CE 3372 Water Systems Design SWMM Dynamic Wave

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 • Dynamic wave approximates solutions to coupled conservation of mass and momentum equations – Presented in next few slides without derivation

Definition Sketch of a Reach

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

Momentum & Force Balance Computational Reach Length

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

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

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

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

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

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)

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

Examples in SWMM • TBD