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EM 111G-2-1408 1 Manh I~O ( 1-06. BASIC PRINCIPLES. From consideration of the principles of conservation of energy and con- sen'ation of mat ter thc following simultaneous differential equations describing unsteady flow in a uniform channel can be derind:" . . Oy+V oV+l uV ' 1-1-- -- -- . '-ox g ox g ot _____n_____hununu______uu___ oV oy oy, . A ox +VB ox +B ot =0 ___uuu__U___U_h_u____"_hun_ (1) (2) In application to the problem of flood routing the five terms in equation (1) and the three terms in equation (2) are known, successively, as follows: Bed-slope term Hydraulic-friction term Depth-t,aper t"rm Velocity-head term Acceleration-head term Prism-storage term Wedge-storage t"rm Rat,,-<>f-rise term Consideration of equation (2) has given rise to numerous procedures of "storage routing," in which the energ:y relationships represcnted by equation (1) generally have been ignored. By introducing equa- tion (I), more theoretically acceptable methods of routing are possible but these suffer the handicap of greater complexity. These methods are beyond the scope of this chapter. Such methods are discussed by Gilcrest,' Thomas," and other writers cited in the list of references. By alternative methods of development, the following equations for unsteady flow in a rectangular channel, in which the term .fiij rcpresents celerity of a wave in shallow water, can be derived: · (' , dx=(V:l:.fiij) dt __uuu__n___u__u________u_nnu_ (3) d (V:l:2.Jgy)=g(i-i,) dt _____m__U____h__mu_m______U (4) Equstions (3) and (4) ha....e been developed into a flood-routing method known as the "method of charactcristics." Solutions by t,bis method are by graphical procedures. The method has been used in developing stage and discharge hydrographs in a short stretch of river valley downstream of a dam which hns been assumed to fail.' Thus far, the applications generally have bee,n made for channels of uniform shape and constant slope inasmuch as the application becomes more cumbersome for irregular channels. Gilcrest' and Re' hove demonstrated the procedures used in the method of characteristics, CHAPTER 2 COEFFICIENT METHOD OF ROUTING 2-01. GENERAL. Early development ;md practical application of the coefficient 'method was made by Gerald T, McCarthy and others, in connection with studies of the MuskingumConservancy District Flood-Control Project mnde by the Corps of Engineers in 1934 and 1935. . The method and its applica" tions have been d€>scrib<>d in num('f'OUS paperS.~ 14 15 11 . The coefficient method is hy no means an exact method of routing hydrographs inasmuch as only u few of the terms sbo,,"n in (.quations (I) and (2) are considered in the derivation. The method is adequate for many pUI'poSes, partir\lla~ly in the planning and designing stages of f1ood-eontrol or multiple- purpose projects: Tbe method may be used not only, for 'routing discharge hydrographs but also for, rouling holdouts, i.e., reductions in natural flows rcsultHig from the control of floods by reservoirs. The .~Ur:'".~~r1 ~'"loO"'T. l..n \nl.5 t':'.umer rtkr Lo cumber-ed rt'krt'pee~ Ilst.e ,/ 2