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<br />8 <br /> <br />(5) Channel slope is small. <br /> <br />The following basic equations are employed: <br />(1) Flow-continuity equation: <br /> <br />~ = q <br /> <br />(2) Sediment-continuity equation: <br /> <br />aQs <br />-+ <br />ax <br /> <br />Ab <br />(1 - ^) at = qst <br /> <br />(3) Flow-energy equation: <br /> <br />(z + D <br /> <br />V2 <br />+ a 2gh= <br /> <br />(z + D <br /> <br />y2 <br />+ a 2g)2+ Ht+ Hl.v <br /> <br />where <br />Q & Qs = water and sediment discharges <br />q = lateral water inflow per unit width <br />A = bed cross-section area <br />b <br />q = lateral sediment inflow <br />Sl. <br />^ = porosity of bed material <br />z = channel bed elevation <br />D = flow depth <br />H = total head above datum <br />a = correction factor for velocity head <br />V = mean flow velocity <br />Ht= friction loss = s~x <br />HI.V =losses due to all other factors except friction = Stv~X <br /> <br />4. Sediment-Transport Function: <br />The sediment discharge per unit width, qs' is expressed by <br /> <br />Vb c <br />qs = a y <br /> <br />.... (2-7) <br /> <br />....(2-8) <br /> <br />....(2-9) <br /> <br />.... (2-10) <br />