Formulation of Mathematical Watershed-Flow Model

by Cheng-Lung Chen, (A.M.ASCE), Prof. of Civ. Engrg.; Dept. of Civ. Engrg., Utah State Univ., Logan, UT; formerly, Assoc. Prof. of Civ. Engrg., Dept. of Civ. Engrg., Univ. of Illinois, Urbana, IL,
Ven Te Chow, (M.ASCE), Prof. of Hydro. Engrg.; Dept. of Civ. Engrg., Univ. of Illinois at Urbana-Champaign Campus, Urbana, IL,


Serial Information: Journal of the Engineering Mechanics Division, 1971, Vol. 97, Issue 3, Pg. 809-828


Document Type: Journal Paper

Abstract: In a macroscopic hydrodynamic approach, a set of one-dimensional spatially varied unsteady flow equations, that include terms for lateral mass flux, lateral momentum flux, overpressure head due to raindrop impact, and boundary shear, are derived from the equation of continuity and the Navier-Stokes equations for the three-dimensional flow of viscous incompressible fluid in cooperation with the kinematic and dynamic boundary conditions on the water and ground surfaces of a watershed. The Darcy-Weisbach equation is employed to evaluate the friction slope, and the laminar uniform flow equation for the Darcy-Weisbach friction coefficient coupled with the Kármán-Prandtl logarithmic resistance equation for turbulent flow is used to simulate, as a first approximation, the unknown function of the Darcy-Weisbach friction coefficient for watershed surface flow. The proposed mathematical model for watershed surface flow consists of a set of quasilinear partial differential flow equations of hyperbolic type with the appropriately prescribed initial and boundary conditions.

Subject Headings: Water flow | Watersheds | Flow resistance | Flow simulation | Turbulent flow | One-dimensional flow | Three-dimensional flow | Fluid flow

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