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Title:Spatially varied open-channel flow equations
Author(s):Yen, Ben Chie
Contributor(s):University of Illinois at Urbana-Champaign
Subject(s):Water resources center
Water resources center--Illinois
Hydrology and hydraulics
Energy equation
Flow resistance
Fluid mechanics
Homogeneous fluid
Momentum equation
Nonhomogeneous fluid
Nonuniform flow
Open-channel flow
Spatially varied flow
Unsteady flow
Water flow
Geographic Coverage:Illinois (state)
Abstract:Recent development and improvement in numerical techniques and computer capability enables more accurate numerical solutions of spatially varied flow problems such as various phases of urban storm runoffs. Consequently, it is desirable to re-examine fundamentally the compatibility of the flow equations used in solving unsteady spatially varied flow problems. To achieve this goal, the continuity, momentum, and energy equations for unsteady nonuniform flow of an incompressible viscous nonhomogeneous fluid with lateral flow into or leaving a channel of arbitrary geometry in cross section and alignment are formulated in integral form for a cross section by using the Leibnitz rule. The resulted equations are then transformed into one-dimensional form by introducing the necessary correction factors and these equations can be regarded as the unified open-channel flow equations for incompressib1.e fluids. The flow represented by these equations can be turbulent or laminar, rotational or irrotational, steady or unsteady, uniform or nonuniform, gradually or rapidly varied, subcritical or supercritical, with or without spatially and temporally variable lateral discharge. Flow equations for certain special cases are deduced from the derived general equations for the convenience of possible practical uses. Conventionally used various equations for open-channel flows are shown to be simplifications and approximations of special cases of the general equations. The inherent difference between the flow equations derived based on the energy and momentum concepts is discussed. Particular emphasis is given to the differences among the energy dissipation coefficient, the frictional resistance coefficient, and the total-head loss coefficient. Common hydraulic practice of using the Chezy, Manning, or Weisbach formulas to evaluate the dissipated energy gradient or the friction slope is only an approximation.
Issue Date:1971-12
Publisher:University of Illinois at Urbana-Champaign. Water Resources Center
Genre:Report (Grant or Annual)
Sponsor:U.S. Department of the Interior
U.S. Geological Survey
Rights Information:Copyright 1972 held by Ben Chie Yen
Date Available in IDEALS:2016-05-23

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