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<br />1 <br /> <br />I <br /> <br />EM 1110-2-1601 <br />1 July 70 <br /> <br />c <br /> <br />APPENDIX IV <br /> <br />Notes on Derivation and Use of Hydraulic <br />Properties by the Alpha Method <br /> <br />. <br /> <br />i. General. Appendix A of reference 89t is reproduced here, with minor <br />!%lodifications and rearrangements, to illustrate use of the .. Alpha" method <br />, for determining the local boundary shear and composite roughness. The <br />I <br />i,\lpha computations are applicable to uniform and gradually varied flow prob- <br />'lems. Computations for effective average channel roughness k with and <br />without considering the energy correction factor are included as well as com- <br />: putations for Manning's n. The necessary basic equations and a computation <br />, procedure are given in the paragraphs that follow. illustrations of the <br />Alpha method applied to the effective channel roughness problem are given in <br />plates IV-1 through IV-4. <br />2. Basic Procedure and Equations. a. The cross section (plate IV-i) is <br />divided into subsections bounded by vertical lines extending from water sur- <br />face to the wetted perimeter. The, mean velocity in the vertical of the sub- <br />section is given by V and the subsection discharge by V A . The integer <br />n n n <br />subscript n defines the channel subsection. As explained in Chow3 (para 6-5), <br />a simplifying assumption becomes necessary. It is assumed that the energy <br />grade line has the same slope across the entire cross section, that S in the <br />familiar Chezy equation (V = C (RS) 1/2) is constant at each subsection, and <br />that the following pro-portion may be written <br /> <br />Vn::(CR1/2)n <br /> <br />(IV-i) <br /> <br />where C is Chezy's coefficient and R is the hydraulic radius. <br /> <br />. <br /> <br />t Raised .umbers refer to similarly numbered references in Appendix 1. <br /> <br />IV-1 <br /> <br /> <br />--~~'~~ <br />