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<br />8 <br /> <br />For small slope angles e, cos e ~ 1, d ~ y and dd/dx ~ dy/dx so <br /> <br />that Eq. (2-3) can be expressed as <br /> <br />~ _ So - Sf <br />dx - 1 - "d(Vz/2g)/dy <br /> <br />(2-4) <br /> <br />v2 <br />a- <br />2g <br /> <br />--- <br /> <br />to datum <br />Energy <br />-- slope" S <br />-- F' <br />~-- <br /> <br />--- <br /> <br />n <br />-~ <br /> <br />Line parallel <br /> <br />- <br /> <br />d cos e <br /> <br /> <br />d <br /> <br />Channel 51 <br />OPe" S <br />o <br />dk. <br /> <br />I ' I <br />I e-{l <br /> <br />z <br /> <br /> <br />~. <br /> <br /> <br />Datum <br /> <br />@ <br /> <br />Fig. 2-1. Conditions of gradually-varied-flow. <br /> <br />Expressions for the friction slope, such as the Manning or Chezy <br /> <br />Equations, can then be substituted into this equation to provide the <br /> <br />most suitable means for evaluation of dy/dx (the water surface profile). <br /> <br />Water surface profiles are generally classified according to the <br /> <br />slope of the channel and the possible shapes of the water surface for a <br /> <br />channel of given slope. Channel slopes considered in relation to the <br /> <br />present problem are generally classified as sustaining, or falling in <br /> <br />the direction of flow. In a channel of .sustaining slope, the shape of <br />