Velocity Distribution in Uniform Sediment‐Laden Flow
Publication: Journal of Hydraulic Engineering
Volume 118, Issue 2
Abstract
A theoretical model to predict the velocity distribution for sediment‐laden flow is developed by means of a new mixing‐length concept. The solution is obtained as a function of the vertical sediment concentration. The von Kármán coefficient is independent on suspended load and equal to 0.4. The model is applicable to an alluvial‐bed condition as well as a flat‐bed condition. The possibility of adapting the model to clear‐water flow is also discussed. For clear‐water flow, the velocity equation consists of a logarithmic term and power‐series terms that explain the wake effect. The theoretical velocity distribution for sediment‐laden flow departs from the logarithmic law in the outer layer. The magnitude of the departure is larger with the increase in the sediment load. The numerical calculation is carried out and its prediction is compared to five independent sets of experimental data previously obtained. The theoretical result shows good agreement in the whole flow layer with these experimental results.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Cardoso, A. H., Graf, W. H., and Gust, G. (1989). “Uniform flow in a smooth open channel.” J. Hydr. Res., 27(5), 603–616.
2.
Clauser, F. H. (1956). “The turbulent boundary layer.” Advance in applied mechanics 4, H. L. Dryden and T. von Kármán, eds., Academic Press, New York, N.Y., 1–51.
3.
Coleman, N. L. (1981). “Velocity profiles with suspended sediment.” J. Hydr. Res., 19(3), 211–229.
4.
Coles, D. (1956). “The law of the wake in the turbulent boundary layer.” J. Fluid Mech., 1, 191–226.
5.
Einstein, H. A., and Chien, N. (1955). “Effects of heavy sediment concentration near the bed on the velocity and sediment distribution.” Report No. 8, U.S. Army Corps of Engrs. Missouri River Div. Univ. of California, Berkeley, Calif.
6.
Graf, W. H. (1971). Hydraulics of sediment transport. McGraw‐Hill Book Co., Inc., New York, N.Y.
7.
Hino, M. (1963). “Turbulent flow with suspended particles.” J. Hydr. Div., ASCE, 89(4), 161–185.
8.
Hinze, J. O. (1959). Turbulence: An introduction to its mechanism and theory. McGraw‐Hill Book Co., Inc., New York, NY.
9.
Imamoto, H., Asano, T., and Ishigaki, T. (1977). “Experimental investigation of a free surface shear flow with suspended sand grains.” Proc. 17th Congress, International Association for Hydraulic Research, 1, 105–112.
10.
Ismail, H. M. (1957). “Turbulent transfer mechanism and suspended sediments in closed channels.” Proc., ASCE, 77(56), 1–26.
11.
Itakura, T., and Kishi, T. (1980). “Open channel flow with suspended sediments.” J. Hydr. Div., ASCE, 106(8), 1325–1343.
12.
Klebanof, P. S., and Diehl, Z. W. (1951). “Some features of artificially thickened fully developed turbulent boundary layers with zero pressure gradient.” TN2475, National Advisory Committee for Aeronautics, Washington, D.C., 1–55.
13.
Lau, Y. L. (1983). “Suspended sediment effect on flow residence.” J. Hydr. Div., ASCE, 109(5), 757–763.
14.
Laufer, J. (1951). “Investigation of turbulent flow in a two‐dimensional channel.” Report 1033, National Advisory Committee for Aeronautics, Washington, D.C.
15.
Millikan, C. B. (1939). “A critical discussion of turbulent flows in channels and circular tubes.” Proc. 5th Int. Congress of Appl. Mech., Cambridge, Mass., 386–392.
16.
Monin, A. S., and Yaglom, A. M. (1971). Statistical fluid mechanics: Mechanics of turbulence. MIT Press, Cambridge, Mass.
17.
Nikuradse, J. (1932). “Gesetzmässigkeiten der turbulenten Strömung in glatten Röhrn.” Forschungsheft 356, Vereines Deutscher Ingenieure, 3 (in German).
18.
Prandtl, L. (1932). “Zur turbulenten Strömung in Röhren und längs Platten.” Ergebn. Aerodyn. Versuchsanst, Göttingen, 4, 18–29 (in German).
19.
Reynolds, O. (1895). “On the dynamical theory of incompressible viscous fluids and determination of the criterion.” Phil. Trans. Roy. Soc., A123–164.
20.
Rouse, H. (1937). “Modern conceptions of the mechanics of fluid turbulence.” Trans. of ASCE, 102, 463–543.
21.
Samaga, B. R., Rangaraju, K. G., and Garge, R. J. (1986). “Velocity distribution in alluvial channel flow.” J. Hydr. Res., 24(4), 297–308.
22.
Schultz‐Grunow, F. (1940). “Neues Reibungswiderstandgesetz für glatte Platten.” Luftfahrtforsch, 17(8), 239–246.
23.
Townsend, A. A. (1956). The structure of turbulent shear flow. Cambridge Univ. Press, Cambridge, Mass.
24.
van Kampen, H. F. A., and Nap, E. N. (1988). Sediment concentrations and sediment transport in case of irregular non‐breaking waves with a current. Delft Univ. of Tech., Delft, the Netherlands.
25.
Vanoni, V. A. (1946). “Transportation of suspended sediment by water.” Trans., ASCE, 111, 67–133.
26.
Vanoni, V. A., and Nomicos, G. N. (1960). “Resistance properties of sediment‐laden structures.” Trans., ASCE, 125(3055), 1140–1167.
27.
von Kármán, T. (1930). “Mechanische Ähnlichkeit und Turbulenz.” Nachr. Ges. Wiss. Göttingen, Math.‐Phy. Kl., 58‐76 (in German).
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 118 • Issue 2 • February 1992
Pages: 229 - 245
Copyright
Copyright © 1992 ASCE.
History
Published online: Feb 1, 1992
Published in print: Feb 1992
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.