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<br />'. <br /> <br />EM 111G:-2-U08 <br />1 Mareh 1960 <br /> <br />I <br />I <br />'. <br /> <br />If the inflow ordinates are I" I" I, <br /> <br />1.+ 1, and n is the number of subreaches, <br /> <br />O'+1=Cl 1,+", I.+c, 1,+ . . . . +c,,+1 I.+l__nnnh______(33) <br /> <br />where. <br /> <br />1 <br />cl=211 <br /> <br />n <br />"'=2' <br /> <br />n(n-l} <br />c,= 2'2\ <br /> <br />n(n-l)(n-2) <br />c,= 2'3! <br /> <br />n(n-l)(n-2) . . . . (2) <br />c,,= 2'(n-1)! <br /> <br />n! 1 <br />c,,+'=2.n!=2. <br /> <br />Routing constants ure shown in plate No. 10 for various numbers of routing sub reaches and their use is <br />shown in plate No. 11 for a 4-step reach, each subreach having a tra.vel time of 0.5 da.y=<l.t/2. <br />c. B"sis of Method. Further considerations of the method disclose its properties. In figure 8 <br />let hydrograph A be defined by discharges 10, I., I.. . . . I. at times 1", t" to, ' . . . . t. with time <br />intervals <l.t so short the discharge varies linearly in the interval. Hydrograph B is the same hydro- <br />graph trans1at~d without change in shape to a downstream point to which the travel time is I1t/2. The <br />discharges at time t" to, . . . . . t,,+1 are (10+1,)/2, (I.+I,}/2, . . . . . (1.-.+1.)/2. <br /> <br />Hydro'Jraph A <br /> <br /> <br />Hydro'Jroph B <br />H yd ro'J ra ph C <br /> <br />UJ <br />~ <br />a: <br /><l: <br />:J: <br />(,) <br />(/) <br />o <br /> <br />to <br /> <br />t I <br /> <br />t2 <br /> <br />t3 <br /> <br />t.. t5 <br />TIME <br /> <br />t6 <br /> <br />tT <br /> <br />ts <br /> <br />t9 <br /> <br />Figure 8. <br /> <br />15 <br />