#### Start Date

6-28-2016 1:30 PM

#### Recommended Citation

Bonakdari, H., Khozani, Z. (2016). Shear Stress Distribution Prediction in Circular Channels Using Tsallis Entropy. In B. Crookston & B. Tullis (Eds.), Hydraulic Structures and Water System Management. 6th IAHR International Symposium on Hydraulic Structures, Portland, OR, 27-30 June (pp. 128-136). doi:10.15142/T3390628160853 (ISBN 978-1-884575-75-4).

#### Abstract

Detailed knowledge of flow and shear stress distribution in channels is essential in accurately calculating the rates of sediment transport and deposition for geomorphic adjustment. Circular cross sections are usual in sewer channels and the sedimentation of suspended material is a significant matter in such sections. In this study, an analytical model is extended to predict the shear stress distribution in circular channels based Tsallis entropy concept. A new formula for estimating shear stress distribution in circular channels is derived by maximizing the Tsallis entropy subject to mass conservation. The distribution derived from the Tsallis entropy is examined using experimental data. The Tsallis entropy-based shear stress distribution appears to be in reasonable agreement with the measurements. According to the results, with increasing flow depth the proposed model showed good fit with the laboratorial outcomes and with mean Root Mean Square Error (RMSE) of 0.0516 it presented high performance in predicting shear stress distribution in circular channels. The results of equation derived of Tsallis entropy were compared with the results of another equation based Shannon entropy that proposed by other researchers. Based the results the proposed model with PE of 0.0083 performed better than equation based Shannon entropy with PE of 0.0091. In highest flow depth both models performance was the same but for other flow depths the proposed model performs better than Shannon entropy. The principal differences between the measured and calculated data are the results of secondary circulation, which are not included in the calculation. The main advantage of these new equations is that they are simpler than previous equations extracted with the entropy concept; besides, their parameters can be easily acquired based on a quadratic equation and it is not necessary to solve complicated equations to obtain the entropy parameters. Since the obtained equations are simpler than those based on the entropy concept, and their results are more accurate they can be applied confidently for circular channels.

Shear stress distribution prediction in circular channels using Tsallis entropy

Portland, OR

Detailed knowledge of flow and shear stress distribution in channels is essential in accurately calculating the rates of sediment transport and deposition for geomorphic adjustment. Circular cross sections are usual in sewer channels and the sedimentation of suspended material is a significant matter in such sections. In this study, an analytical model is extended to predict the shear stress distribution in circular channels based Tsallis entropy concept. A new formula for estimating shear stress distribution in circular channels is derived by maximizing the Tsallis entropy subject to mass conservation. The distribution derived from the Tsallis entropy is examined using experimental data. The Tsallis entropy-based shear stress distribution appears to be in reasonable agreement with the measurements. According to the results, with increasing flow depth the proposed model showed good fit with the laboratorial outcomes and with mean Root Mean Square Error (RMSE) of 0.0516 it presented high performance in predicting shear stress distribution in circular channels. The results of equation derived of Tsallis entropy were compared with the results of another equation based Shannon entropy that proposed by other researchers. Based the results the proposed model with PE of 0.0083 performed better than equation based Shannon entropy with PE of 0.0091. In highest flow depth both models performance was the same but for other flow depths the proposed model performs better than Shannon entropy. The principal differences between the measured and calculated data are the results of secondary circulation, which are not included in the calculation. The main advantage of these new equations is that they are simpler than previous equations extracted with the entropy concept; besides, their parameters can be easily acquired based on a quadratic equation and it is not necessary to solve complicated equations to obtain the entropy parameters. Since the obtained equations are simpler than those based on the entropy concept, and their results are more accurate they can be applied confidently for circular channels.