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<br />This substitution yields a variation of the Manning equation <br /> <br />__ 1.49 AR2/3S1/2 , <br />il <br /> <br />(3) <br /> <br />n <br /> <br />and the variables are as defined above. The Manning equation has been <br /> <br />used extensively as an indirect method for computing discharges or <br /> <br />depths of flow in natural channels. Equations 1 and 3 were developed <br /> <br />for conditions of uniform flow in which the water-surface slope, friction <br /> <br />slope, and energy gradient are parallel to the streambed, and the area, <br /> <br />hydraulic radius, and depth remain constant throughout the stream reach. <br /> <br />It is assumed that the equation is also val id for the nonuniform reaches <br /> <br />usually found in hydraul ic studies of channels and flood plains and that <br /> <br />the velocity distribution is logarithmic (Chow, 1959). The Manning <br /> <br />equation has provided reI iable results when used within the range of <br /> <br />verified channel-roughness data. The selection of appropriate n values, <br /> <br />however, requires considerable experience, even though extensive guidel ines <br /> <br />are avai lable. <br /> <br />Many studies based on hydraul ic theory pertaining to flow resist- <br /> <br />ance have been made and are summarized by Chow (1959), Limerinos (1970), <br />I <br />Carter and others (1963). A study by Bray (1979), who evaluated a <br /> <br />number of equations used to predict roughness coefficients of gravel-bed <br /> <br />streams, found that the equations of Limerinos (1970) were the most <br /> <br />accurate. <br /> <br />1 <br />