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Modeling Bed Shear Stress Distribution in Rectangular Channels Using the Entropic Parameter

1
School of Engineering, Basilicata University, Viale dell’Ateneo Lucano 10, 85100 Potenza, Italy
2
Department of Mathematics, Computer Science and Economics, Basilicata University, Viale dell’Ateneo Lucano 10, 85100 Potenza, Italy
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(1), 87; https://doi.org/10.3390/e22010087
Received: 8 December 2019 / Revised: 6 January 2020 / Accepted: 8 January 2020 / Published: 10 January 2020
The evaluation of bed shear stress distribution is fundamental to predicting the transport of sediments and pollutants in rivers and to designing successful stable open channels. Such distribution cannot be determined easily as it depends on the velocity field, the shape of the cross section, and the bed roughness conditions. In recent years, information theory has been proven to be reliable for estimating shear stress along the wetted perimeter of open channels. The entropy models require the knowledge of the shear stress maximum and mean values to calculate the Lagrange multipliers, which are necessary to the resolution of the shear stress probability distribution function. This paper proposes a new formulation which stems from the maximization of the Tsallis entropy and simplifies the calculation of the Lagrange coefficients in order to estimate the bed shear stress distribution in open-channel flows. This formulation introduces a relationship between the dimensionless mean shear stress and the entropic parameter which is based on the ratio between the observed mean and maximum velocity of an open-channel cross section. The validity of the derived expression was tested on a large set of literature laboratory measurements in rectangular cross sections having different bed and sidewall roughness conditions as well as various water discharges and flow depths. A detailed error analysis showed good agreement with the experimental data, which allowed linking the small-scale dynamic processes to the large-scale kinematic ones. View Full-Text
Keywords: Tsallis entropy; entropic parameter; bed shear stress distribution; rectangular channels; flow velocity; error analysis Tsallis entropy; entropic parameter; bed shear stress distribution; rectangular channels; flow velocity; error analysis
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Mirauda, D.; Russo, M.G. Modeling Bed Shear Stress Distribution in Rectangular Channels Using the Entropic Parameter. Entropy 2020, 22, 87.

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