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<br /> 0.84 <br /> 0.82 <br />" 0.80 <br />U <br />~ <br />Z <br />w 0.78 <br />U <br />u: <br />u. 0.76 <br />w <br />0 <br />U <br />w 0.74 <br />~ <br />a: <br /><( 0.72 <br />::c <br />U <br />(/) <br />Cl 0.70 <br /> 0.68 <br /> 0.66 <br /> 0.6 <br /> <br />EXPLANATION <br /> <br />o DATA SET 1 <br />. DATA SET 2 <br />o DATA SET 3 <br />. DATA SET 4 <br />D. DATA SET 5 <br />& DATA SET 6 <br /> <br />// <br /> <br /> <br /> <br />0.8 <br /> <br />1.0 <br /> <br /> <br />1.2 <br /> <br />1.4 <br /> <br />1.8 <br /> <br />1.6 <br /> <br />RATIO OF HEAD ON WEIR TO HEIGHT OF WEIR CREST <br />ABOVE FLUME FLOOR, h/W <br /> <br />Figure 21. Variation of discharge coefficient wilh ralio of the head on the weir to Ihe height of the weir cresl above the flume floor. <br />Each regression line represents a different set of calibration data. <br /> <br />between stations 20 and 40 (upstream from the slot). Slopes <br />for the base reach then were compared statistically, at con. <br />fidence coefficients of 90 and 95 percent, with counterpart <br />slopes for reaches adjacent to the base reach to ascertain <br />whether or not the slopes of the adjacent reach were likely <br />to be from the same slope population as those for the base <br />reach. If so, elevations from the adjacent reach were in- <br />cluded with elevations from the base reach to form a new <br />base reach, and slopes for the new, longer base reach were <br />redetermined by linear regression. These slopes, in turn, <br />were compared with slopes from the next adjacent reach to <br />establish if all slopes were part of the same population. This <br />process of extending the length of the base reach was contin- <br />ued until it was evident that the slopes for Ihe adjacent and <br />base reaches were different. The average slope for the run <br />was then taken as the average of the least-squares slopes <br />from all sets of elevations for the base reach. <br />The analysis procedure is based on the premise that <br />changes in slope occur abruptly between the uniform and <br />nonuniform reaches, rather than gradually throughout the <br />entire reach. Although the premise cannot be verified be- <br /> <br />cause of the considerable variations in slopes, graphs of all <br />computed average slopes, which also were used in making <br />judgments about the commonality of slopes, indicate that <br />slope changes in the water surface usually were reasonably <br />abrupt. <br />The data in columns 4 and 5 of table 7 indicate, for <br />each run, the stationing of the end points of the reach for <br />which a uniform slope was presumed to exist; table 5 lists <br />the mean slope values for all runs. For those few runs in <br />which relatively long reaches of common slope were sepa- <br />rated by a short reach of dissimilar slopes, the average slope <br />was determined by using elevations from the entire reach. <br />The precise degree to which computed mean water- <br />surface slopes represent uniform-flow conditions cannot be <br />estimated reliably. However, on the basis of variances of the <br />slope sets used to define the mean slope for each run, most <br />mean slope values (see column 7 of table 5) can be expected <br />(99-percent confidence coefficient) to be well within 25 <br />percent of the true mean slope, except for slopes for the <br />23.5-mm runs, which may be somewhat less accurate. <br /> <br />Hydraulic and Sedimentologic Data 21 <br />