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<br />.1
<br />
<br />.
<br />
<br />HYDRAULIC ENGINEERING ...
<br />
<br />690
<br />
<br />. ed (I r the latter case. According to what is
<br />some of lhe proposed formulae is obtaln 0 hiD is approximalely equal 10 lhe
<br />shown in Fig 3, lhis is mainly due 10 :~e.::",lld:SCh:~e (50 m'ls for Ihe protOlype)
<br />bed D of the bed sediment when alm_, 109 sented by this size when
<br />. ~-Aed " e' lhe pavement layer is better repre
<br />IS exca;u , ., .
<br />raJ'zed bedload Irnnsport begIns.
<br />genel _'
<br />I.H --
<br />
<br />
<br />
<br />~
<br />
<br />0.'
<br />!~
<br />.
<br />OM
<br />l~~
<br />In'
<br />.
<br />I." --'-';;-_-,,!,~
<br />1-11' -- ~--- ..--- J - .--' ~
<br />I t '_.......-.""0_
<br />
<br />\'.
<br />"~
<br />,
<br />i... --- -- --
<br />
<br />...
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<br />u,-- --.- --,-.,--..---,
<br />, , J.-........ ~fM.~
<br />
<br />..
<br />
<br />[J....~..-
<br />
<br />0_.....
<br />
<br />Figure I. Energy loss eq"'li~ based on Dill
<br />Strickler coeffiCient funn
<br />
<br />F' ... E.nctov loss equations based on D'lII
<br />Ilure ~. 0.1 .
<br />Slrikler coefficlC:n1 form
<br />
<br />.., -- --" --
<br />
<br />u-
<br />
<br />
<br />u.
<br />
<br />r" ---
<br />r:
<br />
<br />".
<br />I....
<br />
<br />'. f'::', n ~..I'1
<br />'.~.,,~~,-
<br />u ~--'h
<br />- ----=:.:: ;z .. ..
<br />..
<br />
<br />u
<br />1 ..
<br />., ,-- D
<br />~ .. D
<br />00.'
<br />B ..
<br />.-1 ~ .-
<br />
<br />..
<br />
<br />..
<br />o_~ --
<br />
<br />d'
<br />
<br />O,J, 50
<br />
<br />100 150 zoo 2!1O )00 '50
<br />...~IlIItI"lr.(rtd,,)
<br />
<br />..,
<br />,
<br />
<br />,---,- ~-~ .~
<br />
<br />Pi ure 4. proposed energy loss re'altlon~ fnr
<br />g model and prot()t.ype da18
<br />
<br />F. . D pavement di.meler variation
<br />Igutt'.:J. >>
<br />with discharge (model)
<br />
<br />. I and (2) are used for data filling purposes.
<br />If relations of Ihe form gIven by eqs.( ~ obta'ned'
<br />h . F'lg 4 lhe following equallons are I .
<br />assownm ,
<br />
<br />(5)
<br />
<br />v/ u. = 5.75 log 10 (4.86 R / n.,)
<br />
<br />v/ u. = 3.30 (R/ n.,)0.l1
<br />. eals that different numerical coefficients arC
<br />A comparision of eq.(5) wllh eq. (4) rev Ilh h for lhe former il has been shown
<br />obtained for "real" stream and /Ium~ data, a he O~g to Ihe in/luence of lhe slrcom
<br />Ihat original bed D.. '" D.,~, ThIS may d':" n idealized prismalic-al channel.
<br />geometry because flume expenments correspon 0 a
<br />
<br />(61
<br />
<br />.
<br />
<br />FLOW-BED INTERACTION
<br />
<br />691
<br />
<br />Final discussion
<br />The results of the investigalion reported herein show that energy loss in mountain
<br />torrents can be predicted using Keulegan type of relations, provided that a relative
<br />submergence based on a sediment size representative of the pavement layer
<br />roughness is used. This pavement roughness may be predicted directly by an
<br />independent method or estimated using a larger fraction size of lhe original bed
<br />sediment size distribution. However. it appears that energy IOS5 predictions based on
<br />"real" stream and flume data are different, probably due to lhe influence of the
<br />stream geometry. This is a topic which needs further research. The use of a
<br />prediCled pavement roughness may prove to be a better approximation 10 reality if
<br />lhe bed becomes paved hy /low conditions differenllo those presenlly exisling
<br />
<br />Acknowledgements
<br />The financial support of lhis study was pruvided partially by lhe Civil Engineering
<br />Department of lhe Universily of Chile and lhe National Fund for Scienlific and
<br />Technologycal Development-Chile (FONDECYD, through Proyeclo N"1079/92.
<br />
<br />Rerereot'es
<br />Ayala. L. and Oyarce, 0.(1993). " Energy loss in mountain slreams conditioned by
<br />armouring and beload lrnnsport". XI Chilean Congress, Chilean Sociely of Hydraulic
<br />Engineering, Concepcion, Chile (Spanish).
<br />Ayala, L. (1993). "Flow resistance and sedimenllranspon relalions for high froude
<br />numbers over graded gravel beds" IAHR XXV Congress Tokyo, Japan Sept
<br />Ayala, L. (1991). "Effecl of bed pavemenl on grain resistance 10 /low of mountain
<br />rivers". IAHR XVIV Congress, Madrid, Spain Sept.
<br />Bathurst, J,C. (1985). Flow resistance estimation in mountain rivers. Journal of (he
<br />Hydraulics Division, ASCE, Vol, II N"4, April.
<br />Btay, D.I.(198O). Evalualion of effeclive boundary roughness for gtavel-bed rivers.
<br />Journal of Civil Engineering, Vol. 7, 1980.
<br />Burkham, D.E. and Dawdy, D.R.(1976). Resistance equalion for alluvial-channel
<br />/low. Journal of lhe Hydraulics Division, ASCE, Vol. 102, N"HYIO. Oclober.
<br />Gessler, J. (1965). "Tbe beginnig of bedload movemenl of mixlures invesligaled as
<br />natural armoring in channels". Caltech.
<br />Griffilhs, G. (1981). Flow resistance in gravel-bed rivers". Journal of Ihe Hydraulics
<br />Division, ASCE, Vol.I07, N"HY7, July.
<br />Hey, R.D.(1979). Flow resistance in gravel-bed rivers'. Journal of the Hydtaulics
<br />Division, ASCE, Vol. 105, N"HY4 April.
<br />Jarrell, R.D.(I990). Hydrologic and hydraulic research in mountain rivers". Waler
<br />Res. Bull., A WRA, Vol. 26, N"3, Jun.
<br />Limerino, T.J., 1970. "Delerminalion of Manning coefficienl from measured hed
<br />roughness in natural rivers". U.S Geological Survey Waler Supply Paper 1898-B.
<br />
<br />(I) Prof., Civ.Eng.Dept.,Univ. of Chile, Casilla 228/3, Sanliago, Chile
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