Bagnold number
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The Bagnold number, named after Ralph Alger Bagnold, used in granular flow calculations, is defined by
where m is the mass, D is the grain diameter, γ is the surface tension and μ is the interstitial fluid viscosity.
Bagnold conducted experiments with 1 mm wax spheres suspended in a glycerin-water-alcohol mixture were sheared in a coaxial cylinder rheometer. The rheometer was cleverly designed to measure both the shear and normal forces applied to the walls. He identified two distinct flow regimes: the macroviscous and the grain inertia. These regimes can be distinguished using a quantity that is now referred to as the Bagnold number.
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