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<br />27 <br /> <br />ill/; = 11 (/; <br /> <br />1 <br />+ f <br />o <br /> <br />(/;(1/). - 1)/(1 - /;))~d>. <br /> <br />....(2-42) <br /> <br />A logarithmic-type vertical velocity distribution in normalized form is <br />util i zed: <br /> <br />'I' <br /> <br />1 <br />= 'I'*(K"R.n()./y) + ar) <br /> <br />....(2-43) <br /> <br />where <br />'I' = u/<U> <br />u = local streamwise velocity <br /><U> = depth~averaged streamwise velocity <br />'I' * = U*I<U> <br />y = k/d <br />ks = equivalent roughness height <br /> <br />Finally, depth-averaged, sediment-particle velocity, <Us>, is expressed as <br /> <br />1 <br />= <U> f aill'l' d>. <br />o <br /> <br /><Us> <br /> <br />....(2-44) <br /> <br />where <br /> <br />a ().) = <br /> <br />proportionality coefficient to relate sediment particle <br />velocity, U (y), to the mass-weighted fluid velocity, U(y), <br />s <br />such that Us = aU(y) <br /> <br />Empirical formulas for the rate of scour during stream-bed erosion, E, and the <br />rate of deposition, 0, are expressed by <br /> <br />E = M(-rhce - l)(Cmax-Cb)/Cmax ; T > Tce ....(2-45) <br /> <br />and <br /> <br />o = - V s C b (1 - T h cd) T < T cd <br /> <br />....(2-46) <br /> <br />where <br />M <br /> <br />= <br /> <br />erosion-rate constant <br />bed shear stress <br /> <br />T <br /> <br />= <br />