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1 results

  • 8 - Scaling Theory

  • Vijay P. Singh, Texas A & M University
  • Book:
    Handbook of Hydraulic Geometry
    Published online:
    24 November 2022
    Print publication:
    08 December 2022, pp 245-260

  • 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.