Prediction of the Velocity Contours in Triangular Channel with Non-uniform Roughness Distributions by Adaptive Neuro-Fuzzy Inference System

Document Type : Research Paper


1 Former Graduate Student, Dept. of Civil Engineering, University of Sistan & Baluchestan, Zahedan

2 Assist. Prof., Dept. of Civil Engineering, University of Sistan & Baluchestan, Zahedan


Triangular channels have different applications in many water and wastewater engineering problems. For this purpose investigating hydraulic characteristics of flow in these sections has great importance. Researchers have presented different prediction methods for the velocity contours in prismatic sections. Most proposed methods are not able to consider the effect of walls roughness, the roughness distribution and secondary flows. However, due to complexity and nonlinearity of velocity contours in open channel flow, there is no simple relationship that can be fully able to exactly draw the velocity contours. In this paper an efficient approach for modeling velocity contours in triangular open channels with non-uniform roughness distributions by Adaptive Neuro-Fuzzy Inference System (ANFIS) has been suggested. For training and testing model, the experimental data including 1703 data in triangular channels with geometric symmetry and non-uniform roughness distributions have been used. Comparing experimental results with predicted values by model indicates that ANFIS model is capable to be used in simulation of local velocity and determining velocity contours and the independent evaluation showed that the calculated values of discharge and depth-averaged velocity from model information are precisely in conformity with experimental values.


Aly, A.M.M., Trupp, A.C. & Gerrard, A.D. 1978, "Measurements and prediction of fully developed turbulent flow in an equilateral triangular duct", J. Fluid. Mech., 85, (1), Pp 57-83.
Bandopadhayay, P. C. & Hinwood, J. B., 1973, "On the coexistence of laminar and turbulent flow in a narrow triangular duct", J. Fluid Mech., 59, 775.
Bogle, G. V., 1997, "Stream velocity profiles and longitudinal dispersion", Journal of Hydaulic Engineering, 123(9), 816-820.
Huang, J., Weber, L. J., & Lai, Y.G., 2002, "Three-dimensional numerical study of flows in open-channel junctions", Journal of Hydraulic Engineering, 128(3), 268-280.
Cope, R.C. & Hanks, R. W., 1972, "Transitional flow in isocceles transitional ducts", Ind. Eng. Chem. Fund,1, 105-117.
Cremers, C.J. & Eckert, E.R.G., 1962, "Hot wire measurments of turbulence correlations in a triangular duct", J. Appl. Mech. Trans, 29, 609-614.
Chang, F. J. & Chang, Y. T., 2006, "Adaptive neuro-fuzzy inference system for prediction of water level in reservoir", Advances in Water Resources, 29, 1-10.
Coleman, N.L., 1986, "Effects of suspended sediment on the open-channel velocity distribution", Water Resources Research, 22(10), 1377-1384.
Chiu, C.L. & Tung, N.C., 2002, "Maximum velocity and regularities in open-channel flow", Journal of Hydraulic Engineering, 128(4), 390-398.
Chiu, S.L., 1994, "Fuzzy model identification based on cluster estimation", J. Intell. Fuzzy Syst., 2, 267-278.
Givehchi, M., 2009, "Estimation of depth- averaged velocity and boundary shear stress in an open channel and their use in estimatin the longitudinal diffusion coeffiient", PhD Thesis, University of Mashhad, Iran. (In Persian)
Knight, D.W., Omran, M. & Tang, X., 2007, "Modeling depth-averaged velocity and boundary shear in trapezoidal channels with secondary flows", Journal of Hydaulic Engineering, 133(1), 39-47.
Lane, E.W., 1953, "Progress report on studies on the design of stable channels by the Bureau of Reclamation", Am. Soc. Civil Engineers, 79 (280), 1-30
Maghrebi, M. F., & Givehchi, M., 2010, "Estimating of the depth-averaged velocity and shear stress in triangular open channel", Journal of Water and Wastewater, Vol. 21 No. 2 (74), 71-80. (In Persian)
Sarma, K.V.N., Lakshminaraynan, P., & Rao, N.S.L., 1983, "Velocity distribution in smooth rectangular open channels", Journal of Hydraulic Engineering, 109(2), 270-289.
Sooky, A.A., 1969, "Longitudinal dispersion in open channels", J. Hydr. Div., Am. Soc. Civil Eng., 95(4), 1327-1346.
Teshnehlab, M., Saffarpour, N., & Afyouni, D., 2008, Fuzzy control & fuzzy systems, Translate (written by Wong, L).,2ndEd., K.N. Toosi University of Technology, Tehran, Iran. (In Persian)
Waldon, M. G., 2004, "Estimationof average stream velocity", Journal of Hydaulic Engineering, 130(11), 1119-1122.
Wark, J. B., Samuels, P. G. & Ervine, D. A., 1990, "A practical method of estimating velocity and discharge in a compound channel", White, W. R. (Ed)., River flood hydraulics, Wiley, New York.
Wolpert, D.H., 1992, "Stacked generalization", Neural Networks, 5 (2), 241-259.
Haykin, S., 1999, Neural networks: A comprehensive foundation, 2nd Edition, Prentice-Hall, N.Y.
Jang, J. -S. R., 1993, "ANFIS: Adaptive-network-based fuzzy inference system", IEEE Transactions on Systems, Man and Cybernetic, 23(3), 665-685.
Jeon, J., 2007, "Fuzzy and neural network models for analyses of piles", PhD Thesis, Dept. of Civil Engineering, North Carolina.
Rumelhart, D.E., & McClelland, J. L., 1986, Parallel distributed processing, MIT Press, Cambridge, MA.
Yang, H.C. & Chang, F.J., 2005, "Modeling combined open channel flow by artificial neural networks", Journal of Hydrol.Process, 19, 3747-3762.