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<br />REGIME EQUATIONS FOR VELOCITY AND DISCHARGE <br /> <br />One of the reasons for developing an equation to predict Manning's <br /> <br />roughness coefficient (equation 10) using friction slope and hydraulic <br /> <br />radius as power variables was that the Manning equations (equations 1 <br /> <br />and 3) are in the form of power equations. Therefore, for the simple <br /> <br />case of uniform flow and no other factors affecting bank roughness, <br /> <br />equation 10 could be directly substituted into the Manning equations <br /> <br />(equations 1 and 3). Substituting equation 10 into equations 1 and 3 <br /> <br />results in modified Manning equations for velocity: <br /> <br />v = 3.81 RO.83 50.12 , <br /> <br />( 11) <br /> <br />and for discharge: <br />Q = 3.81 ARO.83 50.12 , (12) <br /> <br />where the variables are the same as defined previously. Equation 11 was <br /> <br />also derived by multiple regression techniques using velocity as the <br /> <br />dependent variable and equation 12 was derived by substituting equation <br /> <br />11 into the continuity equation, equation 2. These equations provide a <br /> <br />3'1 <br /> <br /> <br />means of solving directly for velocity and discharge in uniform natural <br /> <br />channels without the need for subjectively evaluating ~annel roughness <br /> <br />for those cases in which total channel-flow resistance (equation 5) is <br /> <br />I ittle affected by factors other than the base factor, n. <br />