CRITICAL FLOW IN A RECTANGULAR-SHAPED CHANNEL

Abstract

Using the rational relationship, established by the authors in a previous study that links the properties of critical flow and normal flows, the present investigation is related to the critical state of the flow in a rectangular-shaped channel. The main objective is to observe the behaviour of this type of flow under the variation of some flow parameters such as the slope S₀ and the width b of the channel. The relation which governs the critical flow in this form of channel is an implicit relationship for the relative critical depth h_c = y_c/b where y_c is the critical flow depth. It consists of four dimensionless terms which are the relative critical depth defined above, the relative roughness e/b where e is the absolute roughness, the channel slope S₀, and the shear Reynolds number R^*_nc characterizing the flow in a very wide rectangular-shaped channel. To simplify the calculation, the example of the smooth rectangular-shaped channel (e®0) of width b = 1m is first considered to observe the influence of the slope S₀. It was observed that, for the chosen channel, the slope S₀ = 0.0020949472 generates a single critical state of the flow. All the slopes S₀ greater than 0.0020949472 generate two critical flow states corresponding to two different flow rates. Finally, slopes less than 0.0020949472 do not generate any critical state of the flow in the channel. On the other hand, it has also been demonstrated that for a given slope S₀, there is a particular width b₁ of the channel which generates a single critical state of the flow. Widths b less than b₁ do not generate any critical state in the channel, while widths b greater than b₁ engender two critical states of the flow.