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2 - Governing Equations

Published online by Cambridge University Press:  24 November 2022

Vijay P. Singh
Affiliation:
Texas A & M University
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Summary

Physically based approaches to hydraulic geometry relations for width, depth, velocity, and slope require equations of continuity of water, roughness, and sediment transport. Different methods have been employed for different expressions of roughness and sediment transport. Without delving into their underlying theories, this chapter briefly outlines these expressions as they will be invoked in subsequent chapters. Also, unit stream power, stream power as well as entropy have been employed, which are also briefly discussed.

Type
Chapter
Information
Handbook of Hydraulic Geometry
Theories and Advances
, pp. 30 - 64
Publisher: Cambridge University Press
Print publication year: 2022

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References

Ackers, P. (1964). Experiments on small streams in alluvium. Journal of Hydraulics Division, Vol. 90, No. 4, pp. 137.CrossRefGoogle Scholar
Ackers, P. and White, W. R. (1983). Sediment transport: new approach and analysis. Proceedings of Hydraulics Division, ASCE, Vol. 99, No. HY1, pp. 20412060.CrossRefGoogle Scholar
Bathurst, J. C. (1985). Flow Resistance estimation in mountain rivers. Journal of Hydraulic Engineering. ASCE, Vol. 111, No. 4, pp. 625643.CrossRefGoogle Scholar
Begin, Z. B. (1981). The relationship between flow-shear stress and stream patters. Journal of Hydrology, Vol. 52, pp. 307319.CrossRefGoogle Scholar
Bray, D. I. (1979). Estimating average velocity in gravel bed rivers. Journal of Hydraulics Division, ASCE, Vol. 105, pp. 11031122.CrossRefGoogle Scholar
Brown, C. B. (1950). Sediment Transport. Chapter 12 in Engineering Hydraulics, edited by Rouse, H., Wiley, New York.Google Scholar
Chang, H. H. (1979). Minimum stream power and river channel patterns. Journal of Hydrology, Vol. 41, pp. 303327.CrossRefGoogle Scholar
Charlton, F. G., Brown, P. M., and Benson, R. W. (1978). The hydraulic geometry of some gravel rivers in Britain. Report IT 180, Hydraulics Research Station, Wallingford.Google Scholar
Chitale, S. V. (1973). Theories and relationships of river channel patterns. Journal of Hydrology, Vol. 19, pp. 285308.CrossRefGoogle Scholar
Chow, V. T. (1959). Open Channel Hydraulics. McGraw-Hill Book Company, New York.Google Scholar
Cowan, W. L. (1954). Estimating hydraulic roughness coefficients. Agricultural Engineering, Vol. 37, No. 7, pp. 473475.Google Scholar
Dingman, S. L. and Sharma, K. P. (1997). Statistical development and validation of discharge equations for natural channels. Journal of Hydrology, Vol. 199, pp. 1335.Google Scholar
Einstein, H. A. (1942). Formulae for transportation of bed-load. Transactions, ASCE, Vol. 107, pp. 561577.Google Scholar
Einstein, H. A. (1950). The bed-load function for sediment transportation in open channel flows. Technical Bulletin No. 1026, U.S. Department of Agriculture, Soil Conservation Service, Washington, DC.Google Scholar
Einstein, H. A. and Chien, N. (1952). Second approximation to the solution of suspended load theory. Institute of Engineering Research, University of California, Berkeley, Issue 2, Series, 47.Google Scholar
Engelund, F. (1966). Hydraulic resistance of alluvial streams. Proceedings of Hydraulics Division, ASCE, Vol. 92, No. HY2, pp. 315326.CrossRefGoogle Scholar
Engelund, F. and Hansen, E. (1967). A nomograph on sediment transport in alluvial streams. Technical University of Denmark, Copenhagen. p. 63.Google Scholar
