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<br />The procedure is to first find the value of the auxiliary function AF. <br /> <br />AF <br /> <br />= ~s JO.l (Ys l)gd <br />Y s <br /> <br />(5.2) <br /> <br />where: <br /> <br />ds <br />Ys/Y <br />" <br /> <br />representative grain size in mm <br />= specific gravity of sediment grains (= 2.65 for sand) <br />kinematic viscocity of water (= 0.01 cm2/sec) <br />= acceleration of gravity (= 980 cm/sec2) <br /> <br />g <br /> <br />The grain diameter used was 0.3 mm which corresponds to the D.o grain <br />size for the bed material shown in Figure 5.2. The value of the auxiliary <br />function calculated for this grain size was AF = 6.6. The Shields diagram is <br />used to find the dimensionless shear stress '* = 0.04. From this value <br />the critical shear stress can be found from the relationship <br /> <br />'c = '*(Ps - p)gds <br /> <br />(5.3) <br /> <br />where: <br /> <br />'c = critical shear stress in dynes/cm2 <br />Ps = density of sediment grains (= 2.65 g/cm" for sand) <br />p density of water (= 1.00 g/cm") <br /> <br />The critical shear stress for the average sediment particle size on the <br />bed was calculated to be 'c = 1.94 dynes/cm2 = 0.0043 lb/ft2. <br /> <br />3) Sediment Transport Rate - The Keyer-Peter, Ku11er method was used to <br />compute the bedload transport rate based on the shear stresses calculated <br />above (12, p. 193). <br /> <br />Qs = 345.6 <br /> <br />W ( )1.' <br />. T - l'c <br />6s.fy7g <br /> <br />(5.4) <br /> <br />where: <br /> <br />Qs = bedload transport rate in tons/day <br />W = strean width in ft. <br />Y = unit weight of water (= 62.4 lb/ft") <br />g = acceleration of gravity (= 32.2 ft/sec2) <br /> <br />6~ = specific gravity of submerged sediment (= 1.65) <br /> <br />, actual shear stress in lb/ft2 <br />'c critical shear stress in lb/ft2 <br /> <br />The transport rate was converted from tons/day to cubic feet per day (1 <br />ton/day = 21. 7 ft"/day for sand). By computing these transport rates for <br />a given discharge the amount of scour can be estimated from the computational <br />reach corresponding to the cross section at river miles 1197.2 and 1198.9. <br />The length of the reach was approximately L=1800 ft. and the width was <br />approximately W=lOOO ft. The procedure used was to calculate Qs at a cross <br />section upstream and downstream from the cross section of interest. <br />Subtracting the sediment flow out of the reach from the sediment flow into the <br />reach gave the net amount of material removed Q~. The SCOur rate for a <br />given flow conditions was from the relationship: <br /> <br />, <br />SR = Qs/WL <br /> <br />(5.5) <br /> <br />59 <br />