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<br />26 were demonstrated by Figs. 6, 8, and 10. These phenomena were supponcd
<br />by the best data available to the writer. The slight scatterings in Figs. 7.9.
<br />and II are mainly due to the fact that these data werc not collected under ,
<br />the condition that only one variable was allowed to vary while other variabks
<br />remained unchanged. It would be of great interest to compare the accuracy
<br />of Eq. 26 and other equations by means of a comparison among calculated ;,
<br />results from different equations and the measured results of a natural river.
<br />Vanoni, ct al. (33), used some well-known equations for the computation at
<br />the total sediment discharge and made a comparison with the measured data ,~~
<br />from Niobrara River (4). As shown in Fig. Ii, these computed results arc iD
<br />great disparity with the measurements. When the total sediment concentrations; ~:
<br />':~
<br />calculated by Eq. 26 were multiplied by their corresponding water discharges
<br />and then plotted on Fig. 12, they agree very well with the measured data. ,,(>
<br />The superiority of Eq. 26 over the other equations is apparent.
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<br />SUMMARY AND CONCLUSIONS
<br />
<br />Two interrelated problems, incipient motion and sediment transport, have
<br />been studied in this paper. An exhaustive search of published related data was
<br />made to support the theories proposed herein.' The data llsed in determining
<br />the criterion for incipient motion cover the hydraulically smooth, transition.
<br />and completely rough regimes. The data used in verifying the proposed dimen.
<br />sionless unit stream power equation cover diversified conditions with particle
<br />size ranging from 0.15 mm to 1.71 mm; channel width from 0.44 ft (0.134 m)
<br />to 1,746 ft (532 m); channel depth from 0.037 ft (0.010 m) to 49.9 ft (15.2
<br />m); water temperature from 00 C to 34.30 C; average water velocity from 0.75
<br />fps (0.229 mps) to 6.45 fps (1.97 mps); slopc from 0.000043 to 0.0279; and
<br />total sediment concentration from 10 ppm to 585,000 ppm. This study has reached
<br />the following conclusions:
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<br />1. The writer has some reservations on using Shields diagram as the criterion
<br />for incipient motion. Derived from basic concepts in fluid mechanics and boundary
<br />laycr thcory, and supportcd by 153 sets of data indcpcndcnUy collected by
<br />eight investigators, Eqs. 18 and 19 should provide engineers with a simple and
<br />direct criterion for incipient motion. These two equations may also be considered
<br />as a scour criterion for stable channel design and other related engineering
<br />designs.
<br />2. The concept of equiiibrium or maximum concentration is very useful in
<br />simplifying the problem of sediment transport. Alluvial channel flow can be
<br />maintained at an equilibrium condition only if the condition that (VS - V crS)/ Cf
<br />is maintained at a minimum value can be satisfied. This maximum or equilibrium
<br />concentration per effective unit stream power depends on the constraints applied
<br />to the flow.
<br />3. The concept of unit stream power obtained from the study of stream
<br />morphology, which deals with the cumulated result of sediment transport, is
<br />shown applicable to the study of sediment transport itself. Unit stream power
<br />is the most important variable in the study of total sediment concentration.
<br />4. The concept of unit stream power can be applied to the study of sediment
<br />transport despite the existence of different bed configurations. This concept
<br />
<br />.
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<br />INCIPIENT MOTION
<br />'j 10 . I' h
<br />;' . f a frecly dcveloped allUVIal channc WIt
<br />'can also be apphed to the sftudY 0 . ht to mcandering, and finally to a braided
<br />its channel patterns changmg rom stratg
<br />channel. . I' t temperature and water
<br />'. 5. The effects of the. variations of par~lc e Size, ':t~e~r These studi'es indicate
<br />'depth on the total s~dhlment cOfnct~~t~~~~n c~~~a~\~risti~S of sediment transport
<br />that Eq. 26 agrees Wit some 0
<br />observed in alluvial channels. _. .. E 26 is simple and straightfor-
<br />6. the computation proc~ss Involved .In USl?g lq. nal sis and concepts of unit
<br />ward. This equation is derIved from dlm~nslOnad ~ Y 'f'ed by data obtained
<br />. t hon an IS ven I
<br />stream power and maximum conce~~;al st;eams which cover diversified fl?w
<br />from laboratory flumes and ~om~ na. I E 26 with the incipient mohon
<br />, and sediment co~ditions. ThiS dimen;I~~ e~ss pr~.pos~d herein for engineers to
<br />criterion determlOed by Eqs. 18 an , 1 . . both laboratory flumes
<br />use in predicting the total sediment concentratIOn In
<br />and natural streams.
