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<br />., <br /> <br />EM I11O-Z-UOS <br />1 MlU'eh 11$0 <br /> <br />o <br />>- <br /> <br /> <br />WedQe <br /> <br />L6y <br />storaQe: KX (l- 0): <br />2 <br />Prism storage: KO: Lyo <br /> <br />1---. <br /> <br />>- <br /><l <br /> <br />-..... 0 <br /> <br />r <br /> <br />L <br /> <br />1 <br /> <br />Figure 6 <br /> <br />tangulac channel, the wedge storage and the prism storage for the unit width can be expressed as shown <br />on the figure and it can be shown by substitution that <br /> <br />X OLly. <br />2y.{I-0) <br /> <br />The value of <br /> <br />(I-O)/Lly is ~ (J) <br /> <br />when eyaluated by differentiating the Manning discharge equation, if the slope is assumed constant. <br />Therefore, X=0,3for a wide rectangular channel where c.hanges in discharge are small and therc is no <br />yariation in slope for such a change in discharge, Under similar conditions the X value for a tril\ngular <br />channel section increases uniformly from 0.375 at Lly/y.=O to 0.438 at. Lly/y.=O.5. Similar evaluations of <br />X can be made {or other shapes of cross section, The significant point in these evaluations is that, within <br />the limits of the noted assumptions, X depends primarily on the shape of the cross section and the expo- <br />nent of y in t.he ~fanning discharge equation and is relatively independe.nt of river slope, roughne.ss <br />coefficient, and length of routing reach. <br />The hydrographs shown in figures 6 and 7 indicat.e that, in application of the coefficien't method, <br />the value of X is not independent of reach length, as might be inrerred from an analysis such as that <br />described aboye. In esch of these figureshydrogrsphs are shown for a reach which has been divided into <br />subreaches {or the purpose of routing. In figure 6, an X value of y. applies to all routings. The hydro- <br />graphs !\t the downstream end of the reach are shown to be dependent on the number and therefore the <br />length of the subreaches. In figure 7, the cffect of subreach length has been count.erbalanced by varying <br />the value of X, Three hydrographs are represented wit.hin the width of line of the outflow hydrograph. <br />The first, for a routing through four subreachcs with X=y. and Llt=K=I, is thus shown to be practi- <br />cally equiyalent to a routed hydrograph through eight, subreaches with X=O and Llt=K=i\ and to a <br />hydrograph routed twice with x=o and Llt=K,= 1 and lagged by T,=2. Therefore it is possible to <br />route a hydrograph by the coefficient method with so-called wedge st.orage, or by a reservoir-t.ype routing <br />or by a reservoir.lag method depending on whether X, the subreach length, or T" respectively, is the <br />characteristic whose yn]ue can be dctermined most satisfactorily prior t<l a routing computation. <br />b, Eval!\ation of X. One method of evaluating X from actual hydro graphs has heen giyen in para- <br />grapl1 2-09, A second method consists or making trial routings with different values of X until one is <br />found which satisfactorily reproduc,es the out,f]ow hydrograph. This procedure may be necessary if the <br />floo<1-'/o'avc travel time in a reach between gaging stations exceeds Llt/2X. In this case it is convenient <br />to make the routings in "n" suhrcaches of travel time K=Llt such that nK equals the travel time of the <br />recorded data, This procedure is slltisfactory on streams .of relatively unirorm cross section and slope <br />and having constant or small trihutary inflows, a good example being the Columbia Riyer in Washington <br />from Grand Coulee gage to Trinidsd gage. Plate No.5 shows a trial routing through this reach for a <br />minor rise in September 1945, The time for flood-wave travel through the reach for this rise was 24 hours <br /> <br />9 <br />