Nondimensional Expression of Unsteady Canal Flow

By appropriate choice of reference variables, dimensionless governing equations and initial and boundary conditions of unsteady canal flow have fewer independent parameters than do their dimensioned counterparts; the same information can be expressed more compactly. With design discharge and normal depth as references, unsteady flow is governed by cross-sectional shape factors, Froude number at normal depth, and the dimensionless length, as well as initial and boundary conditions. A particular dimensionless form of the Saint-Venant equations was found to have the same appearance as the dimensioned equations. Dimensionless \ig, the ratio of weight to mass in the dimensioned real-world equations, is now related to the Froude number at normal depth in the dimensionless equations. The Manning units coefficient, normally used to express the Manning formula in English or metric systems, in the dimensionless system relates to the shape of the channel cross section under normal flow conditions. Dimensionless results are interpreted in real-world terms by specifying normal flow depth and Manning roughness. With the normal Froude number given, all pertinent dimensioned variables follow directly from dimensionless results.