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<br />16 <br /> <br />qt = lateral water inflow per unit width <br />G = volumetric sediment-transport rate <br />B = movable-bed width <br />y = movable-bed elevation <br />h = water-surface elevation <br />a = velocity-head correction factor <br />A = cross-section area <br />HL = head loss between sections k-1 and k <br /> <br />4. Sediment-Transport Function: <br /> <br />Five options are available for cOll1luting bed-material transport rates: <br />Laursen's relationship, as modified by Madden for large rivers (Laursen, <br />1958); Toffaleti's formula (Toffaleti, 1968); Yang's stream-power formula <br />(Yang, 1973); DuBoys' formula (Brown, 1950); and a special relationship <br />between unit-width sediment-transport capacity and the product of flow depth <br />and energy slope which is developed for a particular river reach. <br /> <br />Laursen's relationship is expressed by <br /> <br />7/6 <br />qs = 283.39 q ~ Pi(dsi/D) (TOtTc;-1) <br /> <br />....(2-21) <br /> <br />whe re <br />qs = bed-material transport rate per unit width <br />q = water discharge per unit width <br />p. = fraction by weight of the i-th fraction of the bed sediment with <br />1 <br />mean si ze, dsi <br /> <br />D = flow depth <br /> , = Laursen's bed-shear stress due to grain roughness <br />TO <br /> = py2/(58(d50/D)1/3) <br />d50 = median sediment size <br />y = mean flow velocity <br />T = critical shear stress for mean particle size, d . <br /> ci Sl <br /> <br />The second option, the Toffaleti formula, is based on Einstein's bed-load <br />function and various ell1lirical data and is expressed by <br />