Durand's model attempted to find a single formula for sand size and above, but Babcock's data showed that a single formula could not apply. A subsequent group of models is based on Wilson's layered force-balance analysis of slurry flows; applied to friction losses and deposition limit. Models based on variants of this analysis include those by Shook and others at the Saskatchewan Research Council, SRC. Early versions of Wilson's model relied on particle fall velocity to find friction losses, but the classical iterative method of finding fall velocity has now been replaced by a direct method. This is based on the shear Reynolds number of the particle, which can be expressed in terms of the better known Archimedes number, making calculations of slurry friction and limit of deposition involve two principal parameters: the Archimedes number and the diameter ratio d/D.
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