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<br />The method of successive averages allows us to compute the routed failure <br />hydrograph at the end of the typical reach by multiplying the vector of <br />coefficients of a predetermined polynomial expansion (ei) by the ordinate <br />values of the original failure hydrograph: <br /> <br />Qrij = L Qpj ei <br /> <br />Equation 13 <br /> <br />The degree of the polynomial expansion ei is defined as "Number of Routing <br />Steps" as follows: <br /> <br />Number of routing Steps (Nr) = (2)(Th)(Ns) <br />Tp <br /> <br />Equation 14 <br /> <br />where Th = Hydrograph travel time along the typical section (equation 9), <br />Tp = Hydrograph original base time (figure 1), and <br />Ns = Number of slices. or subdivisions of the unrouted hydrograph. <br /> <br />Since the failure hydrograph is triangular without abrupt changes in shape <br />(figure 1), sufficient accuracy is achieved by subdividing it into six <br />slices (Ns = 6) as shown in figure 1. <br /> <br />cfs <br />Qp <br />~p <br />:3 <br />~ <br />3 <br />0 t 2j 11 ~ ~ T rs <br /> <br /> <br />Figure 1: Failure Hydrograph Divided into six Slices <br /> <br />Equation 14 is simplified. <br /> <br />Nr = .!LTh <br />Tp <br /> <br />Equation 15 <br /> <br />Values of ei for up to 15 routing steps (Nr) are available in Appendix 2. <br /> <br />Although the entire routed hydrograph can be computed using equation 13. it <br />is really just necessary to determine the peak value. Qri, since the <br />floodplain map will designate th~ maximum extent of flooding only. Equation <br />13 then becomes; <br /> <br />Qri = maximum L Qpj ei <br /> <br />Equation 16 <br /> <br />11 <br />