# Drag Characteristics of Spheres in Bingham Fluids

*by*Hyoseop Woo, Univ of Cincinnati, United States,

**Abstract:**R.W. Ansley and T.N. Smith's type of drag relation can be traced back closely, if not completely, to the Newtonian drag curve. The equivalent diameter for a sphere in a Bingham fluid is defined as the size of the imaginary, concentric drag envelope surrounding the sphere whose drag characteristics in the Newtonian fluid is equivalent to that of the real sphere in the Bingham fluid. The normalized equivalent diameter is found to be a unique function of the Plasticity number. For falling spheres, the critical Plasticity number, below which the influence of the yield stress on the settling characteristics vanishes as if the sphere fell in the Newtonian fluid, is found to be about 0.01. When the diameter of the sphere concerned in a particular Bingham fluid is larger than the critical diameter for the Bingham fluid, the fall velocity of the sphere can be obtained using the Newtonian drag relation. When it is smaller than the critical diameter, the yield stress of the Bingham fluid should be considered in the drag relation and the fall velocity can be obtained from Ansley and Smith's Bingham drag relation.

**Subject Headings:**Drag (fluid dynamics) | Spheres | Fluid velocity | Plasticity | Yield stress | Curvature | Friction

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