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May 7. 1999 Fluvial Geomorphological Assessment Upper Arkansas River Page 65 I I , I I J I I I I I I I I t l I I I 7.3.3.2. Reach Average Hydraulic Analysis The maximum average water surface slope is found at 1M Site I, at approximately 0.9%. The lowest reach average water surface slope is found at 1M Site 5, at approximately 0.5% (Table 7,6, App. B.l), The maximum reach average velocities are found in 1M Site 1 and IM Site 4, ranging between 3.0 and 4.9 fps, in which both have steep water surface slopes and split flows around island features. The lowest reach average channel velocities are found at IM Site 3, which range between 2.5 and 3.6 fps (Table 7.6, Figure 7.4). Reach average shear stresses show that 1M Site I has the largest reach average shear stress values ranging between 0.9 and 1.8 psf, Steep water surface slopes, as well as increased hydraulic radii resulting from a high terraced bank on the left side increase the shear stress values. The lowest reach average shear values are found in 1M Site 5, ranging between 0.6 and 1.0 psf(Table 7.6, Figure 7.5). The largest hydraulic depths, up to the 5-year recurrence interval discharge, occur at 1M Site 3. Beyond the 5-year discharge, 1M Site 6 has the largest hydraulic depth values, up to 3.4 ft. The minimum values of hydraulic depth for all of the study reaches occur at 1M Site 5, ranging between 1.5 and 2.7 ft for all peak discharges (Table 7.6, Figure 7.6). 7.4. Incipient Motion Analysis Incipient motion is defined as the point at which a bed material particle under hydraulic influences is on the verge of initiating motion. Sizes and frequency of sediment in motion, or mobilized, are dependent upon the range of hydraulic conditions present, primarily energy slope and hydraulic radius. Incipient motion calculations utilizing Shield's criteria are as follows: 'tc = D, y, F* (Eqn. 7.3) 'tc = critical shear stress (ft2) D, = diameter of sediment particle (ft) y, = submerged unit weight of sediment (103 lbs/ft3) F* = dimensionless Shield's parameter The equation listed above was rearranged to determine the size of bed material at incipient motion for a given flow condition, D, = 'tc ly,F* (Eqn 7.4) Shear stress for the bed is given by the following: 't= Y w R Sr (Eqn 7,5) 't = bed shear stress (ft2)