عنوان مقاله [English]
نویسندگان [English]چکیده [English]
Estimation of flow velocity distribution is considered to be one of the main issues in the open channels, sewers, and rivers. Occurrence of the maximum velocity phenomenon below free surface (Dip phenomenon), is cause of concern and complexity for estimation of the velocity distribution in open channel flows. In this paper, the velocity distribution in the narrow sewer combined channels was estimated using the entropy theory, and the impact of different cumulative distribution functions on the velocity distribution has been investigated. Accuracy evaluation of Marini and Chiu entropy functions in the estimation of the velocity distribution and parameters suggested that a new model with higher accuracy can be proposed in order to optimizethe velocity estimation in these types of channels. Also, the comparison between field data of former studies and the result of proposed model indicated that the proposed model is in accordance with field data in the different levels and depths of channel. The results also showed acceptable accuracy of the proposed model in the velocity distribution estimation (R2=0.86, relative error = 11%, MAPE = 7.84% and RMSE = 0.0758). Further, comparison of proposed model and Chiu velocity distribution model shows that the proposed model has better performance in spite of more simplicities than other existing models.
Barbe, D. E. 1990. Probabilistic analysis of bridge scour using the principle ofmaximum entropy. Ph. D. Thesis. Louisiana State University, Baton Rouge.
Bonakdari, H. 2011. Entropy and its application in computation of velocity distribution in sewers. Proceeding of the World Environmental and Water Resources Congress: Bearing Knowledge for Sustainability. California, United States.
Bonakdari, H. and Moazamnia, M. 2015. Modeling of velocity fields by the entropy concept in narrow open channels. KSCE J. Civil Eng. 19(3): 779-789.
Bonakdari, H., Larrarte, F., Lassabatere, L. and Joannis, C. 2008. Turbulent velocity profile in fully-developed open channel flows. Environ. Fluid Mech. 8(1): 1-17.
Chiu, C. L. 1987. Entropy and probability concepts in hydraulics. J. Hydraul. Eng. 113(5): 583-600.
Chiu, C. L. 1988. Entropy and 2-D velocity distribution in open channels. J. Hydraul. Eng. 114(7):
Chiu, C. L. 1989. Velocity distribution in open channel flow. J. Hydraul. Eng. 115(5): 576-594.
Chiu, C. L. 1991. Application of entropy concept in open-channel flow. J. Hydraul. Eng. 117(5): 615-628.
Chiu, C. L. and Chiou, J. 1986. Structure of 3-D flow in rectangular open channels. J. Hydraul. Eng. 109(11): 1050-1068.
Chiu, C. L. and Lin, G. F. 1983. Computation of 3-D flow and shear in open channels. J. Hydraul. Eng. 112(11): 1424-1440.
Cui, H. 2011.Estimation of velocity distribution and suspended sediment discharge in open channels using entropy. M. Sc. Thesis. Texas A&M University, College Station, TX.
Cui, H. and Singh, V. P. 2012. On the cumulative distribution function for entropy-based hydrologic modeling. T- ASABE. 55(2): 429-438.
Esmaeili-Varaki, M., Ghorbani-Nasralah-Abadi, S. and Navabian, M. 2013. Evaluation of entropy based chiu’s method for prediction of the velocity distribution and discharge in rivers. J. Water Soil Conserv. 20(6): 147-164. (in Persian)
Farsadizadeh, D., Hosseinzadeh Dalir, A., Ghorbani, M. A. and Samadian-Fard, S. 2011. Estimation of flow velocity distribution in smooth-bed open channels with a smooth bed using entropy theory and genetic programming. Water Soil Sci. (Agr. Sci.). 21(3): 61-74 (in Persian)
Guo, J. and Julien, P. Y. 2006. Application of modified log-wake law in open-channels. Proceeding of the World Environmental and Water Resource Congress: Examining the Confluence of Environmental and Water Concerns. May 21-24.Omaha, Nebraska, United States.
Jaynes, E. T. 1957. Information theory and statistical mechanics 2. Phys. Rev. 108(2): 171-190.
Larrarte, F. 2006. Velocity fields within sewers: An experimental study. Flow Measure. Instrum.
Luo, H. 2009. Tsallis entropy based velocity distributions in open channel flows. M. Sc. Thesis, Texas A&M University. College Station, TX.
Luo, H. and Singh, V. P. 2011. Entropy theory for two-dimensional velocity distribution. J. Hydrol. Eng. 18(2): 331-339.
Marini, G., De Martino, G., Fontana, N., Fiorentino, M. and Singh, V. P. 2011. Entropy approach for 2D velocity distribution in open-channel flow. J. Hydraul. Res. 49(6): 784-790.
Moazamnia, M. and Bonakdari, H. 2014. Velocity distribution and estimation of discharge in sewers by shannon entropy concept. Bimonthly J. Water Wastewater. 25(2), 26-35. (in Persian)
Shannon, C. E. 1948. A mathematical theory of communication. At. & T. Tech. J. 27(3): 379-423.
Tsallis, C. 1988. Possible generalization of Boltzmann-Gibbs statistics. J. Stat. Phys. 52(1-2): 479-487.