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<br />max {xM } ~ m Yo <br /> <br />(17) <br /> <br />or <br /> <br />" <br /> <br />max { xM} ~ m So <br /> <br />(18) <br /> <br />, <br /> <br />For given values of 10, M andC, Eq. 18 must be satisfied for all possible <br />values of So in the respective range. Hence Eq. 18 is rewritten as <br /> <br />max { xK } ~ m . max { So } <br /> <br /> <br />In this case one obtains from Eqs. 3c, d <br /> <br />(So ~ 0.010) <br /> <br />(19) <br /> <br />S - - (~)2 Yo <br />o - g - - 4/ J <br />Cu Ro <br /> <br />For any fixed value of Yo maximum value of S results when n attains its <br />maximum permissible value of 0.150. For sucR value of n, Yo is varied over <br />its range and the maximum value of So is found. If the latter is less <br />than 0.010, it is inserted into Eq. 19. Otherwise max [ So }= 0.010. <br /> <br />(20) <br /> <br />:;. <br /> <br />4. Arrangement of the Graphs <br /> <br />The dimensionless flood graphs are arranged in three sets, one for <br />each of the dam-break flood variables, namely tw, YM and tM. For easier <br />identification and use each set is included in a separate Appendix. In <br />Appendix A the dimensionless graphs for the time of arrival of the wave <br />front, tw, are given, Figs. Al to A15. Appendix B contains the dimension- <br />less graphs for the maximum flood level, YM, Figs. Bl to B15. Finally <br />in Appendix C the diemsnionless graphs for the time of occurrence of the <br />maximum flood level, tM, are found, Figs. Cl to C15. <br /> <br />In each Appendix there are three subsets, one for each value of the <br />cross-section exponent M, that is M = 0, 0.50 and 1. In each subset <br />individual sheets are arranged in ascending values of fo' <br /> <br />5" Example of USing the Graphs. <br /> <br />An approximately prismatic river valley is 400 ft . and 600 ft wide <br />at distances, respectively, 20 ft and 86 ft from the valley floor. <br />The roughness of the valley is estimated at n = 0.070 and the slope is <br />approximately So = 0.001. Water is impounded behind a dam at 86 ft <br />depth. It is reQuired to determine the flood characteristics in case <br />the dam instaneously and completely collapses. <br /> <br />7 <br />