|
<br />CHANSON: COMMENTARY
<br />
<br />\)1.15
<br />
<br />magnitude in the longitudinal and lateral directions. Grallt's
<br />11')<)7, elJuati"ns (J), (H), and (13)1 use "I' empiriealllow resis-
<br />1.UH:C L'orrdalilllls imply a "uniformly distributed" boundary
<br />shear stress. SUL'h an assumption is fl.:futed by this paper's
<br />n;slIlts l Figure I).
<br />Further, Gmllf"s []l)l)71 developments deriving from his "hy-
<br />pu(lh::-.is" arc based 011 i:mpiriL:..ll correlations which do not
<br />rclkd the physiL'al natun..: of the energy losses nor the intcr~
<br /><.\1.:(io\1s bclwl.:Cll the now and the Illovabk boundaries. In an
<br />alluvial I.:l1ill1lld, the boundary friction is rdated to the skin
<br />lridillll (ur grain-relaLed J"ril.:lioll) and to thl: form losses
<br />caused by the bcJ forms. Althuugh lhi.: skin frictiun shear stress
<br />(ur I.:Jrcclivi.: she.Ll" slfL:SS) Illay be cakubh.::u accurately, thl.::
<br />L'~tilllah:: of thl.:: bL'd-form sl1.::u. ~tr.:ss is diflkult. Fundamcntal
<br />L'.\pl.:rillll.::nts in irn.:gular npL'1l ehannds [Kuz/!mipOllf amI Ape/t,
<br />19S.1] ~lh)wL'J that thi.;' hll"ln lossi.;'s cuuto account for up to lJ2%
<br />or the lolalloss. For unLlular !lows, thl.::re is little experimental
<br />lbta 10 pr.:uict aecuratl.::ly Ill.: form loss(:s associatl.::J with the
<br />~till1dillg \\"a\'.: beu furllls, but this situation dot:s not justify tht::
<br />u~c uf ..\J\crall hed sh.:ar stress" corrclalions.
<br />III ~ullllnary, GrllJ/(s 11l)97j hypothesis of critical flow cannot
<br />hI,.' cOI1~idl.:rcd as all ultimate simplitication. Tht:: pn.:scnt dis-
<br />cussi\Jll and tll.: works or I/lwi amI Nakaglllva [1992\, CJWI/SUIl
<br />Ill)l)) \. (.lulI/soll amI MUlIIes lllJlJ5], (iml tv!ollles alld ClEUI/SUIl
<br />II \Ni'.q highlightl.::u thc compkxity of undular Hows.
<br />
<br />Appendix: Calibration of Pitot Tuhe
<br />
<br />Th.: Pilot tubl.: ..va~ c:dihrall.:d in uniform Clluilihriunl Bows.
<br />Till,.' calillf:ttioll curvl.: (IJiLut tube velocity Vl.;'l"SllS boundary
<br />slle:ll" stress) was best lil1\,;'d by
<br />
<br />T" = 3.IS21 ViIl27-"
<br />
<br />was ~imildr to calibratioll curves ubtaineu by Preston! IlJ541 and
<br />rUld I ] ()1l51 and McllI/osh Ill)()()j who used the same t.;xperi-
<br />1111.:l1tal Ch<llllld. I kre To is the boundary sheilr ~trt.;ss and VI> is
<br />the vdocity measured by the Pitut tube lying on thl;; bed.
<br />
<br />Notation
<br />
<br />A cross-scctioll area (m:!),
<br />LJ free-surface width (m).
<br />/)1/ hydraulic diamt.;ter (m).
<br />" lIow depth (m),
<br />d,. critical nuw lkpth (m).
<br />E mean speeilie energy (01),
<br />I Darcy friction factor.
<br />y gravity con~lant (m/s2).
<br />J/ Jlli:<lll total head (111).
<br />(J Ji~charge (m.l/s).
<br />
<br />Sf friction slope,
<br />V mean Ilow velocity (m/s), V = Q/A,
<br />V" vducity (m/s) measured close to Ihe dwnncl hed.
<br />IV channel width (m),
<br />x longitudinal coon.linatc (m).
<br />z cruss-waVt: coordinate (m), z ::;: 0 at the wall.
<br />z" bed elevation (m),
<br />/) mean chanllel slope,
<br />T" bed shcar stri:~S (Pa).
<br />
<br />Referenees
<br />
<br />(7)
<br />
<br />Bakhllll.:tdl, 13. A., 0 NeravnumefllUIll Dwijenii Jidkll~li v ()lkJ)II)ll1
<br />Rusk (VarieJ Flow ill Open Channd), Sl. Pelershurg. Ru~~i;L. IljJ~.
