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<br />EM 1110--2-1(08
<br />I Much 1960
<br />
<br />c
<br />
<br />where the \'irl ual or "working" discharge D represents a hypothetical steady flow that would result in
<br />storage, in a gi\'en reach, equal to that produced with given values of actual inflow I and actual outflow
<br />O. From this equation, the value of 0 in tcrms of D, I and X is
<br />
<br />x
<br />0=D-1_X(I-D)-- - - - - - - - - _. - _. - - - __ - - u n _ ____ _ _ (25)
<br />
<br />By appending a subscrip! I 0" a subscript 2 to each of the discharge symbols in equation (25) the equa-
<br />tion hecomes applicable to the beginning or ending, respectively,. of a time period At. By combining
<br />equation (25) with the continuity equation,
<br />
<br />S,-'--S,=0.5 At [(I,+I,)- (O.+O,)J_ __ __ _ __ __ _ __ _ n_ u _un _ _(6)
<br />
<br />and rollectin~ on the left 0.1l \'alues known at the beginning of the time interval,
<br />
<br />0,5 At, rI,+I,)+S,(l-X)-0.5D, Llt=
<br />S,(I-xj +0.5 D, At=R,___ __ _ _ _ ... _ n _ n _u n u __ _n __ (26)
<br />
<br />where R is a working yalue and an indl'x of storage. The comparable equation for the preceding step
<br />of the routing is
<br />
<br />8, (1- X) +0,5 D, Llt=R.__ _ _ _ __" u _ __ n n _ uu n. n n n (27)
<br />
<br />R,= R, +0,5(I, + I,)At-D,LlL... _. _ _ _ _ _ _ _. _ _ _ __ _ _. _ _ _ _ _ _. (28)
<br />
<br />"lid therefore, hy sllbtracting
<br />
<br />This mcthoc[ of flood rOllting may be l'ompared with the coefficient method by combining equations
<br />(24) and (5) 10 yield .
<br />
<br />s= KD... _. _ _ _ _' _ _ _... _ _.. _ _. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ (29)
<br />
<br />which if comhined with equntion (2i) gin's
<br />
<br />R=D(K- KX+O,5 At) _ _ _ _. __. _ ___ _ _ ___ n _ ____.___ _ n(30)
<br />
<br />(
<br />"
<br />
<br />Jr K and Xure hoth constant" the flood routin~ throllgh use of the working values is a graphical solution
<br />of the coefficient ml'thod, Howeyer, K in particular need not he taken at a constant value, in which
<br />case a graphil'ul plot or R \'crsus D rcsulls in a curve.
<br />
<br />3-03. DEVELOPMENT OF STORAGE.OUTFLOW CURVES. The rouling of a hydrograph through
<br />a reuc'h rl'quin's a prior ,It'termination of values of tho working discharge D representing a hypothetical
<br />flow find II,e working vulue H. rl'preselltinp: the storagc, It is conveniellt to show the relationship of
<br />D to R hy' a graph, which is t,'rmed a "working curve." ,
<br />Inusmuch as this mdhocl alld the coefficient method arc dl'rivcd from the same assumptions, the
<br />pfl'yious discllssiolls rcgarding dderminution of At, K, X, and rcach length apply as much to this method
<br />IlS to lhc' ,'oeffil'icnt method. The symhol K although not shown in the routing equations is present in
<br />till' working yalue R. Till' det,'rminatioll of I'l'ach length, At, K, and X by the methods previously
<br />di5l'1l5,,'cl permits the Hulllution of D from c''1l1ation (24), S from equation (29), and R from <''Illation
<br />(:1O). ,\ working cUn'e of D versus R, such us shown in plate No, 6, may thc'n be plotted. The R-D
<br />1'"lutiollship also muy he determined from inflow and outflow hydrographs of a reach by the inverse
<br />}lJ'O(.{'g!; of fl()()cll'outil\~.
<br />]f tI". Aow eon,litions in a reach an' affectecl hy un indl'p'endent vuriahle; the eonditions may be
<br />l'l',H'l'sl'nlc'c1 hy a family of R-D curv('s haying the iHdepelldl'nt variahle as n parameter. If the indo-
<br />pc.nd,'ntyuriahle is trihutary inflow alld if till' tl'ihutHry inflow and main stream flow each affect t.h,'
<br />flow, and hrn{'(' the storage', of the' othrt', tll('1I two :-Ids of pnrnmrlrrs fl.t'(\. 1\r<'C'ssury, the t.ributary flow
<br />hc'ing tll" parlln",l"r for the R-D ,'urVl'S for till' muin stl'!'Hm llnd thr m.in stem flow bcing t),e parameter
<br />for th,' ){-D ellO\'eR for the tributary )'('ue)" In this C'IlSl' K Hncl x: should hI' detcrmined from storage
<br />IInder flowline profil"s us disc'u"r,[ in pnrngraph 2-10, in ol'llc'r 10 eomput,. values of D and R,
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