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<br />4 <br /> <br />(4) Channel slope is small. <br /> <br />The following basic equations are employed: <br />(1) Flow-continuity equation: <br /> <br />where <br /> <br />dQ = q <br />dx <br /> <br />.... (2-1) <br /> <br />(2) Sediment-continuity equation: <br /> <br />aQ <br />~+ <br />ax <br /> <br />aAb <br />(1-A)iit =qsL <br /> <br />.... (2-2) <br /> <br />(3) Flow-energy equation: <br /> <br />2 2 <br />02V2 01V1 <br />Y2 + - = y + - + he <br />2g 1 2g <br /> <br />.. .. (2-3) <br /> <br />(4) Energy head-loss equation: <br />2 2 <br />02V2 01V1 <br />he = LSf + cl2"9 - 2"91 <br /> <br />....(2-4) <br /> <br />Q & Qs = water and sediment discharges in volume units <br />q = lateral water inflow per unit width <br />Ab = bed cross-section area <br />q . = lateral sediment inflow in volume per unit time and length <br />SA. . <br />A = poros ity of bed sed iment <br />Yl & Y2 = water-surface elevations at ends of reach <br />Vl & V2 = mean velocities at ends of reach <br />01 & O2 = velocity-head correction factors for flow at ends of reach <br />he = energy head loss <br />L = discharge-weighted reach length <br />Sf= representative friction slope for reach <br />C = expansion or contraction loss coefficient <br />