The objective of this study is to analyze the behavior of critical flow in a parabolic channel as a function of all the parameters that influence the flow, such as the slope of the channel S0, the absolute roughness and the kinematic viscosity. To do this, we applied two rational relations, namely, the relationship of the critical flow condition and the general formula of the discharge. The combination of these two relations results in an implicit relation consisting of five dimensionless terms that are the dimensionless critical depth  , where yc is the critical depth and B is the linear dimension of the channel, the dimensionless normal depth , where is the normal depth, the relative roughness , the longitudinal slope S0, and the modified Reynolds number. This implicit relationship was applied to a parabolic channel with a linear dimension B = 1 m in the whole domain of turbulent flow. The detailed study of the rational equations governing the critical and normal flows leads to intriguing results in addition to the establishment of other fundamental relations and significant graphs.


Critical depth, Critical flow, Discharge, Normal depth, Parabolic channel, Slope.

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