Fredsoe, J. (1982). Shape and dimensions of stationary dunes in rivers. Journal of Hydraulic Research, Vol. 108, No. 8, pp. 932946.Google Scholar
Griffiths, G. A. (1979). Rigid boundary flow resistance of gravel rivers. Ministry of Works Development, Water and Soil Division, Report WS127, p. 20.Google Scholar
Griffiths, G. A. (1981). Flow resistance in coarse gravel bed rivers. Journal of Hydraulics Division, ASCE, Vol. 107, No. HY7, pp. 899918.CrossRefGoogle Scholar
Henderson, F. M. (1966). Open Channel Flow. Macmillan, New York, p. 522.Google Scholar
Hey, R. D. (1979). Flow resistance in gravel bed rivers, Journal of Hydraulics Division, ASCE, Vol. 105, pp. 365379.Google Scholar
Hogg, I. G. G., Guganesharajah, K., Gunn, P. D. S., and Ackers, P. (1988). The influence of river regime on the flood management of Sukkur barrage, Pakistan. International Conference on River Regime, Hydraulics Research Station, Wallingford.Google Scholar
Holtorff, G. (1983). The evolution of meandering channels. Proceedings of the Second International Symposium on River Sedimentation, pp. 692705, Nanjing, China.Google Scholar
Jarrett, R. D. (1984). Hydraulics of high gradient streams. Journal of Hydraulic Engineering, Vol. 110, pp. 15191529.Google Scholar
Julien, P. Y. and Wargadalam, J. (1995). Alluvial channel geometry: Theory and applications. Journal of Hydraulic Engineering, Vol. 121, No. 4, pp. 312325.Google Scholar
Kellerhals, R. (1987). Stable channels with gravel-paved beds. Journal of Waterways Division, ASCE, Vol. 93, No. 1, pp. 6384.CrossRefGoogle Scholar
Keulegan, G. B. (1938). Laws of turbulent flow in open channels, Journal of Research, National Bureau of Standards, U.S., Vol. 21, pp. 707741.CrossRefGoogle Scholar
Lane, E. W. and Carlson, E. J. (1953). Some Factors Affecting the Stability of Canals Constructed in Coarse Granular Materials. International Association for Hydraulic Research, Minneapolis, MN.Google Scholar
Leopold, L. B. and Maddock, J. T. (1953). The hydraulic geometry of stream channels and some physiographic implications. U.S. Geological Survey Professional Paper 252, pp. 1–57.Google Scholar
Leopold, L. B. and Wolman, M. G. (1957). River-channel patterns: braided, meandering and straight. USGS Professional Paper 282-B, U.S. Geological Survey, Washington, DC, pp. 3885.Google Scholar
Leopold, L. B., Wolman, M. G., and Miller, J. P. (1964). Fluvial Processes in Geomorphology, W. H. Freeman, San Francisco.Google Scholar
Limerinos, J. T. (1970). Determination of the Manning coefficient from measured bed roughness in natural channels.Google Scholar
Low, H. S. (1980). Effect of sediment density on bed-load transport. Journal of Hydraulic Engineering, Vol. 115, No. 1, pp. 124138.Google Scholar
Meyer-Peter, E. and Muller, R. (1948). Formula for bed load transport. International Association of Hydraulic Research, Second meeting, Stockholm, p. 39.Google Scholar
Mussetter, R. A. (1989). Dynamics of mountain streams. Ph.D. Dissertation, Department of Civil Engineering, Colorado State University, Fort Collins.Google Scholar
Pacheco-Ceballos, R. (1990). Transport of sediments: Analytical solution. Journal of Hydraulic Research, Vol. 27, No. 4, pp. 501518.Google Scholar
Riggs, H. C. (1976). A simplified slope-area method for estimating flood discharges in natural channels. Journal of Research, U.S. Geological Survey, Vol. 4, pp. 285291.Google Scholar
Shannon, C. E. (1948). A mathematical theory of communications, I and II. Bell System Technical Journal, Vol. 27, pp. 379443.CrossRefGoogle Scholar
