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Derivation of Hunt equation for suspension distribution using Shannon entropy theory

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  • Kundu, Snehasis

Abstract

In this study, the Hunt equation for computing suspension concentration in sediment-laden flows is derived using Shannon entropy theory. Considering the inverse of the void ratio as a random variable and using principle of maximum entropy, probability density function and cumulative distribution function of suspension concentration is derived. A new and more general cumulative distribution function for the flow domain is proposed which includes several specific other models of CDF reported in literature. This general form of cumulative distribution function also helps to derive the Rouse equation. The entropy based approach helps to estimate model parameters using suspension data of sediment concentration which shows the advantage of using entropy theory. Finally model parameters in the entropy based model are also expressed as functions of the Rouse number to establish a link between the parameters of the deterministic and probabilistic approaches.

Suggested Citation

  • Kundu, Snehasis, 2017. "Derivation of Hunt equation for suspension distribution using Shannon entropy theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 488(C), pages 96-111.
    • Handle: RePEc:eee:phsmap:v:488:y:2017:i:c:p:96-111
    DOI: 10.1016/j.physa.2017.07.007
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    References listed on IDEAS

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    1. Einstein, Hans Albert, 1950. "The Bed-Load Function for Sediment Transportation in Open Channel Flows," Technical Bulletins 156389, United States Department of Agriculture, Economic Research Service.
    2. Kumbhakar, Manotosh & Ghoshal, Koeli, 2016. "Two dimensional velocity distribution in open channels using Renyi entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 546-559.
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    1. Kazemian-Kale-Kale, Amin & Bonakdari, Hossein & Gholami, Azadeh & Khozani, Zohreh Sheikh & Akhtari, Ali Akbar & Gharabaghi, Bahram, 2018. "Uncertainty analysis of shear stress estimation in circular channels by Tsallis entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 558-576.
    2. Ghoshal, Koeli & Kumbhakar, Manotosh & Singh, Vijay P., 2019. "Distribution of sediment concentration in debris flow using Rényi entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 267-281.

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