Velocity Distribution in Open Channels: Combination of Log-law and Parabolic-law

Authors: Snehasis Kundu, Koeli Ghoshal

Abstract:

In this paper, based on flume experimental data, the velocity distribution in open channel flows is re-investigated. From the analysis, it is proposed that the wake layer in outer region may be divided into two regions, the relatively weak outer region and the relatively strong outer region. Combining the log law for inner region and the parabolic law for relatively strong outer region, an explicit equation for mean velocity distribution of steady and uniform turbulent flow through straight open channels is proposed and verified with the experimental data. It is found that the sediment concentration has significant effect on velocity distribution in the relatively weak outer region.

Keywords: Inner and outer region, Log law, Parabolic law, Richardson number.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1075428

References:

[1] D. Coles, "The law of the wake in turbulent boundary layer," Journal of Fluid Mechanics, vol. 1, pp. 191-226, 1956.
[2] I. Nezu, and W. Rodi, "Experimental study on secondary currents in open channel flow," Proceedings of the 21st IAHR Congress, pp. 115- 119, Melbourne: IAHR, 1985.
[3] I. Nezu, and H. Nakagawa, "Turbulence in open-channel flows," Balkema, Rotterdam NL., 1993.
[4] S. Vedula, and A. R. Rao, "Bed Shear from Velocity Profiles: A NewApproach," Journal Hydraulic Engineering, vol. 111, no. 1, pp. 131-143,1985.
[5] V. A. Vanoni, "Velocity Distribution in Open Channels," Civil Engineering, ASCE, vol. 11, no. 6, pp. 356-357, 1941.
[6] J. B. Francis, "On the cause of the maximum velocity of water flowing in open channels being below the surface," Trans. ASCE, vol. 7(1), no. 1, pp. 109-113, 1878.
[7] F. P. Stearns, "On the current meter, together with a reason why the maximum velocity of water flowing in open channel is below the surface," Trans. ASCE, vol. 7, pp. 331-338, 1883.
[8] J. O. Hinze, "Turbulence," McGraw-Hill, New York, 1975, pp. 698-699.
[9] G. H. Keulegan, "Laws of turbulent flow in open channels," J. Res., Nat. Bureau of Standards, vol. 21, pp. 707-741, 1938.
[10] K. V. N. Sarma, B. V. R. Prasad, and A. K. Sarma, "Detailed Study of Binary Law for Open Channels," Journal Hydraulic Engineering, vol. 126, no. 3, pp. 210-214, 2000.
[11] V. A. Vanoni, “Transportation of suspended sediment by water,” Transaction of ASCE, vol. 111, pp. 67-133, 1946.
[12] H. A. Einstein, and N. Chien, “Effects of heavy sediment concentration near the bed on velocity and sediment distribution,” U. S. Army Corps of Engineers, Missouri River Division Rep. No.8, 1955.
[13] V. A. Vanoni, and G. N. Nomicos, “Resistance properties in sedimentladen streams,” Trans., ASCE, vol. 125, pp. 1140-1175, 1960.
[14] C. Elata, and A. T. Ippen, “The dynamics of open channel flow with suspensions of neutrally buoyant particles,” Technical Report No.45, Hydrodynamics Lab, MIT. 1961.
[15] N. L. Coleman, “Effects of suspended sediment on the open-channel velocity distribution,” Water Resources Research, vol. 22, no. 10, pp. 1377-1384, 1986.
[16] G. Parker, and N. L. Coleman, “Simple model of sediment-laden flows,” Journal of Hydraulic Engineering, ASCE, vol. 112, no. 5, pp. 356-375, 1986.
[17] F. Cioffi, and F. Gallerano, “Velocity and concentration profiles of solid particles in a channel with movable and erodible bed,” Journal of Hydraulic Engineering, ASCE,, vol. 129, no. 3, pp. 387-401, 1991.
[18] J. Guo, “Turbulent velocity profiles in clear water and sediment-laden flows,” Ph.D. dissertation, Colorado State University, Fort Collins, CO 1998.
[19] X. Wang, and N. Qian, “Turbulence Characteristics of Sediment-Laden Flow,” Journal Hydraulic Engineering, vol. 115, no. 6, pp. 781-800, 1989.
[20] S. Q. Yang, S. K. Tan, and S. Y. Lim, “Velocity Distribution and Dip-Phenomenon in Smooth Uniform Open Channel Flows,” Journal Hydraulic Engineering, vol. 130, no. 12, pp. 1179-1186, December 2004.
[21] X. Wang, Z. Y. Wang, M. Yu, and D. Li, “Velocity profile of sediment suspensions and comparison of log-law and wake-law,” Journal Hydraulic Research, vol. 39, no. 2, pp. 211-217, 2001.
[22] J. Guo, and P. Y. Julien, “Turbulent velocity profiles in sediment-laden flows,” Journal Hydraulic Research, vol. 39, no. 1, pp. 11-23, 2001.