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The Open-Channel Toolbox TM Peter Wilcock

Conservation Relations Conservation of Mass (Continuity) Conservation of Energy Conservation of Momentum. Constitutive Relations Flow Resistance Sediment Transport. The Open-Channel Toolbox TM Peter Wilcock. Conservation of Mass (Continuity). Mass is neither created nor destroyed

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The Open-Channel Toolbox TM Peter Wilcock

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  1. Conservation Relations Conservation of Mass (Continuity) Conservation of Energy Conservation of Momentum Constitutive Relations Flow Resistance Sediment Transport The Open-Channel Toolbox TM Peter Wilcock

  2. Conservation of Mass (Continuity) • Mass is neither created nor destroyed • Inputs = outputs • Inputs and outputs for fluid flow are discharge • Vel x Flow Area U1A1 = U2A2

  3. Conservation of Momentum (Force-balance) NCED and “beige” slides by Peter Wilcock/ Johns Hopkins Univ A

  4. Unsteady, nonuniform flow • Flow accelerates in space and time 1-d St. Venant eqn. Rearranged 1-d St. Venant eqn.

  5. H1 Potential Energy and Kinetic Energy • Bernoulli energy equation • H = d + Z + V2/2g + losses • d = depth • Z = elevation above datum, e.g. sea level • V = velocity of flow • g = gravity H1

  6. Conservation of Energy • Energy is neither created nor destroyed • Two components • kinetic ( ) • potential (z+h) • Energy is also converted to heat, hf • H1 =H2 + hf

  7. http://ga.water.usgs.gov/edu/hyhowworks.html

  8. Flow Resistance (Metric) Multiply by 1.49 for English units • Relation between velocity, flow depth, basal shear stress, and hydraulic roughness • A variety of relations exist including • Manning’s • Chezy • Empirical • The big unknown: n Using continuity,

  9. LWD covering less than 2% of the streambed can provide half the total roughness or flow resistance. This results in a finer streambed substrate. Buffington and Montgomery 1999, WRR 36, 3507-3521 Manga and Kirchner, 2000, WRR 36, 2373-2379.

  10. Sediment Load • Sources: • Chemical weathering (dissolved) • Human activity • Mass wasting • Slopewash • Rill and gully formation • Channel scour • Bed • Cutbanks

  11. What does transport depend on? • The strength of the flow, the fluid, and the sediment • Strength of the flow = shear stress • The sediment = grain size and density • The fluid = water density and water viscosity (its resistance to deformation)

  12. Sediment transport Emmett and Wolman (2001) • Directly expressed in terms of sediment supply and water supply • Shear stress is a descriptor of transport rate Meyer-Peter and Muller: General Form:

  13. How to measure sediment transport?

  14. Sediment Transport and Incipient Motion • They are not the same • sed trans = mass flow rate per unit time • incipient motion = moves or not moves (binary: 0 or 1) • What they share • f(shear stress) • transport depends on the fluid force applied to the bed

  15. Tractive Force or Incipient Motion Shield’s equation • Grain motion is driven by shear stress, t • Units of force/unit area: psf, psi, Pa • Critical shear stress, tc • Shear stress needed to get a grain of a given size moving • Shield’s number or dimensionless shear stresst*

  16. motion no motion Shield’s diagram

  17. http://www.uwsp.edu/gEo/faculty/lemke/geomorphology/lecture_outlines/03_stream_sediment.htmlhttp://www.uwsp.edu/gEo/faculty/lemke/geomorphology/lecture_outlines/03_stream_sediment.html

  18. g=

  19. Problem Site 9 on the White River

  20. Try it 5 m 2m For a rectangular channel 5 m. wide by 2 m. deep (running full), with a slope of 2% What is the basal shear stress? Remember, hydraulic radius R = A/WP

  21. Try It • A basketball has a diameter of ~ 10 inches. • What is the critical shear stress required to just move a basketball-sized rock in a river? • For the channel in the last problem is the rock mobile?

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