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Hydraulic Geometry

Hydraulic Geometry. Brian Bledsoe Department of Civil Engineering Colorado State University. Regime Theory / Hydraulic Geometry (e.g. Lacey 1929, Leopold and Maddock 1953). Channel parameters may be sufficiently described with power functions utilizing Q as the sole independent variable.

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Hydraulic Geometry

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  1. Hydraulic Geometry Brian Bledsoe Department of Civil Engineering Colorado State University

  2. Regime Theory / Hydraulic Geometry (e.g. Lacey 1929, Leopold and Maddock 1953) Channel parameters may be sufficiently described with power functions utilizing Q as the sole independent variable

  3. At-a-Station Downstream Hydraulic Geometry - Exponents b is width, f is depth, and m is velocity

  4. Downstream hydraulic geometry

  5. The Basic Issue Predicting channel width / depth in the context of heterogeneous bed and bank conditions w, h, S, v • Continuity • Friction loss • Sediment transport or incipient motion • ???

  6. Three General Approaches Empirical • Regime Equations / Hydraulic Geometry • Lacey, Simons and Albertson, Blench, USACE, Julien and Wargadalem, many others including “regional curves” • Context-specific - require judgment / caution “Rational / Analytical” • Copeland Method (now in HEC-RAS) • Lateral Momentum Transfer - Parker • Millar Extremal / Variational / Thermodynamic • Minimum S, VS, Fr, dVS/dw • Maximum f, Qs, Qs/S

  7. Hydraulic Geometry Approachin Stable Channel Design • Rooted in regime theory of Anglo-Indian engineers • Canal design • Low sediment loads • Low variability in Q • Does not directly consider sediment load (slope equations are dangerous for sand bed channels) • Neglects energy principles and time scales of different adjustment directions • Fluvial system is actually discontinuous, e.g. tributaries, variability in coefficients

  8. Downstream hydraulic geometry equations for width provide an important channel design and analysis toolDepth, velocity, and slope equations are less reliable

  9. Some Factors Affecting a • Vegetation / soils / light interactions • Root reinforcement and depth / bank height • Woody debris inputs and bank roughness • Bank cohesion / stratigraphy / drainage • Freeze / thaw • Sediment load • Flow regime (e.g. elevation of veg. on banks) • Return period of extremes vs. recovery time • Lateral vs. vertical adjustability / time • Historical context

  10. Downstream Hydraulic Geometryand Boundary Sediments Schumm (1960) Richards (1982)

  11. Hey and Thorne (1986)All Veg. Types

  12. Hey and Thorne (1986) Separate Veg. Types

  13. Hey and Thorne (1986) Grassy banks  a = 4.33 1-5% tree / shrub  a = 3.33 5-50% tree / shrub  a = 2.73 > 50% tree / shrub  a = 2.34 Andrews (1984) Thin  a = 4.3 Thick  a = 3.6 Downstream Hydraulic Geometryand Vegetation

  14. Hey and Thorne (1986) and Charlton et al. (1978) data

  15. Davies-Colley (1997) and Hession et al. (2003) data

  16. Grass Forest Log Channel Width 10 -100 km2 Log Watershed Area

  17. Root Density (ml l-1) % Silt and Clay

  18. Vegetation Density, Stiffness, Root Reinforcement ? Bank Cohesion Suspended Sediment Load Bed Material Size / Braiding Risk Values of a in w = aQ0.5

  19. Summary • Downstream hydraulic geometry relationships for width can provide a useful, additional relationship in channel design • Selection of the coefficient a is complicated and requires consideration of many factors • Vegetation effects tend to override sedimentary effects • Processes are scale-dependent?

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