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<br />10 <br /> <br />. <br /> <br />SQ1/4 can be considered a transitional range when streams are classified as <br /> <br />intermediate or transitional. <br /> <br />. <br /> <br />2.2.1.5 The Longitudinal Profile <br /> <br />The longitudinal profile of a stream shows its slope or gradient. Since <br /> <br />. <br /> <br />a river channel or river system is generally steepest in its upper regions, <br /> <br />most river profiles are concave upward. Shulits (1941) provided an equation <br /> <br />for the concave horizontal profile in terms of distance along the stream <br /> <br />. <br /> <br />s = S <br />x 0 <br /> <br />-aX <br />e <br /> <br />(2-4) <br /> <br />where, S the slope at any station a distance X downstream of reference <br /> x station, <br /> S = the slope at a reference station J <br /> 0 <br /> a = a coefficient of slope change. <br />Similarily, the bed material normally reduces in size downstream. The change <br />in particle size with distance downstream can be expressed as <br /> <br />. <br /> <br />. <br /> <br />-sx <br />D50x = DSOo e <br /> <br />(2-5) <br /> <br />where, <br /> <br />DSOx <br /> <br />= median size of bed material at distance <br />reference station, feet, <br /> <br />x <br /> <br />downstream of a <br /> <br />. <br /> <br />D500 = median size of bed material at the reference station, feet, <br /> <br />s <br /> <br />= a wear or sorting coefficient that is dependent on river <br />characteristics and flow conditions. <br /> <br />. <br /> <br />It is clear that these exponential functions can only give a very general <br /> <br />idea of the longitudinal bed profile. The general curve is disturbed by <br /> <br />the presence of bends. Hence, the longitudinal slope of the thalweg will <br /> <br />. <br /> <br />never completely follow a simple functional relationship. Moreover, the <br /> <br />presence of confluences and tributaries influences the main river as far <br /> <br />as bed level and grain size are concerned. <br /> <br />. <br /> <br />. <br />