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<br />Similarly, equations 10 and 11 can be used to estimate the velocity <br /> <br />and discharge, respectively. <br /> <br />The values obtained are: <br /> <br />v = 3.81 (7)0.83 (0.02)0.12 = 12.0 ft/s (3.66m/s), and <br /> <br />Q = 3.81 (1000) (7)0.83 (0.02)0.12 = 12,000 ft3/s (340 m3/s). <br /> <br />These steps could be repeated for other flow depths to develop relations <br /> <br />between estimated roughness and depth of flow and between velocity, <br /> <br />discharge, and depth of flow. If there had been additional factors <br /> <br />affecting flow resistance, the value of n computed here would have been <br /> <br />the base n value and would have been adjusted appropriately using <br /> <br />equation 5. <br /> <br />FLOW REGIME IN STEEP CHANNELS <br /> <br />Standard hydraulic theory and analysis indicate that when slope <br /> <br />exceeds critical slope--that is, when the Froude number exceeds unity-- <br /> <br />higher velocities and supercritical flow result. Petersen and Mohanty <br /> <br />(1960) observed extended reaches of supercritical flow; however, these <br /> <br />were observed in flume studies of steep-gradient streams. The field <br />I <br />data collected for this study (table 1) and those of Barnes (1967), <br /> <br />Limerinos (1970), Thompson and Campbell (1979), Bathurst (1978), Bray <br /> <br />(1979), Judd and Peterson (1969), and Kellerhals (196]) included slopes <br /> <br />as steep as 0.052, indicate that the Froude numbers for flow in steep- <br /> <br />gradient streams are less than unity. The combined effects of channel <br /> <br />and cross-section variations create extreme turbulence and energy losses <br /> <br />..7 <br />::- <br />_,,,,, h.....1 <br /> <br />that result in increased flow resistance. The characteristic turbulence <br /> <br />of a steep-gradient stream is shown in a photograph (fig. 7) taken at <br /> <br /> <br />the Arkansas River site (table 1, site 1). Studies of the flow resistance <br /> <br />4~ <br /> <br />