<br />
<br />HY10 INCIPIENT MOTION
<br />'<. '32. Vanoni, V. A., and Brooks, N. H.t "Laboratory Studies of the Rou~hness a~d
<br />Suspended Load of Alluvial Streams," Sedimentation Labo.ratory MRD Sedtment Serres
<br />No. II. California Institute of Technology, Pasadena, Cahf., Dec., 1957. pp. 35-:36.
<br />33. Vanoni. V. A., Brooks, N. H.t and Kennedy, J. F., "Lecture Notes on Sediment
<br />Transportation and Channel Stability," Report KH-RI, W. H. Kcck Laboratory.of
<br />Hydraulics and Water Resources, California Institute of Technology, Pasadena, Cahf.,
<br />1%0, 140 pp. . f S d' L d
<br />34. Vanoni, V. A., and Nomicos, G. N., "Resistance Properties 0 c Imcnt~ a cn
<br />Streams," Journal of the Hydraulics Division, ASCE. Proe. Paper 2020. May, 1959,
<br />pp.77-107. . 1 Ch I"
<br />35. White, C. M., "The Equilibrium of Grains on the Bcd. of an Alluvia anne,
<br />Proceedings of the Royal Society, London, England, Senes A, Vol. 174, 1940, pp.
<br />332-338. S d" U S
<br />36. Williams, G. P., "Flume Experiments on the Transport of a Coarse an, ..
<br />Geological Survey Professional Paper 562-B, 1%7, 31 pp.
<br />37. Yang, C. T., "Potential Energy and Stream Morphology," Water Rescources Research,
<br />Vol. 7, No.2. Apr., 1971, pp. 311-322.
<br />38. Yang, C. T., "On River Meanders," Journal of Hydrology, Vol. 13, No.3, 1971,
<br />pp.231-253.
<br />39. Yang, C. T., "Formation of Riffles and Pools," Water Resources Research, Vol.
<br />7 No.6, Dcc.. 1971. pp. 1567-1574. .
<br />40 Yang C T "Unit Stream Power and Sediment Transport," Journal of the Hydrauhcs
<br />. Division: A'SCE, Vol. 98, No. HYlO, Proc. Paper 9295, Oct., 1972.. pp. ~805,~1826.
<br />41. Yang, C. T., and Sayre, W. W., "Stochastic Model for Sand DisperSIOn, Journal
<br />of the Hydraulics Division, ASCE, Vol. 97, No. HY2, Proc. Paper 7892, Feb., 1971,
<br />pp. 265-288.
<br />
<br />OCTOBER 1973
<br />
<br />HY10
<br />
<br />~,: .
<br />
<br />10. Jordan, P. R., "Fluvial Sediment of the Mississippi River at 51. Louis, Missouri,"
<br />U.S. Geological Survey Water-Supply Paper 1802, 1965,89 pp.
<br />11. Kalinske, A. A., "Criteria for Determining Sand-Transport by Surface-Creep and
<br />Saltation," TranslJctions, American Geophysical Union, 1942, pp. 639-643.
<br />12. Kennedy, J. F., "Stationary Waves and Antidunes in Alluvial Channels," W. M.
<br />Keck Laboratory of Hydraulics and Water Resources Report No. KH-R-2, Californi.1.
<br />Institute of Technology, Pasadena, Calif., Jan., 1%1, 110 pp.
<br />13. Kramer, H., "Sand Mixtures and Sand Movement in Fluvial Models," Transactions.
<br />ASCE. Vol. tOO, Paper No. 1909. 1935, pp. 798-838.
<br />14. Liu, H. K., closure to "Mechanics of Sediment-Ripple Formation," Journal of ,ht
<br />Hydraulics Division, ASCE, Vol. 84, HY5, Proc. Paper 1832, Oct., 1958, pp. 1832-10..
<br />1832-12. !
<br />15. Maddock, T., Jr., "Hydraulic Relations for Sind-Bedded Streams," 5cdi~entation
<br />Symposium to honor Prof. H. A. Einstein, H. W. Shen, ed., 1972, pp. 15-1-15-22.
<br />16. Mostafa, M. G., discussion of "Effects of Water Temperature on Bed-Load Move-
<br />ment," by J. J. Franco, Journal of the Waterways and Harbors Division, ASCE,
<br />Yol. 95, No. WW2, Proc. Paper 6528, May, 1%9, pp. 244-247.
<br />17. Nomicos, G. N., "Effects of Sediment Load on the Velocity Field and Friclion
<br />Factor of Turbulent Flow in an Open Channel," thesis presented to the California
<br />Institute of Technology, at Pasadena, Calif., in 1956 in partial fulfillment of the
<br />requirements for the degree of Doctor of Philosophy.
<br />18. Schlichting, H., Boundary Layer Theory, 4th cd., translated by J. Kestin, McGraw-Hili
<br />Book Co. Inc., New York, N.Y., 1%2, pp. 509-526.
