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<br />UYI>R^lIUC ENGINEERING 't)4
<br />
<br />Bcd lIIah:ri.ll l'(shilllC lador) {it'ncml Fnrllluln
<br />Il)O (" III " 011.070. li50'"
<br />I)K,1 (" 1.4 ,,:.: u.lIsa. IUC4""
<br />IJCm (" 2.K ,,:-~ ().()S()). /)901'11
<br /> .... .. . ..
<br />
<br />lbill~ (' Ilhe errnr WOlS nppttlxllll:llcly 45% willie III lite c.ISt: nl usmg lh~ sll.IJlC l.lelnT
<br />indicaled in lhe l:lhlc :lhuve. the ll\'cragc error WIIS rcduct.'tl hi 1.I.X'%,.
<br />Then Ihe I.imcrillus 11.lrl11ul:I WIIS vulid.llcd :nul IIU chanJ,:,c is rCllllircd In miuimi:lC Ihe
<br />emlTs. VCllid:ltiun 1t.':lds tu an IIverngc error of 14.5% (scl'li~urc I).
<br />UlIthufS"S li.lrInlllll v.ivl.:s un avem!!.c error of 22%. Jurrcl's rnrmulill!-ivcs un aVCr:l!tc crrnr
<br />of IC}lt!... Mildrid's Ihrlllul,ls were ohl:liuc..-d with Ihi~ d..ln nnd Ihe lIvcrul,tc error is 1.1.()% Il'll
<br />7) and 1.1.3% respectively (sce ligurc 2).
<br />
<br /> i , 'I . 'l~.....j
<br />J.~ i ! ")">4 ,.j
<br /> ,
<br /> / ; 'I ,
<br /> , ... -l~"" ; '.
<br />B! j/ . . t ! ~ I . h
<br />; , . ,
<br /> ki,.,.<I' ,. . ..
<br />" o 100, ~ ~..:~. ,
<br /> , ~.: L '1 I_~ , ' . /
<br />I.~ ; . . ,
<br />;r' ' ,I . ~ ,.-",0
<br /> , ,{.? ': I . .-,1:
<br />'i " , .
<br /> I I . ,/.... 1 ...( 1
<br /> I.' .. I.~ I,~
<br />..~ 1I.~ . t I.~ l.~ J.~ , .,~
<br /> Mf'M'11RI.n Mt,Al'1 "UAMn"I"""1 , Mf,A!<olllttl'''U,AN\t'I.IIl'II'I''''1
<br />
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<br />
<br />,,~
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<br />
<br />HO I.. I'n..-dieted mcan velocily Ii.lrl~q. 4
<br />(l.imcrill\ls) versu~ measured mean velncity
<br />(lJsing ('hilean datu. Madrid 19(2).
<br />
<br />FIG 2.. I'redieted me:1ll vl.:lncity lilr hi. 7
<br />(Mnllridl versus mcasurcllmcall velocity
<br />(llsing ('hi lean data. M<ldrid It)1)2l.
<br />
<br />The nruremcntiuncd results suggest that Ihe equutiullS designed explicitly li)r lIIUlIlllllill
<br />rivers arc 1101 yel well proven, or arc restricted In snme range (If roughnes.... Semilogarilhmk
<br />equations work as well as nny othcr (3. 4).
<br />
<br />I'ROIILI'M ANALYSIS . .
<br />Till: roughnc ,,, in II 1I11lunlnin river depends on ma.llY ullespluincd nl~~~~r~ IIlt.:hlthng
<br />tlllhulcnee. scdimcnllr.lIlsllor1. and waler jumps. ^cconJm~ tnlhe lalesl emruncal. resl::lIlh.
<br />thl'le is nul nil accurnte empiricallilflllul.. In eslillmtc rllllghness tlmt Cim Ill' llpphe,1 hi 0I1l~
<br />range ur roughness heeause mosl ofllll'l1J have hcen ubtuinellllsing ~ueal ri,'er d:lt:.l. .
<br />Analyzing the rcstlll ublained using equllli'lll 1. vlllidated with ('111 lean dala , II IS ('Illsslhlc-
<br />In Ilf(l('luse the cstimalinn of" hy:
<br />
<br />n "" nh+ An
<br />Where nh is the base value of rntlghncss and can be ublaint.."lI hy:
<br />
<br />(I))
<br />
<br />(3.4. Ii,.)l 0.183(D84)l (",)
<br />IIh = m ~ -. =---J~~-'--'
<br />21 n
<br />'1 his expression WIIS delermined by nmlli('llc regression usin~ (J2 nhservlltitllls of ('hilt:.1ll
<br />
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<br />
<br />t{()l f(jIINESS ('()EH;I( 'IENT-.RIVI-:RS
<br />
<br />flY'
<br />
<br />rivers.. III espressinn II, ^n C:1I1 be eslimalt:d by Ihe liJllnwing lldil11el1simml expres..iul1:
<br />
<br />J.~ ,.AII- f(.\y."....J.l1)
<br />(/)84)' .
