Shear Stress in Smooth Rectangular Open-Channel Flows
This article has a reply.
VIEW THE REPLYThis article has a reply.
VIEW THE REPLYPublication: Journal of Hydraulic Engineering
Volume 131, Issue 1
Abstract
The average bed and sidewall shear stresses in smooth rectangular open-channel flows are determined after solving the continuity and momentum equations. The analysis shows that the shear stresses are function of three components: (1) gravitational; (2) secondary flows; and (3) interfacial shear stress. An analytical solution in terms of series expansion is obtained for the case of constant eddy viscosity without secondary currents. In comparison with laboratory measurements, it slightly overestimates the average bed shear stress measurements but underestimates the average sidewall shear stress by 17% when the width–depth ratio becomes large. A second approximation is formulated after introducing two empirical correction factors. The second approximation agrees very well ( and average relative error less than 6%) with experimental measurements over a wide range of width–depth ratios.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The writers thank the two anonymous reviewers and Associate Editor Professor D. A. Lyn for their critical and constructive comments.
References
Babaeyan-Koopaei, K., Ervine, D. A., Carling, P. A., and Cao, Z. (2002). “Velocity and turbulence measurements for two overbank flow events in River Severn.” J. Hydraul. Eng., 128(10), 891–900.
Berlamont, J. E., Trouw, K., and Luyckx, G. (2003). “Shear stress distribution in partially filled pipes.” J. Hydraul. Eng., 129(9), 697–705.
Bocchiola, D., Menduni, G., and Ward, D. (2003). “Testing block probes for wall shear stress measurement in water flows.” J. Hydraul. Eng., 129(1), 102–109.
Cheng, N. S. (2002). “Exponential formula for bedload transport.” J. Hydraul. Eng., 128(10), 942–946.
Chien, N., and Wan, Z. H. (1999). Mechanics of sediment transport, ASCE, New York.
Chiu, C. L., and Chiou, J. D. (1986). “Structure of 3-D flow in rectangular open-channels.” J. Hydraul. Eng., 112(11), 1050–1068.
Chiu, C. L., and Lin, G. F. (1983). “Computation of 3-D flow and shear in open channels.” J. Hydraul. Eng., 109(11), 1424–1440.
Coleman, N. L. (1986). “Effects of suspended sediment on the open-channel velocity distribution.” Water Resour. Res., 22(10), 1377–1384.
Cruff, R. W. (1965). “Cross-channel transfer of linear momentum in smooth rectangular channels.” Water-Supply Paper, 1592-B, U.S. Geological Survey, Center, Miss., B1–B26.
Einstein, H. A. (1942). “Formulas for the transportation of bed-load.” Trans. Am. Soc. Civ. Eng., 107, 561–597.
Ghosh, S. N., and Roy, N. (1970). “Boundary shear distribution in open-channel flow.” J. Hydraul. Div., Am. Soc. Civ. Eng., 96(4), 967–994.
Graf, W. (1971). Hydraulics of sediment transport, McGraw-Hill, New York.
Guo, J. (1998). “Turbulent velocity profiles in clear water and sediment-laden flows.” PhD dissertation, Colorado State Univ., Fort Collins, Colo.
Guo, J. (1999). “Discussion of Mechanism of energy transportation and turbulent flow in a 3D channel by S. Q. Yang and S. Y. Lim,” J. Hydraul. Eng., 125(3), 319–320.
Guo, J., and Julien, P. Y. (2001). “Turbulent velocity profiles in sediment-laden flows.” J. Hydraul. Res., 39(1), 11–23.
Guo, J., and Julien, P. Y. (2002). “Boundary shear stress in smooth rectangular open-channels.” Advances in Hydraulics and Water Engineering, Proc. 13th IAHR-APD Congress, Vol. 1, Singapore, 76–86.
Hu, C. H. (1985). The effect of the width/depth ratio and side-wall roughness on velocity profile and resistance in rectangular open-channels. MS thesis, Tsinghua Univ., Beijing.