<br />BakhmcLdf, B. A., Hydra//{in uf 0/11.:11 C!WlllIl'l!>, hi ~J., J29 pp.,
<br />McCraw-Hill, New York, 11.)31.
<br />B~ILin, II., Rechcn:hes Expcrimenlalcs sur I'Ecllldemenl de rE.ut Jans
<br />ks CanallX DCl.:utLverb (E.xperimental Re:'Ol.;'an::h nil \Vah.'r FIIl\\ ill
<br />.open Chanlld~), J~kll/()in:s preSel/f(:.v pilI" diras .\t/I'i/ll1.'J Ii 1:.klldl'lIIil'
<br />des Scil.'lICn, Paris, Fralll::e, 19, 1-494, IH65.
<br />Iklangl.;'r, J. 13., E!l.!JI/i SlIr fa SolUlioll NWllerit/lIC: de III/dl/lles /'ruhlt'mn
<br />Re!lIliJ~.1I11 Afo/H.l.:lllellt /Jemlt/llenl tlc:.~ l:.:lIIIX Cuural/It's, (E:'Osay on till.:
<br />NUlllerical Solution of SUIll~ Prohll:ms rr.:btivl.;' 10 Str.:aJy Huw Ilf
<br />Watr.:r), Carilian-Goeury, Paris, HQH.
<br />Chan:'Ooll, B., Flow dlaracteristics ot" unlluhtr hyllraulic jumps: COII\-
<br />Pllrisull with ncar-crilical llows, Rep. Cff.J.5/95, 202 pp., Uni.... nl"
<br />Quecl1:'Olanll, AusL, 1\,1\,15.
<br />Chanson, 1-1., Fr~l:-surface flows with ncar-critical flow conditions,
<br />ClIl/. J. Cit'. EII!j., 2J(6), 1272-12H4, IlJ9h.
<br />Chanson, H., anJ J. S. rvlontes, Characteristics of unllulM hydraulil.'
<br />jumps: Expr.:rimcntal apparatus anJ !low palll.;'fllS, J. /I)"dl"ll/ll. I:"I/!:i.,
<br />/:l1(2), 12'J-14-t, 1\J95.
<br />GraLlI, G. E., Critical [low constrains now hydraulics in nwnik-hl.;'d
<br />strl.;'iLlllS: A new hypothesis, lVala Rc.\'ullr. He.\'" 33, .149-.1.'ii'i, IIJ97.
<br />I h:ndersoll, F. M., Op('// dWIlIle! }low, MiLl.;'Millan, New York, (1)6/1.
<br />Illlai, S., and T. Nakagawa, On tranSVl.'rsl.: varialiullnf vdodly and hl.'d
<br />~hl.'ar ~tress in hydrauli..: jumps ill it rl.:l.;'tangulal" (Jpcn cbannd, ..let./
<br />Mec".,1)3, 1\}I-l03, 1992.
<br />KaLl.;'lllipUllr, A. K., and C. J. Apdt, Effr.:cts uf irregularity of f(Jnn (HI
<br />l.'1Il.;'rgy lossl.;'s in UPl.;'1l channel llnw, ,-It/Jf. CiI'. !:.'lIb. hailS., CI:.]5,
<br />294-299, 19i'iJ.
<br />Ml.;'lnIO~h, J. C., Ilydraulic characteristics in channel:'O of complex cro~s.
<br />Sl.:I..tiOIl, Ph.D. thl.;'sis, -187 pp., Univ. of QueenslanJ, Queen~JanJ,
<br />AU:itralia, IlJlJ(J.
<br />Monl~s, J. S., <lnd H. Chanson, Characteristics of undular hydraulic
<br />jump~: Rl.'su\ts and calculations, J. f/ydralll. Eng., 12-1(2), 102-105,
<br />1<)9H.
<br />Paid, V. C, Calibration of th~ Preston tub~ und limitations on its ll~e
<br />in pressure graJir.:nts, 1. FIlIid Mecll., 23(1), IgS-208, llJll5.
<br />Preston, J. H., Th~ Jeterminution of turbulent skin friction by means
<br />of pilot tuhes, 1. R. AervllIltll. Soc., 58, 195-1.
<br />
<br />H. Chanson, Department of Civil Enginc~ring, UniversilY or
<br />QUl.;'enslanJ, Brisbane, Queensland ..tun, Australia. (e-mail:
<br />h.chansonQ{'mailbox.uq.cdu.uu)
<br />
<br />(Received June 11, 1997; revised Octobr.:r 13, IlJ98;
<br />aco.:pled October 13, II.)9H.)
<br />
<br />
|