Volume 17, Numéro 4, Pages 73-80

Critical Flow In A Rectangular-shaped Channel

Authors : Achour Bachir . Amara Lyes .


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 c = yc/b where yc is the critical flow depth. It consists of four dimensionless terms which are the relative critical depth defined above, the relative roughness /b where  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 (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.


rectangular channel ; critical depth ; critical flow ; normal depth ; channel slope ; channel width ; relative critical depth