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8 - Scaling Theory

Published online by Cambridge University Press:  24 November 2022

Vijay P. Singh
Vijay P. Singh
Affiliation:
Texas A & M University
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Summary

Empirical equations of downstream hydraulic geometry, entailing width, depth, velocity, and bed slope, can be derived using the scaling theory. The theory employs the momentum equation, a flow resistance formula, and continuity equation for gradually varied open channel flow. The scaling equations are expressed as power functions of water discharge and bed sediment size, and are applicable to alluvial, ice, and bedrock channels. These equations are valid for any value of water discharge as opposed to just mean or bank-full values that are used in empirical equations. This chapter discusses the use of scaling theory for the derivation of downstream hydraulic geometry. The scaling theory-based hydraulic geometry equations are also compared with those derived using the regime theory, threshold theory, and stability index theory, and the equations are found to be consistent.

Keywords

Downstream hydraulic geometrymomentum equationcontinuity equationscalingflow resistance equationgradually varied flow
Type
Chapter
Information
Handbook of Hydraulic Geometry
Theories and Advances
 , pp. 245 - 260
Publisher: Cambridge University Press
Print publication year: 2022

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  • Scaling Theory
  • Vijay P. Singh, Texas A & M University
  • Book: Handbook of Hydraulic Geometry
  • Online publication: 24 November 2022
  • Chapter DOI: https://doi.org/10.1017/9781009222136.009
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  • Scaling Theory
  • Vijay P. Singh, Texas A & M University
  • Book: Handbook of Hydraulic Geometry
  • Online publication: 24 November 2022
  • Chapter DOI: https://doi.org/10.1017/9781009222136.009
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Scaling Theory
  • Vijay P. Singh, Texas A & M University
  • Book: Handbook of Hydraulic Geometry
  • Online publication: 24 November 2022
  • Chapter DOI: https://doi.org/10.1017/9781009222136.009
Available formats
×