Minimum Specific Energy and Transcritical Flow in Unsteady Open-Channel Flow

Abstract

The study and computation of free surface flows is of paramount importance in hydraulic and irrigation engineering. These flows are computed using mass and momentum conservation equations, their solutions exhibiting special features depending on whether the local Froude number (F) is below or above unity, thereby resulting in wave propagation in the upstream and downstream directions or only in the downstream direction, respectively. This dynamic condition is referred to in the literature as critical flow and is fundamental to the study of unsteady flows. Critical flow is also defined as the state at which the specific energy and momentum reach a minimum, based on steady-state computations, and it is further asserted that the backwater equation gives infinite free surface slopes at control sections. So far, these statements were not demonstrated within the context of an unsteady-flow analysis, to be conducted in this paper for the first time. It is demonstrated that the effects of unsteadiness break down critical flow as a generalized open-channel flow concept, and correct interpretations of critical flow, free surface slopes at controls, minimum specific energy, and momentum are given within the context of general unsteady-flow motion in this paper.