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<br />25 <br /> <br />(1) Flow is one dimensional and hydrostatic pressure prevails at any <br />point in the channel. <br />(2) Similarity of both velocity and suspended-sediment concentration <br />profiles in a vertical at all locations in the flow field is assumed. <br />(3) The resi stance coeffi c ient for the unsteady fl ow is the same as that <br />for a steady flow. <br />(4) Channel slope is small. <br /> <br />The following basic equations are employed: <br /> <br />(1) Flow-continuity equation: <br /> <br />~=.!.~+s <br />at b ax - <br /> <br />.... (2-37) <br /> <br />(2) Sediment-continuity equation: <br /> <br />aC aC a aC <br />at + uaS ax = ax (Dx ax) + S <br /> <br />.... (2-38) <br /> <br />(3) Flow-momentum equation: <br /> <br />l.!!+ l.!!+ ah + S = D <br />at uax gax ge <br /> <br />....(2-39) <br /> <br />where <br />h = water-surface elevation <br />b = mean channel width <br />q = i nfl ow rate to a node <br />s = lateral inflow or outflow rate <br />C = mass concentration <br />u = longitudinal component of sediment-particle velocity <br />as <br />D = turbulent mass diffusivity in the logitudinal direction <br />x <br />S = source/sink term produced by scour or deposition <br />u = mean flow velocity <br />S = friction slope <br />e <br />