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Shear Rate Summary 1 Shear rate: a short history 25 May 2004 Bagnold, 1954 dU/dy, a term in the dimensionless shear strain group, represents the rate of shearing of the grains over one another if dU/dy is large, grain inertia dominates if dU/dy is small, fluid viscosity dominates Assumptions: - uniform shear strain and the grains are moving with the fluid - dU/dy constant through time, driven by external forces - kinetic energy is constant - grain motion includes collisions - elastic grains - the movement of the displaced fluids is of a random nature in relation to that of the grains (density of fluid does not enter) “successions of glancing collisions as one layer overtakes the next slower layer” Pressure = force/area = mass*acceleration/area = (momentum/time)/area dU , enters into the momentum and into the Mean relative velocity U kbD dy expression for the number of collisions per time 1 f U Py 2mU cos i = (grain/area)(1/time)(mass)(velocity) s bd dU cos i Py aif D dy 2 2 Shear Rate Summary 2