Analytical Investigation of Longitudinal Velocity Theories in Flow Vertical Direction

Authors

1 Ph.D of water structures engineering, Sari Agricultural Sciences and Natural Resources University,Sari, Iran.

2 Faculty of Engineering, University of Maragheh, Maragheh, Iran.

3 Associate Professor, Department of Water Engineering, Sari Agricultural Sciences and Natural Resources University,Sari, Iran.

Abstract

< p >Computation of longitudinal velocity in the vertical direction and extracting the applied theories have been conventional manner from past years among the hydraulic engineers. In many previous investigations, the researchers have tried to extract some applied equations, separately, by dividing the flow depth namely from bed to water surface to various regions. As it is accepted by all of the researchers, the laminar sublayer zone has a linear velocity profile while out of this zone, the velocity simulation follows a logarithmic law which its accuracy in estimation of the velocity decreases by increasing the distance from the bottom of the channel. Also, it is not applicable for dip phenomenon which occurs bellow the free surface. In the current study, 12 experimental data series, operated under different experimental conditions, were collected from previous researches. Also, three common theories of log law, log- wake law, and modified log- wake law have been applied to simulate longitudinal velocity profile in the vertical direction. Finally, it is seen that the modified log- wake law has a better agreement with the experimental data, and also it can be operated for predicting the dip phenomenon bellow the free surface. For solving the equation of the mentioned theory, the factors of von Karman, wake strength, and shear velocity are assumed unknown. Then, the mentioned parameters have been extracted using a non-linear optimization technique of the least square curve fitting.

Keywords

References

Absi R, 2011. An ordinary differential equation for velocity distribution and dip- phenomenon in open channel             flows. Journal of Hydraulic Research 49(1):82-89.  
Bagnold BRA, 1955. Some flume experiments on large grains but little denser than the transporting fluid and their implications. Proceedings of the Institution of Civil Engineers 4(2):174-205.
Binesh N and Bonakdari H, 2014. Longitudinal velocity distribution in compound open channels: comparison of different mathematical models. International Research Journal of Applied and Basic Sciences :8(9):1149-1157.
Bonakdari H, 2007. Velocity profile in turbulent boundary layers. Pp. 1-6, 32nd Congress of the International Association of Hydraulic Engineering & Research, July, Venice, Italy.
Bonakdari H and Ahadi MS, 2013. Comparison of different models for evaluating the velocity profiles in narrow sewers. Journal of Basic and Applied Scientific Research 3(12):273-288.
Chiu CL, 1987. Entropy and probability concept in hydraulics. Journal of Hydraulic Engineering, ASCE 113(5):583-600.
Cioffi F and Gallerano F, 1991. Velocity and concentration profiles of solid particles in a channel with movable and erodible bed. Journal of Hydraulic Research 29(3):387-401.
Coles D, 1956. The law of the wake in the turbulent boundary layer. Journal of Fluid Mechanics 1(2):191-226.
Coleman NL, 1986. Effects of suspended sediment on the open- channel velocity distribution. Water Resources Research 22(10):1377-1384.
Einstein HA and Chein N, 1955. 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.
Elata C and Ippen AT, 1961. The dynamics of open channel flow with suspensions of neutrally buoyant particles. Technical Report No.45, Hydrodynamics lab MIT.
Gonzalez JA, Melching CS and Oberg KA, 1986. Analysis of open- channel velocity measurements collected with an acoustic Doppler current profiler. Pp.1-8, Reprint from RIVERTECH 96 Proceedings from the1st International Conference on New/Emerging Concepts for Rivers Organized by the International Water Resources Association Held September 22-26, 1996, Chicago, Illinois, USA.
Gosh TK, 2016. Logarithmic velocity profile for turbulent flow in straight rough pipe and evaluation of Karman constant with boundary layer Reynolds number- A complete solution. International Journal of Scientific & Engineering Research 7(2):157-162.
Guo J, 2013. Modified log-wake-law for smooth rectangular open channel flow. Journal of Hydraulic Research 52(1):121-128.
Guo J and Julien PY, 2003. Modified log-wake law for turbulent flow in smooth pipes. Journal of Hydraulic Research 41(5):493-501.
Jafari F, Abbaspour A and Hosseinzadeh Dalir A, 2016. Numerical investigation of velocity profiles in open channels with rough bed. Water and Soil Science-University of Tabriz 26(3.1):81-93. (In Farsi)
Kundu S and Ghoshal K, 2012. Velocity distribution in open channels: combination of log-law and parapolic-law. World Academy of Science, Engineering and Technology 6:2145-2152.
Meftah M and Moussa M, 2015. A modified log-law of flow velocity distribution in partly
obstructed open channels. Environmental Fluid Mechanic 16(2):453-479.
Nikuradse J, 1933. Laws of Turbulent Flow in Rough Pipes, Translation by National Advisory Committee for Aeronautics, Technical Memorandum 1292, NACA, Washington.    
Parker G and Coleman NL, 1986. Simple model of sediment-laden flows. Journal of Hydraulic Engineering 112:356-375.
Preston JH, 1954. The determination of turbulent skin friction by means of pitot tubes. Journal of Royal Aeronautical Society 58(518):109-121.
Sarma KVN, Prasad BVR and Sarma AK, 2000. Detailed study of binary law for open channels. Journal of Hydraulic Engineering 126:210-214.
Shiono K and Feng T, 2003. Turbulence measurements of dye concentration and effects of secondary flow on distribution in open channel flows. Journal of Hydraulic Engineering 129(5):373-384.
Stearns EP, 1883. A reason why the maximum velocity of water flowing in open channel is below the surface. Transactions of the Journal of American Society of Civil Engineers 7(1883):331-338.
Vanoni VA, 1946. Transportation of suspended sediment by water. Transactions of the American Society of Civil Engineers 111:67-133.
Vanoni VA and Nomicos GN, 1960. Resistance properties in sediment- laden streams. Transactions of the American Society of Civil Engineers 125:1140-1167.
Yang SQ, Tan SK and Lim SY, 2004. Velocity distribution and Dip phenomena in smooth uniform open channel flow. Journal of Hydraulic Engineering, ASCE 130(12):1179-1186.
Water and Soil Science
Volume 30, Issue 1
May 2020
Pages 15-28

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