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<br />EM 1110-2.1416 <br />15 Oct 93 <br /> <br />~OOB..a 13,1~.1' <br /> <br />. <br />~ 1011000 <br />. <br /> <br />1:10:10111'018 &IVZa <br /> <br /> <br /> <br />o <br /> <br />... <br /> <br />.., <br /> <br />. <br />o <br /> <br />... <br /> <br />... <br /> <br />A>' <br /> <br />'I' <br /> <br />.. <br /> <br />.. <br />1 <br /> <br />D...,.3 <br /> <br />"0"0" <br /> <br />HAV""" D.. ''I'A''. <br />HAVla 20' ..ea. sTAOB <br />II''''Vla ao. I.ea. OLO.. <br /> <br />" <br />1 <br /> <br />'r' <br /> <br />".......3 <br /> <br />Figure 5-13. Hydrographs for the illinois River at Havana with ovarbenk storage <br />Increased by 20 percent <br /> <br />prediction techniques is presented: flfSt hydraulic tech- <br />niques, which simulate the wave motion by solving the <br />mathematical equations governing the unsteady flow in <br />the reach, and then hydrologic techniques, which com- <br />pute outflow hydrographs directly from predetermined <br />reach characteristics and a given inflow hydrograph. The <br />effects that the assumptions characterizing a model have <br />on its applicability are discussed. <br /> <br />b. Hydrologic routing versus hydraulic routing. In <br />the nineteenth and early twentieth centuries, the <br />approaches used 10 analyze problems associated with the <br />movement of water were fragmented among different <br />professions in accord with the area of endeavor affected <br />by the particular case of water motion. The assumptions <br />developed to allow solutinn of these complex problems <br /> <br />5-18 <br /> <br />varied widely in the different fields in accord with the <br />inventiveness of the researcher and were generally unre- <br />lated. Classical hydrodynamicists studied the mathe- <br />matics of potentia! flow of a perfect fluid, which water <br />under certain circumstances imperfectly imitates. Mathe- <br />maticians studied laminar flow, a turbulence-free <br />phenomenon in which fluid mixing takes place only on a <br />molecular level. Laminar flow is rarely seen in rivers; <br />the high Reynolds numbers and boundary roughness of a <br />typical river make turbulent flow the norm. Hydraulic <br />engineers developed empirical formulas for head loss in <br />turbulent flow in pipes. Because of the greater complexi- <br />ties of open channel flow, engineers devised assumptions <br />and computational schemes to be as simple as possible <br />for analyzing river flows. <br /> <br />e <br /> <br />\ <br /> <br />. <br /> <br />.. <br /> <br />e <br /> <br />. <br />., <br /> <br />. <br />. <br /> <br />e <br />