Hydraulic Significance of Transitional Behaviours of Flows in Channel Transitions and Controls : Application of Geometric Theory of Differential Equation to Surface Configuration of Transition Flow in Divergent or Convergent Channels

Abstract

As one of the research projects of clear formulation in hydraulic characteristics of transitional behaviours from subcritical to supercritical or vice versa, this paper deals with the hydraulic behaviours of channel characteristics in geometry and boundary to the functional variety of channel transitions and controls in divergent or convergent channels. The gradually varied flow in divergent or convergent channels changes its flow regime at a singular point of surface profile equation imposed by particular discharge and channel characteristics, and consequently the theoretical approach in analysis of hydraulic behaviours of transition flow will be established with the application of the geometric theory of differential equation, which is known in problems of non-linear mechanics. The classification of singular points as transitional points and the significance of transitional characteristics of flow passing through a transitional point, and especially from a standpoint of practical hydraulic engineering, those for flows of Chézy and Manning are presented. The present procedure of analysis is applied not only to the flow behaviours discussed in this study but also to the flow with side in- or outflows and similar problems in the hydraulics of open channel flows.