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CE 3372 Water Systems Design

CE 3372 Water Systems Design. SWMM Dynamic Wave. Dynamic Wave. Used when: Need to investigate backwater effects; gradually varied flow Need to investigate looped systems Need to approximate overland flow and inundation Need to investigate time-varying flow. St. Venant Equations.

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CE 3372 Water Systems Design

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  1. CE 3372 Water Systems Design SWMM Dynamic Wave

  2. Dynamic Wave • Used when: • Need to investigate backwater effects; gradually varied flow • Need to investigate looped systems • Need to approximate overland flow and inundation • Need to investigate time-varying flow

  3. St. Venant Equations • Dynamic wave approximates solutions to coupled conservation of mass and momentum equations • Presented in next few slides without derivation

  4. Definition Sketch of a Reach

  5. Conservation of Mass Gain/Loss in the Depth Prism Lateral Inflow q Discharge across section faces

  6. Momentum & Force Balance Computational Reach Length

  7. Conservation of Momentum • Pressure-integral (to compute pressure forces) Forces on wall taper Forces on end faces

  8. Conservation of Momentum • Linear Momentum Balance • Result of some calculus Net momentum entering cell Pressure force, end sections Pressure force, bank taper Gravitational force Friction force opposing flow Total acceleration in the cell

  9. Coupled Equations • Continunity • Momentum Normal Gradually Varied Fully Dynamic, Shallow Wave

  10. Dynamic Wave • Obviously complex because there are so many pieces • Need a program (some way to make all the calculations) • SWMM, HEC-RAS are the most common tools for these kinds of calculations

  11. Dynamic Wave • Big differences are: • SWMM • uses explicit finite-difference formulation; fewer boundary condition restrictions at the cost of speed. • can do looped systems without much fuss • Integrated hydrology

  12. Dynamic Wave • Big differences are: • HEC-RAS • uses implicit finite-difference formulation; more boundary condition restrictions, but faster. • Looped systems tricky • Does not do circular sections very well • River systems, culverts, bridges, etc. • Hydrology is independent (usually by HEC-HMS)

  13. Dynamic Wave in SWMM • Change the routing method • SET BOUNDARY CONDITIONS • SET TIME WINDOW and STEP SIZE carefully • Usually have to add storage elements to have things work better

  14. Examples in SWMM • TBD

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