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<br />12 <br /> <br />(1) The river channel is sufficiently straight and uniform that the one- <br />dimensional flow approximation can be employed. <br />(2) Hydrostatic pressure prevails at any point in the channel, and the <br />water-surface slope is small. <br />(3) The density of sediment-laden water is constant over the cross <br />section. <br />(4) The resistance coefficient for the unsteady flow is assumed to be the <br />same as that for a steady flow. <br /> <br />The following basic equations are employed: <br />(1) Flow-continuity equation: <br /> <br />tl u. - <br />ax +Tat-qt-O <br /> <br />.... (2-15) <br /> <br />(2) Sediment-continuity equation: <br /> <br />ao aAd <br />a / + (1 - ^) at - qs = 0 <br /> <br />.... (2-16) <br /> <br />(3) Flow-momentum equation: <br /> <br />H- + a (~~V) + gA * = pgA(So- Sf+ Dt) <br /> <br />....(2-17) <br /> <br />where <br /> <br />o & Os = water and sediment discharges <br />T = aA/ay <br />y = f1 ow depth <br />A = cross-section area for water <br />Ad = sediment volume deposited per unit channel length <br />qt = qs + qw <br />qs = lateral sediment inflow <br />qw = lateral water inflow <br />^ = porosity of bed material <br />V = mean flow velocity <br />B = momentum correction factor <br />p = density of water <br />