Velocity Distribution in Open Channels: Combination of Log-law and Parabolic-law
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.
[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.
[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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:59593", author = "Snehasis Kundu and Koeli Ghoshal", title = "Velocity Distribution in Open Channels: Combination of Log-law and Parabolic-law", 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.", volume = "6", number = "8", pages = "1071-8", }