<br />
<br />(II)
<br />
<br />here hi is the !-'rumle IIlIllIher. Sf li-iclilln slupe alld K/DR.l is Ih.... reliltive sllhl11er~ence.
<br />
<br />I'Ll IW Ri'.SISTANn. U.)\IA'llllN lOR LAIWE-SCAI.I'.\II' 11O\lOIINISS IKIIIK'II I
<br />(hi the hasis ,If the d;al;l puhlished hy Ilalhursl C 11)8~, relaled In II.K. ri\'Crs alld the data
<br />puhlished hy Jarrel (1'184) of ('(llnradtl rivers, the h1llt1wiltg express;ll" ",liS delermined hi
<br />estimale the M:mning resistallce cm~lliciet11.
<br />
<br />1.7462. Sf""" (/J84)l
<br />II -10.183 + III(-~ ~-~---"1I' ~_. .0-
<br />. J"JII!hll J
<br />'( K
<br />
<br />H1'
<br />
<br />"",'here the ht..d IIli1lerinl sile (1)84) is ennsidl.'rcd in mclefS. Using Ihis cmpiricllllillnlula 10
<br />est;lllille thc me,," velucity, the mcnll error is affiml 5.7%. Ihe grelltest error is e411allo 21%.
<br />II is impur1:lI1t Itllllenlillll IImt IIll' d.ll<lllscd III csHl1li1le Ihis li'rnllllil ,-=ul1sidl'rs II T:U1!!C lit"
<br />sllmlllluws.lhe highest heillJ:!. equalltl to.] m1/s.
<br />
<br />H.oW IlESISTAN,'F El)IIA'1l0N FOIlINTEllMI'IJIA1E SCA,E OF ROIIl a INI'SS
<br />()nlhe Imsis (Irthe dala l'ublislll.:d hy Mtldrid (It)t)2) rchllcd II) (.2meilsurcs c(lllecled ill Il'
<br />t'hile:m rivers with relillive scales tlf roughness belwecn I and 12,:1,. the fnllU\vill~
<br />cxprcssitllls were determined In cslinmle lhe Manning resistunce cllefficil'nl.
<br />
<br />I. lUl 4 ,,\.,.nllm.( 1:.1 )un"lI (/)K4)'~
<br />n-=IO.IK3+ln( - ..--. -J--'-rl!{i,-~ --......,--)1. J-~--_.-
<br />'l K
<br />
<br />IU,
<br />
<br />1.325l)'.VlIll'm.( 1~Il)nll~I~I (1J5())~
<br />II ;~I().211)+ln(.----~---"- ;r-l~~-~---'----)I'---J. ,..
<br />h ~
<br />
<br />(14)
<br />
<br />lhe bed lIlilleril.ll sile is c(lIlsidered in melers. t Ising Ihis elll('liricilllinllltlla In estimate the
<br />llle:1lI velllCily,lhe mean emIr is tlllly 2.2%. the gre:llcsl crror is 1."lIlIal 1\11).9% ( II~nrc 4).
<br />I'he rllll~e "I' 11m..' uf Ihe dilla used in the dl'tenninllliull uf linmulas I.l mill 1,1 r:l11~C
<br />hetween 17lm.l/s and 2.71I11.1/s. II is iml'ur1alll 1(1 melllitlllllUlt the smne dlllll \\'lIS IIsed In
<br />estimate the semilugarilhlllic l,..qU<llit1l1 (7) :nul wilh lhis new approilch Ihe crrtJr was rCllllced
<br />frtnn IJ.(I% tn nn1y 2.2% . This Ic:tds liS In helieve Ihul this upprnnch hcllcr cxpluills Ihe
<br />phCl101l~ellnn nl" rtlughlless in nUIIIIII.lin rivers IIUln d()f,,':s Ihe se,"ilu~llrithlllic ilPllfl1ilch.
<br />
<br />V AI.IIlATION 01' TilE H IRMIII.AS I'ROI'OSEIl
<br />II WllS illlllt)ssihle In valid:lle equal ion 12 wilh ('hile<ln data hcellU!>C Ihere nre 1I11
<br />IlIcnsurel1lenl sill'S in Illnees with hi~h scales or mughness. Bul lhe vllliduliun w"s IlllUle
<br />usinl!, nuulder Creel River dllta hcc 'lllUme nud Zevenhcrgell 1')85). .lllc lIVCrll~C' errnr ill
<br />Ihe eslil11alinn (11" Ihc mean velucily is 2.7 %.. the !!retltl'sl errnr i!t cquill It) 4.8% hCl'
<br />1i~lIrc J). III order lulesl Ihe validily tlf C411i11iuns I.l and 14 dil1t1 Wil!t used 1"1"1\111 the II K.
<br />lnull"t.lumdt1. rllc ;tVera~e ermr ill the es1inmli,tIl ufthc lIICilll velocity is (1.3%., the ~re;lh:sl
<br />
<br />...-.......... .
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