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against the reach-average median grain size, DSO. The average D50 of the bed surface sediment in <br />the study reach is 0.069 m. Normalizing the individual values of z by the average D50 of 0.069 m <br />(and appropriate constants) gives the relation shown below (Fig. 26). This relation is identical to <br />the one shown above, except in this case the dimensionless shear stress is used as the dependent <br />variable; the coefficient in the best-fit relation changes accordingly but the exponent is the same <br />(0.40). <br /> <br /> 0.040 <br /> <br /> 0.035 <br /> <br /> 0.030 <br />w <br /> <br /> <br />M 0.025 <br /> <br /> 0.020 <br /> <br />a <br /> <br />c 0.015 <br /> <br /> 0.010 <br /> <br /> 0.005 <br />5 <br /> <br /> 0.000 <br /> 0 100 200 300 400 500 <br /> Discharge (m31s) <br />Figure 26. Relation between dimensionless shear stress and discharge, RM 176, <br />assuming constant grain size. <br />The threshold dimensionless shear stress, *,, for initial motion in this reach was <br />estimated to be 0.025, based on the relation of Mueller et al. (2005) with a reach-average slope <br />of 0.002. The relation shown above indicates that this threshold is reached at a discharge of 286 <br />m3/s. This value is within 3% of the previous recommended discharge for initial motion, Q, = <br />278 m3/s (Pitlick et al., 1999; Pitlick and Cress, 2000). <br />The smooth curve defining the reach-average dimensionless shear stress was developed <br />for a single grain size, which simplifies the analysis, but does not account for the fact that the <br /> <br /> <br /> <br /> • <br /> • <br /> ? _ 0.40 <br />? • Rz _ 0.511 <br /> <br />52