De Saint-Venant Equations Experimentally Verified

by Willem Brutsaert, Asst. Prof. of Hydro.; New Mexico Inst. of Mining and Tech., Socorro, NM,

Serial Information: Journal of the Hydraulics Division, 1971, Vol. 97, Issue 9, Pg. 1387-1401

Document Type: Journal Paper


The unsteady spatially varied flow equations (De Saint-Venant equations) are being solved by implicit finite differences with explicit description at the boundaries. Imposition of improper boundary conditions which violate the physics of the problem resulted into either violation of continuity or numerical instability problems or meaningless results. The magnitude of the spatial increment used in this implicit solution scheme was critical on steep slopes (2.0%). The temporal distribution of flow and time to equilibrium was altered considerably depending on the specified value of Δx. Hydrographs on milder slopes (0.5% and 1.0%) were affected to a progressively lesser extent as the channel slope was decreased. The time to equilibrium flow starting from a dry bed was nonlinear with respect to change of channel length, channel slope, and rate of lateral inflow. For a given channel length and slope, time to equilibrium approached a constant for high rates of later inflow.

Subject Headings: Slopes | Equilibrium | Verification | Flow distribution | Flow duration | Inflow | Gradually varied flow | Unsteady flow

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