<br />
<br />
<br />ACKNOWLEDGMENT
<br />
<br />" art b the Water Resources Center of the
<br />This study was supportcd 10 P 14 31~OOOI-3881 Office of Water Resources
<br />University of IIhnOls under Grant ' . Th 'ks are due to T Maddock,
<br />U S D t en! of the Intenor. an ' .
<br />Research, '.. eiar m d B C Yen for their review of the manuscnpt and
<br />Jr., C. F. Nord~n, . r., an .. writer a reciates the assistance offered
<br />suggestions for Its Improveme~t. TheS S k PP d R A Sinclair in computer
<br />by C. G. Lnnnquist, J. C. NeIll, A. . cvu, an . .
<br />analysis.
<br />
<br />APPENDIX (.-REFERENCES
<br />
<br />ld R A "An Approach to the Scdiment Transport Problem from General
<br />I. Bagno , ... . IS P 'essional Paper 422-1, 1%6. 37 pp.
<br />Physics, ,. U.S. Geologica urvey roJ'O d' " f "Sediment Transportation
<br />D I Hand Herbertson, J. ., ISCUSSlon 0 . f S d' t
<br />2. Barr. . ." .., h Task Committee on PreparatIOn 0 e (men a-
<br />Mechanics: Initialion of MotIon, .bY t c. Y"t A Yanoni Chmn. Journal of the
<br />. M I Committee on Sedimentation, 10. , , 1%6
<br />tlon a~ua.... SCE Y I 92 No HY6 Proc. Paper 4959. Nov.. , pp.
<br />HydrauliCS DIVISIOn, A ,0 . , . ,
<br />248-2:3.N H "Mechanics of Streams with Movable Beds of Fine Sand,.' Proceedings.
<br />3. Broo s, . .. N 668 A 1955 pp 668-1-668,28.
<br />ASCE, Vol. 81, Separate o. ,HPr....C m' uw"tion of Total Sediment Discharge,
<br />4. Colby, B. ~., and HemdbreeN. Cb' k.... UOSPGeological Survey Water-Supply Paper
<br />Niobrara River near Co y, eras a. ..
<br />1357, 1955. 187 .~p. 'r W t r Temperature on Bcd-Load Movement,'. Journal
<br />5. Franco, J. J., Effccts 0 b a CD' .' ASCE Vol 94, No. WW3, Proc. Paper
<br />of the Waterways and Har ors IVISlOn, ,.
<br />6083 Aug" 1%8. pp. 343-352. . . WI" U.S. Geological
<br />G'lb' t K G "The Transportation of Dcbns by Runnmg a er,
<br />6. I er, . ., . 3
<br />Survey Professional P~per 86, .9.14,26 TPP, rt M Graw-HiII Book Co. Inc., New
<br />7. Graf, H. P., HydrauliCS of Sediment ranspo, c
<br />York. N.Y., 1971,513 pp. d' h d E V "Summary of Alluvial Channel
<br />G H P Simons D B an RIC ar son, . ., d pl' I
<br />8. uy, ." ,..., 1956-1961" US Geological Survey an rOJcsslOna
<br />Data from Flume Expenment, ,. .
<br />Paper 462-1, 1966,96 pp. 'k D Q "Investigations of Sediment Transportation,
<br />9. Hubbell, D. W.., and Matej .a, N' b';aska ,. US. Geological Survey Water-Supply
<br />Middle Loup River at Dunnmg, e , .
<br />Paper 1476, 1959. 123 pp.
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