Imamoto, H., and Ishigaki, T. (1988). “Measurements of secondary flow in an open channel.” Proc., 6th IAHR-APD Congress, Kyoto, Japan, 513–520.
Johnson, W. (1942). “The importance of side-wall friction in bed-load investigation.” Civ. Eng. (N.Y.), 12, 329–331.
Julien, P. Y. (1995). Erosion and sedimentation, Cambridge University Press, Cambridge, U.K.
Kartha, V. C., and Leutheusser, H. J. (1970). “Distribution of tractive force in open-channels.” J. Hydraul. Div., Am. Soc. Civ. Eng., 96(7), 1469–1483.
Keulegan, G. H. (1938). “Laws of turbulent flow in open-channels.” Natl. Bur. Stand. Circ. (U. S.), 21, 709–741.
Knight, D. W. (1981). “Boundary shear in smooth and rough channels.” J. Hydraul. Div., Am. Soc. Civ. Eng., 107(7), 839–851.
Knight, D. W., Demetriou, J. D., and Homed, M. E. (1984). “Boundary shear in smooth rectangular channels.” Agric. Water Manage., 110(4), 405–422.
Knight, D. W., and MacDonald, J. A. (1979). “Open-channel flow with varying bed roughness.” J. Hydraul. Div., Am. Soc. Civ. Eng., 105(9), 1167–1183.
Leighly, J. B. (1932). “Toward a theory of the morphologic significance of turbulence in the flow of water in streams.” Univ. of Calif. Publ. Geography, 6(1), 1–22.
Lundgren, H., and Jonsson, I. G. (1964). “Shear and velocity distribution in shallow channels.” J. Hydraul. Div., Am. Soc. Civ. Eng., 90(1), 1–21.
Lyn, D. A. (1986). “Turbulence and turbulent transport in sediment-laden open-channel flows.” Rep., W. M. Keck Laboratory of Hydraulics and Water Resources, California Institute of Technology, Pasadena, Calif.
Lyn, D. A. (2000). “Regression residuals and mean profiles in uniform open-channel flows.” J. Hydraul. Eng., 126(1), 24–32.
Muste, M., and Patel, V. C. (1997). “Velocity profiles for particles and liquid in open-channel flow with suspended sediment.” J. Hydraul. Eng., 123(9), 742–751.
Myers, W. R. C. (1978). “Momentum transfer in a compound channel.” J. Hydraul. Res., 16(2), 139–150.
Naot, D., and Rodi, W. (1982). “Calculation of secondary currents in channel flow.” J. Hydraul. Div., Am. Soc. Civ. Eng., 108(8), 948–968.
Nezu, I., and Nakagawa, H. (1993). “Turbulence in open-channel flows.” IAHR Monograph Series, A. A. Balkema, Rotterdam, The Netherlands.
Noutsopoulos, G. C., and Hadjipanos, P. A. (1982). “Discussion of Boundary shear in smooth and rough channels by D. W. Knight.” J. Hydraul. Div., Am. Soc. Civ. Eng., 108(6), 809–812.
Spiegel, M. R. (1993). Complex variables, McGraw-Hill, New York.
Tracy, H. J. (1965). “Turbulent flow in a three-dimensional channel.” J. Hydraul. Div., Am. Soc. Civ. Eng., 91(6), 9–35.
White, F. M. (1991). Viscous fluid flow, McGraw-Hill, New York.
Yang, S. Q., and Lim, S. Y. (1997). “Mechanism of energy transportation and turbulent flow in a 3D channel.” J. Hydraul. Eng., 123(8), 684–692.
Yang, S. Q., and Lim, S. Y. (1998). “Boundary shear stress distributions in smooth rectangular open channel flows.” Proc. Inst. Civ. Eng., Waters. Maritime Energ., 130(3), 163–173.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 131 • Issue 1 • January 2005
Pages: 30 - 37
Copyright
© 2004 ASCE.
History
Received: Jan 29, 2002
Accepted: Aug 9, 2004
Published online: Jan 1, 2005
Published in print: Jan 2005
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.