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Comparison between Shannon and Tsallis entropies for prediction of shear stress distribution in open channels

  • Hossein BonakdariEmail author
  • Zohreh Sheikh
  • Mohtaram Tooshmalani
Original Paper

Abstract

The concept of Tsallis entropy was applied to model the probability distribution functions for the shear stress magnitudes in circular channels (with filling ratios of 0.506, 0.666, 0.826), circular with flat bed (filling ratios of 0.333, 0.666), rectangular channel (1.34, 2, 3.94, 7.37 aspect ratios) and compound channel (with relative depths of 0.324, 0.46). The equation for the shear stress distribution was obtained according to the entropy maximization principle, and is able to estimate the shear stress distribution as much on the walls as the channel bed. The approach is also compared with the predictions obtained based on the Shannon entropy concept. By comparing the two prediction models, this study highlights the application of Tsallis entropy to estimate the shear stress distribution of open channels. Although the results of the two models are similar in the circular cross-section, the differences between them are more significant in circular with flat bed and rectangular channels. For a wide range of filling ratio values, experimental data are used to illustrate the accuracy and reliability of the proposed model.

Keywords

Entropy Open channel Sediment Wall Bed 

Notes

Acknowledgments

The authors would like to express their appreciation to the anonymous reviewers for their helpful comments and to Ellen Vuosalo Tavakoli for the painstaking editing of the English text.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Hossein Bonakdari
    • 1
    • 2
    Email author
  • Zohreh Sheikh
    • 1
    • 2
  • Mohtaram Tooshmalani
    • 1
    • 2
  1. 1.Department of Civil Engineering, Faculty of EngineeringRazi UniversityKermanshahIran
  2. 2.Water and Wastewater Research CenterRazi UniversityKermanshahIran

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