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<br />EM 1110-2.1601 <br />1 Jul 91 <br /> <br />has been retained in several procedures because of its <br />wide acceptance and simplicity of use. This applies <br />particularly to varied flow profiles, pulsating flow, and the <br />design of free-surface hydraulic models. <br /> <br />b. Friction losses. <br /> <br />(I) The importance that friction plays in the determi- <br />nation of flow characteristics in channels cannot be over- <br />stressed. Three equations (Chezy's, Manning's. and <br />Darcy's) are in general use for the determination of losses <br />due to friction. These equations expressed as friction <br />slope Sf' i.e., slope of the energy grade line, are <br /> <br />(a) Chezy: <br /> <br />v2 <br />SJ~- <br />C2R <br /> <br />(2.1) <br /> <br />(b) Manning: <br /> <br />SJ ~ <br /> <br />V2n2 <br />2.2IR 413 <br /> <br />(2-2) <br /> <br />(c) Darcy: <br /> <br />2 <br />S ~ ]V <br />J 8Rg <br /> <br />(2-3) <br /> <br />where <br /> <br />v ~ velocity <br /> <br />C = Chezy coefficient <br /> <br />f = Darcy-Weisbach resistance <br />coefficient <br /> <br />g = acceleration of gravity <br /> <br />The relation between the coefficients in these equations <br />can be expressed as <br /> <br />2-2 <br /> <br />C R1/6 <br /> <br />1.486 n <br /> <br />lO.8 <br />-(1!2 <br />, <br /> <br />(2-4) <br /> <br />(2) When determining friction coefficients. it should <br />be recognized that the mergy grade line and therefore the <br />friction coefficient include uniformly occurring turbulence <br />and eddy losses as well as the friction loss. Equivalent <br />roughness for the same reason. Special. locally occurring <br />turbulence and eddy losses are to be determined sepa- <br />rately as covered in hydraulic textbooks and elsewhere in <br />this manual. <br /> <br />c. Friction coefficients. <br /> <br />(I) The equations for using equivalent roughness to <br />determine friction coefficients (plate 3) are <br /> <br />(a) For hydraulically smooth channels <br /> <br />(5.2RnJ <br />C ~ 32.6 10glO l-C <br /> <br />(2-5) <br /> <br />(b) For hydraulically rough channels <br /> <br />C = 32.6 10glO (12~2R) <br /> <br />(2.6) <br /> <br />where R" is the Reynolds number. <br /> <br />(2) For the channel surface to be hydraulically <br />smooth, the equivalent roughness must be less than the <br />critical value given by paragraph 8.12 of Chow (1959). <br /> <br />kc ~ [~ J (~ ) <br /> <br />(2-7) <br /> <br />where v is the kinematic viscosity of water. <br /> <br />e <br /> <br />, <br /> <br />e <br /> <br />. <br /> <br />e <br />