<br />19. Schumm, S. A., and Khan, H. R., "Experimental Study of Channel Patterns,"
<br />Geological Society of America Bulletin, Vol. 83, June, 1972, pp. 1755-1770.
<br />20. "Sediment Transportation Mechanics: Initiation of Motion," Progress Report of the
<br />Task Committee on Preparation of Sedimentation Manual, Vito A. Vanoni, Chmn,
<br />Journal of tlte Hydraulics Division, ASCE, Vol. 92, No. HY2, Proc. Paper 4738,
<br />Mar" 1%6. pp. 291-314.
<br />21. Shames. I. H., Mechanics of Fluids, McGraw-Hill Book Co. Inc., New York, N.Y.,
<br />1%2,322 pp.
<br />22. Shields, A., "Anwendung der Aenlichkcitsmechanik und der Turbulentzforschung auf
<br />die Gcschiebebewegung, Berlin, Germany, 1936; translated by W. P. Ott and J. C.
<br />van Uchelen as "Application of Similarity Principles and Turbulence Research to
<br />Bcd-Load Movement," California Institute of Technology, Pasedena, Calif.
<br />23. "Some Fundamentals of Particle Size Analysis," Report No. 12, Inter-Agency Commit-
<br />tee on Water Resources, Subcommittee on Sedimentation, SI. Anthony Falls Hydraulic
<br />Laboratory, Minneapolis, Minn., Dec., 1957,55 pp.
<br />24. Stall, J. B., and Yang, C. T., "Hydraulic Geometry and Low Streamflow Regimen,"
<br />University of Illinois Water Resources Center Research Report No. 54, July, 1972,
<br />31 pp.
<br />25. Steel, R. G. D., and Torrie, J. H., Principles and Proceedures of Statistics, McGraw-Hill
<br />Book Co., Inc., New York, N.Y., 1%0, pp. 284.
<br />26. Stein, R. A., "Laboratory Studies of Total Load and Apparent Bed-Load," Journal
<br />of Geophysical Research, Vol. 70, No.8, Apr., 1965, pp. 1831-1842.
<br />27. "Studies of River Bed Materials and Their Movement, with Special Reference to
<br />the Lower Mississippi River," Report No. 17, U.S. Waterways Experiment Station,
<br />1935. 161 pp.
<br />28. Taylor, B. D., and Vanoni, V. A., discussion of "Effects of Water Temperature
<br />on Bcd-Load Movement," by J. J. Franco, Journal of the Waterways and Harbors
<br />Division, ASCE, Vol. 95, No. WW2, Proc. Paper 6528, May, 1%9, pp. 247-255.
<br />29. Taylor, B. D., and Yanoni. V. A., "Temperature Effects in Low-Transport, Flat-Bed
<br />Flows," Journal of the Hydraulics Division, ASCE, Yol. 98, No. HY8, Proc. Paper
<br />9105. Aug., t972, pp. t427-1455.
<br />30. Tison, L. J., "Studies of the Critical Tractive Force of Entrainment of Bed Material,"
<br />Proceedings, International Association for Hydraulics Research, Minnesota Interna-
<br />tional Hydraulics Convention, Minneapolis, Minn., 1953, pp. 21-35.
<br />31. Vanoni, V. A., "Measurements of Critical Shear Stress for Entraining Fine Sediments
<br />in a Boundary Layer," California Institute of Technology, Pasadena, Calif., Report
<br />No. KH.R,7, May. 1%4.47 pp.
<br />
<br />The following symbols are used in this paper:
<br />
<br />coefficients related to I and J;
<br />roughness function;
<br />drag coefficients;
<br />total sediment concentration, in parts per million by weight;
<br />depth of water;
<br />median sieve diameter;
<br />drag, lift, and resistant forces acting on sediment particle,
<br />respectively;
<br />Darcy-Weisbach friction coefficient;
<br />gravitational acceleration; .
<br />coefficients in dimensionless unit stream power equatIOn;
<br />number of data;
<br />water discharge;
<br />total sediment discharge;
<br />wd/v = fall velocity Reynolds number;
<br />U.djv ~ shcar velocity Reynolds number;
<br />correlation coefficient between data and results predicted by ,
<br />equation;
<br />water surface slope or energy slope;
<br />shear velocity;
<br />average water velocity;
<br />critical average water velocity at incipient motion;
<br />local velocity at distance y above bed;
<br />
<br />APPEN~X n.-NOTATlON
<br />
<br />aI' a2, bl, b2
<br />B
<br />CD'C~
<br />C,
<br />D
<br />d
<br />
<br />FD' FL' FR
<br />
<br />f
<br />g
<br />I, J
<br />N
<br />Q
<br />
<br />.3
<br />
<br />q,
<br />R,(
<br />R"
<br />r
<br />
<br />S
<br />U.
<br />V
<br />
<br />v"
<br />V,
<br />
<br />
<br />.,
<br />
<br />~
<br />.1
<br />
<br />
|