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<br />EM 111ll-2-1408
<br />1 Ma.reh 1960
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<br />it is of int~r~st t<l note that if the outflow is expressed entirely in terms of inflow, by eliminating 0" the
<br />routing equation (10) becomes
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<br />o.=c;r.+caH+C;C;I.",+C(CI)'I._,CHCD'I._.+ ... ----________ (14)
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<br />where, for ('.onvenienc.e,
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<br />C;=C;C;+C;___h... m. __ ___ __'~ _. _.. _ _ _ _ _. _ ___' (15)
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<br />The coefficients of eneh inflow term will be denot.ed as a routing constant. It may he noted t.hat after
<br />the second t~rm the routing constant is C; times the routing constant of the prior term.
<br />The sum of the eoefficients of equation (10) and of the routing constants of equation (14) totals
<br />unity. Thus it is possible t<l determine conveniently the effect of eaeh inflow term in determining an
<br />outflow 0.. The relative effect for the condition K=At is as follows:
<br />Percenta.ge effect or inflow terms
<br />X-K X-K X-X
<br />25.0 20,0 14.3
<br />56. 3 64. 0 n. 5
<br />14.1 12.8 10.5
<br />3,5 2,6 1.5
<br />1. 1 0.6 0.2
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<br />Inflow term
<br />l..~_.___._______.___
<br />I ~-l~--- - - - -. - - - - - - -. -
<br />. 1.-1_______ .-- ---- - - -.
<br />1,,-1____________ - -- - --
<br />Prior inflo.....su _. _ u. _.
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<br />X-O
<br />33,3
<br />44.4
<br />14. 8
<br />4, 9
<br />2.6
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<br />X-x
<br />o
<br />100
<br />o
<br />o
<br />o
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<br />, Routillg constant
<br />Cl____________________
<br />C~-__________________ _
<br />C~ C~_ _ _____________._
<br />C: CC;)' ___ p ---. - -----
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<br />Total. p ____p_ . __.. _ __ p _ __. n___. n 100,0 100.0 100,0 100,0 100,0
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<br />It is apparent thot for equality of K and 1>t the outflow det,ermined by t.he coefficient, mHhod is largely
<br />dependent on three inflow vn]ues, Eqnation (14) is eonvr,nient for routing if only a portion of a hydro-
<br />graph, for example the rounded nest.,is to b" routed; tIte routing constants may be applied to t.he appro-
<br />priate inflows to determine individual vnln.,s of outflow,
<br />The routing equntiol\ (14) may he applied ,t,o successive sllbreadll's t<l establish routing constants for
<br />relatiYely long reach,'s, Routing constants arc presented in plate No.2 for rea.ches consisting of one to
<br />seven subreaehes, with tt'ovd ,time in each subreach equal to the time intervsl At. The routing constants
<br />also may be determin~d ronwniently by another method, namely by routing a hydrograph with \-alues
<br />of 0,1,0 through th~ dt'sired number of subl'eaches.
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<br />2-04. BASIC FLOOD-ROUTING PROCEDURE. Routing of a hydrograph with equation (7) is not an
<br />involved proeess, In the oxomple in plutc No.1, an inflow hydrograph for Newcomerstown, Ohio, on
<br />a tributary of the \luskingum Rivor, i. ('unsid"l'od t<l be )'I'prescnted adequately by instnhtaneous vslues
<br />of discharge at half-day int~n'als. The discharges are tabulated in column 2, In this example it is
<br />assumed thero is no tributary inflow and no loss in the reach. Also given are the conditions
<br />that K= M=0,5 day and X=o,a, From l"luations (8) o.lld (9) yalues of C\ and C, arc t'omputod. Ncxt
<br />C, is multipli~d in turn hy l'oeh inerpm~nt of inflvw to obtain eolumn 4. Thus, the first e,ntry of column
<br />4 is C, (1,-1,)=)( (7,0-2.0)=0.8. In tI,is o.xample. the first, cntry of column 5 is assumed equnl to the.
<br />inflow at, theeorresponding tilll~. 'rhe first itom in e.ohnnn 3 is c, (1,-0,)=(1/1.2) (2.0-2,0)=0. Thc
<br />second item in column 5 is the summation of ('olumns ~, 4, and 5 of thc prcceding linc. The items of
<br />columns 3 and 5 are de.terrnined "1!"'f'lIately nnt,il t'olumn 5 is ('omplett\d, thus completing the routing.
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<br />2-05. Y ARUBLE COEFFICIENTS. Till' use of ,'on.{ ""t ,'"hlt.s of t,he. {'oeffieients K nnd X throughout
<br />the routing of a flood l~ not o.dequllll' ill nil il1sltult.('s, for ,'xumple, in operatin!'; problems requiring
<br />aCl'urato st.age. fOrt'(,llst" throughout a flood pt'riod.. The> t't\t'fIit'i,'nt, rlwthod m"y be expanded by using
<br />a ,'ariable K or X or hoth, If thesl' ,'o('fli('it'nts un' >lssnmed to vary ns functions of outflow, the, routing
<br />may b~ mnde with sO\'{'I,,,1 ".hll'S, "'H:h "ppli{'able to a 'pet'itie' rango of ontflow discharges, or working
<br />cun'es of C, nnd C, I'lllY h,' plotted against outflow for ns.' n. th,' routing proceeds step by st~p. When
<br />using varying \'ultu's of K nnd X th,' ('omputo,] outflow hydrogrnph may h,' [pund to have more or It'ss
<br />\'olume tlllln the inflow hydrogntl'h. ..\ r,'ucljllsttnt'nt.'of the relntion between the coefficients and out-
<br />flow or stngC' is one mrfills of twinging thr \'olullws into hn.lunrc. How('v(>r. in many ('.85('5, a bettrr pro.
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