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<br />STUDY DF HYDRAULIC GEOMETRY <br /> <br />According to Langbein (1964, p. 301), "Rivers construct their own <br />geometries." The shape of a river channel at any location is a <br />function of flow, the composition of the material moving through <br />the section, and the composition of material forming the bed and <br />banks of the channel. A change in the magnitude of flow will <br />cause a change in velocity, depth, and width. <br /> <br />Leopold and Maddock (1953) showed that some hydraul ic-geometry <br />parameters of stream channels vary with discharge as simple <br />functions at a given river cross section. They found that width, depth, <br />and velocity, when plotted against discharge on logarithmic paper <br />could be expressed by a straight line for a considerable range of <br />discharge. Similar variations in relation to discharge exist along <br />the length of the stream for the same frequency of discharge. The <br />functions derived for other sections along the river differ only <br />in the numerical values of the coefficients and exponents. <br /> <br />Width, depth, and velocity for a particular cross section can be <br />related to discharge by the simple functions: <br /> w = aQb (2) <br /> d = cQf (3) <br /> v = k~ (4) <br /> <br />Because Q = wdv, the sum of the exponents b, f, and m should equal <br />1.00, and the product of the coefficients a, c, and k should equal <br />1.00. Some departure of the sum and product from unity may be <br />expected if the exponents and coefficients are determined from 1 ines <br />fitted to scatter data on graph paper (Brush, 1961). <br /> <br />ANALYSIS OF DATA <br /> <br />Hydraul ic-Geometry Parameters at a Station <br /> <br />Graphs of width, depth, and velocity plotted against discharge were <br />drawn for 117 stations in Kansas and adjoining areas. The lines <br />representing the relations were fitted to the scattered data by eye. <br />The exponents and coefficients vary among stations, but in all <br />instances, straight lines on logarithmic paper define the relations <br />adequately. <br /> <br />4 <br />