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ci m = a constant relating segment i to segment m, the calibrated segment nm = the roughness of the adjacent, calibrated segment The value of ci m may be estimated by similar logic to equation 12, where: ' ci,m = (d')1?6 (16) m where, d. = the particle size in the uncalibrated segment dm = the particle size in the calibrated segment, with the particle size in both cases, the median diameter of the particle size which is larger than 75% of the bed materials. As in the previous discussion, this approach is applicable when changes in roughness are caused primarily by changes in particle size. Roughness related to form and vegetation may be estimated using refer- ences such as Chow (1959) and Barnes (1967). DIRECT DETERMINATION OF THE VELOCITY DISTRIBUTION Figure6 shows a cross section in which the velocity of each channel segment is determined for each of three different discharges. The-average velocity for any channel segment where two or more such velocity measurements have been made, may be related to the total discharge vi = ai Q b 1 (17) where, v. is the mean velocity of the i-th channel segment when the total discharge of the stream is Q. The constants a• and b. are obtained by fitting a least squares regression to tw; or more velocity- discharge data pairs. For discharges not measured, v. is found by applying the empirical constants ai and bi to the discharge for which an estimate of vi is desired. The-concept that.the average velocity in a cross section is related to the discharge by an equation v = a Q appears to be well accepted in the literature (Paris, 1977). The assumption is made that the average velocity in a channel segment is also related to the total stream discharge by an equation of the same form. LIMITATIONS AND ERROR ANALYSIS OF APPROACHES Some of the problems encountered in the application of these methods .J are more serious in the engineering sense than they are for instream flow 2I