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<br />'f <br /> <br />6 <br /> <br />. <br /> <br />These conditions and assumptions allow the use of uniform flow <br /> <br />formulae to evaluate the energy slope of gradually varied flow between <br /> <br />sections. The corresponding roughness coefficient developed for <br />uniform flow is also assumed to apply to gradually varied flow. This <br /> <br />practice has not been precisely confirmed by experiment or theory, but <br /> <br />application of the uniform flow formula to the backwater problem has <br />proven over the years to be a reliable basis for design.l Methods are <br /> <br />developed for the application of gradually varied flow equations to <br /> <br />streams whose flows are near critical even with limitations in the <br /> <br />. <br /> <br />theory and available data. Means are provided for calculation of water <br /> <br />surface profiles which can provide a basis for channel design. <br /> <br />Determination of water surface profiles in the gradually varied flow <br /> <br />analysis involves a step-by-step solution of the energy equation between <br /> <br />adjacent stream sections, with both energy slope between sections and <br /> <br />velocity in the section as unknowns. A trial and error method of <br /> <br />. <br /> <br />solution, is used and becomes feasible with a computer-oriented solution. <br /> <br />Computer programs for solution of flow profiles for either tranquil or <br /> <br />rapid flow have been developed. However, no programs are available for <br /> <br />solution is used and becomes feasible with a computer-oriented solution. <br /> <br />a small change in energy, brought about by either changes in cross- <br /> <br />section or slope, can cause relatively large changes in depth. Five <br />programs for calculation of either tranquil or rapid flow profiles are <br /> <br />reviewed in the following chapter. Three of those programs were used <br /> <br />in the development of the present method. The method is described in <br /> <br />Chapter Ill. <br /> <br />. <br /> <br />lChow, V.T., Open Channel Hydraulics, McGraw-Hill, New York, 1959 <br />