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<br />e <br /> <br />. <br /> <br />~ <br /> <br />. <br /> <br />.- <br /> <br />,e <br /> <br />,. <br /> <br />. <br />. <br /> <br />e <br /> <br />EM 1110-2.1416 <br />15 Oct 93 <br /> <br />101l1lP.ll 13,3'.), <br /> <br />100llDO <br /> <br /> <br />1:'1.1110'8 IIIVIlIt <br /> <br />, <br /> <br /> <br />. <br />. <br /> <br /> <br />..' <br /> <br />... <br /> <br />." <br /> <br />. <br />, <br /> <br />.., <br /> <br />." <br /> <br />OCT ,,"OV <br />1"3 <br /> <br />Pill;: .JAil <br />I <br /> <br />FEll itA" A.... <br /> <br />"A..- _"". ''''1. Aug lIliI. <br />1"1 <br /> <br />KlIoVIUI. 0.. lI'l'Aall <br /> <br />HIloV%Z COH'O%.~ aoo STAO_ <br />HAVI2 CDK'OTIID aoo Fl.OV <br /> <br />Figure 5-16. Hydrogrephs lor the illinois River et Hsvens with flow-Menning's n re". <br />tlonshlp edJusted to reproduce the 1983 flood <br /> <br />(b) In this approach, time is the only variable, and <br />the mathematics of the simulation reduce generally to an <br />ordinary differential equation. This equation relates the <br />sought after time variation of the outflow 10 the given <br />time variation of the inflow and 10 the given response <br />characteristics of the reach, e.g. a storage versus flow <br />relationship. The hydrologic techniques typically solve <br />this differential equation numerically, i.e. algebraically, <br />through the use of fmite-sized time steps. <br /> <br />values for both prof11es can be found. The usual <br />assumptinn is that the shape of the stage and discharge <br />profiles cannot be given a priori for the reach as a <br />whole. It must be broken into a sufficient number of <br />distance steps so that the shape of depth and discharge <br />variation in each can be assumed 10 be a straight line. <br />For this reason, the hydraulic techniques generally <br />require a determination of depth and discharge at a <br />sequence of stations within the reach, even if the condi- <br />tinns are in fact sought at only one point. <br /> <br />(6) The hydraulic approaches explicitly recognize, in <br />addition to the physical principle of mass conservation, a <br />second physical principle, one or another form of conser- <br />vation of momentum. If, then, an assumption is made <br />regarding the shape that graphs of the variation of stage <br />and discharge along the reach would have, absolute <br /> <br />(a) As a result, a characteristic feature of hydraulic <br />approaches is the calculation of flow variables in the <br />interior of the study reach, even if they are not of special <br />interest. For example, to arrive at the outflow <br /> <br />5-21 <br />