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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
1.1 Purpose and Scope
The purpose of this report is to document the stream-network visualization
and schematization, flow-governing equations, and solution procedures used
in the FEQ model to simulate 1-D unsteady flow in a network of open channels
and control structures. The FEQ model and example inputs and outputs may
be obtained by electronic retrieval from the World Wide Web (WWW) at
http://water.usgs.gov/software/feq.html and by anonymous File Transfer
Protocol (FTP) from
water.usgs.gov in the pub/software/surface_water/feq/ directory. Because
flow in a network of open channels and control structures is complex, the
documentation of FEQ involves detailed discussions of many hydraulic-engineering
and numerical-analysis topics. These topics are discussed in the following
order. The basic principles of 1-D unsteady-flow modeling and the relation
between steady flow and unsteady flow are discussed to give readers who
are familiar with steady-flow analysis points of reference for understanding
unsteady-flow analysis. The schematization of the stream system and the
conversion of the physical characteristics of the stream reaches, including
the effects of curvilinearity, into function tables for model applications
are described. The modified dynamic-wave equation used in FEQ is developed
for unsteady flow in curvilinear channels with drag forces on minor hydraulic
structures and channel constrictions determined from an equivalent energy
slope. The equations approximating flow through various hydraulic-control
structures are presented, and conversions of the stage-discharge relations
for these structures into function tables are given. The matrix equation
relating flows and depths at computational nodes throughout the river system
by the continuity (conservation of mass) and modified dynamic-wave equations
is illustrated for four sequential examples. The solution of the matrix
equation by Newton's method is discussed. Finally, the input for FEQ and
the error messages and warnings issued in model simulation are listed.
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