In a circular conduit of diameter D and of a given slope S0, two critical states of the flow may occur for two different discharges. The first one is observed at shallow depths while the second one settles down at greater depths. This statement is the result of the in-depth study carried out on the smooth circular conduit of diameter D = 1m, taken as an example. For this conduit, all slopes S0 greater than S0 = generate the two critical states of the flow. Slopes that are less than this value do not generate any critical state of the flow. The study reveals that the slope S0 =  corresponds to the smallest slope that causes a single critical state of the flow. Other interesting conclusions, fundamental relationships as well as meaningful graphs are drawn from this study, after a detailed examination of the rational equations which govern the critical and normal flows.


Circular conduit, critical depth, normal depth, slope, discharge.

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