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<br /> <br />DRAFT <br /> <br />Sediment Scaling <br /> <br />Sediment models that involve erosion of noncohesive bed material must simulate shear stress (To) <br />because the tractive stress creates the drag force required to overcome the forces holding a particle <br />in place. Tractive stress on a particle will fluctuate because of turbulence. Drag force and <br />turbulence are a function of Reynolds number. A model operated according to Froude scaling does <br />not necessarily simulate tractive forces and sediment erosion accurately. Sediment erosion can be <br />simulated properly by making the model and prototype dimensionless unit sediment discharge rates <br />equal (q,om = q,'p). <br /> <br />The following equations define dimensionless shear stress (T'), Grain Reynolds number (R') and <br />dimensionless unit sediment discharge (q,'). These equations are used to relate model and <br />prototype parameters to determine sediment erosion characteristics. <br /> <br />1. = <br /> <br />u" <br />g;r <br /> <br />"Y <br />("Y. ."y) <br /> <br />[dimensionless shear stress] <br /> <br />(8) <br /> <br />- !!,j' <br />R - v <br /> <br />[Grain Reynolds number] <br /> <br />(9) <br /> <br />q.. = <br /> <br />q, <br />u'd <br /> <br />[dimensionless unit sediment discharge] <br /> <br />(10) <br /> <br />u' = V ~ <br /> <br />[shear velocity] <br /> <br />(11) <br /> <br />Where: <br /> <br />f = the Darcy friction factor <br />d = the sediment particle size <br />u' = the shear velocity <br />v = the kinematic viscosity <br />"y = specific weight of water <br />"Y, = 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 (T.: = T ;), the <br /> <br />4 <br />