Spatially varied open-channel flow equations

Yen, Ben Chie

Permalink

https://hdl.handle.net/2142/90155 Copy

Description

Title

Spatially varied open-channel flow equations

Author(s)

Yen, Ben Chie

Contributor(s)

University of Illinois at Urbana-Champaign

Issue Date

1971-12

Keyword(s)

• Water resources center
• Water resources center--Illinois
• Hydrology and hydraulics
• Energy equation
• Flow resistance
• Fluid mechanics
• Homogeneous fluid
• Hydraulics
• 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.

Publisher

University of Illinois at Urbana-Champaign. Water Resources Center

Type of Resource

text

Language

en

Permalink

http://hdl.handle.net/2142/90155

Sponsor(s)/Grant Number(s)

• U.S. Department of the Interior
• U.S. Geological Survey

Copyright and License Information

Copyright 1972 held by Ben Chie Yen

Owning Collections