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EM 1110--2-1{08 1 March 1%0 cedure (or solving routing problems that would require the use of variable coefficients is the method of using a "working value," R, as an index of storage. This method is discussed in paragraphs 3-01lhrough 3-06. 2-06. TRIBUTARY INFLOW. If a tributary stream enters the main stream within a routing reach and the tributary flows and stages are relatively unaffected by stages on the main stream, an independent variable is introduced into the conditions affecting flood-wave progression. In this case the stages and therefore the storage in the reach depend on the tribu tary inflow as well as on the discharges in the main stem. In a method proposed by Gilcrest' the effect of the independent variable is accounted for by t.he addition to the storage equation of the term Z(F,-F.), where F is tributary inflow. Thus, equation (5) expres>ed in increments and with the added term becomes AS=K(I-X)(O,-O.HKX(I,-I,HZ(F,-F,).mnu_. _ _... _ _.. _.. (16) I , Combining with the continuity equation for the main stem flow AS=O,5 At [(I,-t-I,)-(O.+O')jm_mm_uu__h_______ n _ (6) gives the routing equation where O',-:-O.=C,(I,-O,) +C,(I,-I.)-C,(F,-F,)__ ________ _u_ ___.__._ _ (17) 2Z . . . C, 2K(I-XHAt-- -- -- n - -- - -- -. - -" -- u m -_ u -. .(18) After completing the computation for 0" the value F" must be added to yield the outflow, O,+F" from the reach, Gilcrest' points out that this method generally is not as desirable as one which is presented in paragraph 3-{)5. ... 2-07. FLOOD ROUTING AT A MAJOR JUNCTION. One method of routing in a reach containing a junction was given in paragraph 2-{)6. That procedure is adequate if the effects of discharge from one river upon stages upstream from the junction in the other river are of minor extent, as in the case with streams of steep slope or with relatively small tributaries entering along the main stream. The more general case, in which changes o{ discharge on one stream materially affect stages in the other stream {or some distance upstream from the junction, involves complications for which there apparently has been developed no exact direct solution. An application of the coefficient method to this type of prob- lem has been presented by Gilcrest and Marsh.' That procedure, applied to the junction of the Ohio and Mississippi Rivers, yielded adequate approximate results, but should not be applied indiscriminately to ot.her j unct.ions. No example of routing at a major junction by the method of coefficients will be presented herein inasmuch as a preferable method is presented in paragraph 3-06. 2-08. DETER:<1INATION OF At. The practical consideration in selecting At, the length of the rout- i ng period, is that its value is small enough to define the hydrographs. A secondary consideration is that the water-surface profile in the reach will be relatively straight. The relationship of the value of At to the constant K is discussed in paragraph 2-o9a. A routed hydrograph is relatively insensitive to small changes in At when X and K are held constant. 2-09. DETERMINATION OF K. a. Significance of K. Figures 2 and 3 have been presented by Gilcrest' and others as an example o{ the application of the storage equation (5) to a looped storage curve derived from flood hydrographs {or a river reach. The figures differ in the ordinate seale with the objective being to show that, by a suitable selection of X, the storage loop of figure 2 may be reduced to relatively small loops as shown in figure 3. In these graphs, the value of K for an incremental time period is the reciprocal of the slope o{ the mean line representing storage versus the outflow, t.hat is, K is the change of storage per unit change of discharge. 5