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<br />18 <br /> <br />where <br />GR = volumetric sediment-transport rate at the (k+1)st cross section <br />GL = volumetric sediment-transport rate at the (k-1)st cross section <br />Yp' = movable-bed thickness at the kth cross section at the time <br /> of (j+1)t.t <br />Yp = movable-bed thickness at the kth cross section at the time <br /> of jt.t <br />XL = reach length between (k-1 )st and kth cross sections <br />XR = reach 1 ength between kth and (k+1)st cross sections <br /> <br />Note that the transport capacity is calculated at the beginning of the time <br />interval, and is not recalculated during that interval. However, the <br />gradation of the bed material is recalculated during the time interval in <br />order to account for armoring effects. An equilibrium water depth below which <br />sediment with a particular grain size becomes immobile is introduced using <br />Manning's equation, Strickler's equation, and Einstein's bed-load function: <br /> <br />Deq = (q/(10.21d1/3))6/7 <br /> <br />.... (2-25) <br /> <br />where <br />q = water discharge per unit width <br />d = sediment particle size <br /> <br />A zone of bed between the bed surface and the equilibrium depth is designated <br />the active layer. When all material is removed from the layer, the bed is <br />considered to be co~letely armored for that particular hydraulic condition. <br />When a mixture of grain sizes is present, the equilibrium depth calculations <br />utilize the given gradation curve to relate the quantity of each grain size <br />present in the bed to the depth of scour. The armor layer formed by a <br />previous discharge is tested for stability using Gessler's (1971) stability- <br />analysis procedure. If Gessler's stability number is less than 0.65, the <br />armor layer is treated as unstable and the bed-layer size distribution is <br />computed for the next time step. <br />