a stream channel that is consistent with these assumptions. An appreciation for the approximations of the hydraulic geometry is necessary to prevent overconfidence in the results of the FEQ analysis.


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