Simons, D. B. and Richardson, E. V. (1966). Resistance to flow in alluvial channels. U.S. Geological Survey Professional Paper 422-J, Washington, DC.CrossRefGoogle Scholar
Smart, G. M. (1984). Sediment transport formula for steep channels. Journal of Hydraulic Engineering, Vol. 110, No. 3, pp. 267276.CrossRefGoogle Scholar
Sonkar, R. K. and Ram, S. (2014). Flow resistance in gravel bed rivers. IJSRD - International Journal for Scientific Research & Development| Vol. 2, No. 07, 2014 | ISSN (online): 2321-0613.Google Scholar
Straub, I. G. (1954). Terminal Report on Transportation Characteristics: Missouri River Sediment. University of Minnesota, St Anthony Falls Hydraulics Laboratory, Sediment Series No. 4. Minneapolis.Google Scholar
Strickler, A., (1924), Beiträge zur Frage der Geschwindigheitsformel und der Rauhigkeitszahlen für Strome, Kanale und Geschlossene Leitungen. Mitteilungen des Eidgenössischer Amtes für Wasserwirtschaft, Bern, Switzerland.Google Scholar
van Rijn, L. C. (1984). Sediment transport, Part II. Journal of Hydraulic Engineering, Vol. 110, No. 11, pp. 16131641.CrossRefGoogle Scholar
White, C. M. (1940). The equilibrium of grains on the bed of an alluvial channel. Proceedings of Royal Society, London, Series A, Vol. 174, p. 322.Google Scholar
White, W. R., Bettess, R., and Wang, S. (1987). Frictional characteristics of alluvial streams in lower and upper regimes. Proceedings, Institution of Civil Engineers, Vol. 83, No. 2, pp. 685700.Google Scholar
White, W. R., Milli, H., and Crabe, A. D. (1973). Sediment Transport: An Appraisal of Available Methods. Vol. 2: Performance of theoretical method when applied to flume and field data. Report INT 119, Hydraulic Research Station, Wallingford.Google Scholar
Wong, M., and Parker, G. (2006). Reanalysis and correction of bed-load relation of Meyer-Peter and Müller using their own database. Journal of Hydraulic Engineering, Vol. 132, No. 11, pp. 11591168.Google Scholar
Yalin, M. S. (1963). An expression for bed-load transportation. Journal of the Hydraulics Division, Vol. 89, No. 11, pp. 221250.CrossRefGoogle Scholar
Yang, C. T. (1973). Incipient motion and sediment transport. Journal of Hydraulics Division, ASCE, Vol. 99, pp. 16791704.CrossRefGoogle Scholar
Yang, C. T. (1976). Minimum unit stream power and fluvial hydraulics. Journal of Hydraulics Division, ASCE, Vol. 102, No. HY7, pp. 919934.Google Scholar
Yang, C. T. (1977). The movement of sediment in rivers. Geophysical Surveys, Vol. 3, pp. 3968.CrossRefGoogle Scholar
Yang, S. Q., Tan, S. K., and Lin, S. Y. (2005). Flow resistance and bed form geometry in a wide alluvial channel. Water Resources Research, Vol. 41, W09419, doi: 10.1029/2005WR004211.Google Scholar

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  • Governing Equations
  • Vijay P. Singh, Texas A & M University
  • Book: Handbook of Hydraulic Geometry
  • Online publication: 24 November 2022
  • Chapter DOI: https://doi.org/10.1017/9781009222136.003
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  • Governing Equations
  • Vijay P. Singh, Texas A & M University
  • Book: Handbook of Hydraulic Geometry
  • Online publication: 24 November 2022
  • Chapter DOI: https://doi.org/10.1017/9781009222136.003
Available formats
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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Governing Equations
  • Vijay P. Singh, Texas A & M University
  • Book: Handbook of Hydraulic Geometry
  • Online publication: 24 November 2022
  • Chapter DOI: https://doi.org/10.1017/9781009222136.003
Available formats
×