Open-Channel Flow Equations Revisited

Equations of continuity, momentum, and energy in integral form are formulated herein by integrating over the cross section the corresponding equations for a point and then transformed into one-dimensional form by introducing the necessary correction factors. These one-dimensional equations can be regarded as the unified general open-channel flow equations. The channel can have arbitrary cross sectional shape and alignment with fixed or erodible and impervious or pervious bed. The fluid can be homogeneous or nonhomogeneous, compressible or incompressible, and viscous or inviscid. The flow can be turbulent or laminar, rotational or irrotational, steady or unsteady, uniform or nonuniform supercritical or subcritical, gradually or rapidly varied, and with or without lateral discharge. Based on these equations, the assumptions involved in conventionally used open-channel flow equations such as backwater flow equation and St. Venant equations are examined. The inherent differences between the flow equations derived based on the momentum and energy concepts are compared.