Abstract
A new method is applied to calculate the normal depth in an open channel of parabolic cross section. This is the rough model method whose main particularity is to ignore the flow resistance coefficients, such as Chezy’s coefficient and manning’s roughness coefficient. The method is applied to a referential rough model, whose friction coefficient is constant, which explicitly express the hydraulic and geometric characteristics of the model such as aspect ratio. By means of a non-dimensional correction factor, the normal depth is explicitly deduced. The rough model method is applicable to the entire domain of turbulent flow.
Highlights
Normal depth plays a significant role in the design of open channels and in the analysis of the non-uniform flow as well
The well known Chezy and Manning resistance equation are extensively used. Due to their implicit form, graphical methods have been presented in the past for uniform flow computation in the common rectangular, trapezoidal, triangular and circular cross sections [1,2,3]
The rough model method states that any linear dimension L of a channel and the linear dimension L of its rough model are related by the following equation, applicable to the whole domain of the turbulent flow: L L
Summary
Normal depth plays a significant role in the design of open channels and in the analysis of the non-uniform flow as well. The well known Chezy and Manning resistance equation are extensively used Due to their implicit form, graphical methods have been presented in the past for uniform flow computation in the common rectangular, trapezoidal, triangular and circular cross sections [1,2,3]. The most relevant study is certainly that of Swamee and Rathie [6], in which exact analytical equations for normal depth have been reported for rectangular, trapezoidal and circular cross sections. For round-bottomed triangular, round-cornered rectangular and parabolic cross sections, exact or approximate solutions are not yet available. For these sections, graphical methods have been proposed by Babaeyan-Koopaei [7] for parabola of second degree, using the Manning's resistance equation.
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