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<br />Where: <br />f = the Darcy friction factor <br />d = the sediment particle size <br />. the shear velocity <br />u = <br />v = the kinematic viscosity <br />r = specific weight of water <br />r, = specific weight of sediment <br /> <br />Shields developed a diagram relating dimensionless shear stress to Grain Reynolds number (Vanoni, <br />1975). Shields used this diagram to define critical shear stress. Vanoni (1975) used Taylor's data <br />to show that dimensionless unit sediment discharge at low transport levels falls very close to Shields <br />curve for incipient motion. In order to properly model sediment transport, the dimensionless unit <br />sediment discharge rate (q;) must be the same in model and prototype. Details of scaling sediment <br />transport are outlined in the report "Hydraulic Model Studies of Fuse Plug Embankments" (Pugh, <br />1985). Dimensionless shear stress is a form of the Froude number and the density ratio of <br />sediment to water. If a model is scaled geometrically according to Froude scaling (1m' = 1;), the <br />model unit sediment discharge rate (q;) will be too great for Grain Reynolds numbers ranging <br />between 5 and 100. Therefore, the model sediment size fractions should be adjusted to properly <br />simulate sediment transport in this range. <br /> <br />A diagram of settling velocity (w) of sand and silt particles (fig. 7) illustrates that small particles <br />(less than 1 mm in diameter) settle at slower velocities as the particles become smaller. In order <br />to adjust the sediment discharge rate in the model, particles less than 1 millimeter in diameter are <br />increased in size until the settling velocity is corrected to the proper velocity consistent with Froude <br />scaling. Particles larger than 1 millimeter settle as a function of the diameter (d) to the 1/2 power, <br />consistent with Froude scaling. When the model grain sizes are adjusted for settling velocity, the <br />value of l' decreases while the value of R' increases bringing the model value of q; closer to the <br />same value as the prototype. The grain size distribution of bedload in the South Platte at Oxford <br />Avenue was simulated in the model. Figure 8 shows the prototype and model grain size <br />distributions. The model grain sizes were adjusted as described above to compensate for Reynolds <br />number effects. <br /> <br />MODEL RESULTS AND ANALYSIS <br /> <br />The main areas of the model study were (1) model calibration, (2) boating conditions, (3) sediment <br />studies, and (4) floodflow conditions. These and other areas are discussed in the following sections. <br /> <br />Model Calibration <br /> <br />The model was calibrated to accurately measure discharge, Flow entering the model was measured <br />with a Venturi orifice meter. Orifice plates ranging in size from 1-3/8 to 4-3/8 inches were used. <br />A mercury manometer indicated the differential across the plates. The accuracy of the orifice <br />meter and manometer was also checked with a strap-on sonic flowmeter. The comparison of the <br />orifice with the flowmeter showed less than a 2-percent difference in flow measurement indicating <br />no problem with measurement of flow entering the model. <br /> <br />5 <br />