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Beverloo law for hopper flow derived from self-similar profiles

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Abstract

We use particle simulations to investigate the mass flow in two-dimensional hopper flow and to analyze the dependency of the flow rate with the bottleneck width and the particle diameter. A flow rate law is derived from self-similar velocity and density profiles at the neck. The resulting relation is an enhancement of the Beverloo relation that incorporates the dependency of the density with the neck width. The parameters of the Beverloo relation are interpreted by coupling the hourglass theory with the free-fall arch theory using non-zero arch velocity as accounted by the hourglass theory.

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Authors and Affiliations

  1. School of Civil Engineering, The University of Sydney, Sydney, NSW, 2006, Australia

    Fernando Alonso-Marroquin

  2. College of Petroleum Engineering and Geosciences, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

    Peter Mora

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  1. Fernando Alonso-Marroquin
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  2. Peter Mora
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Correspondence to Fernando Alonso-Marroquin.

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Alonso-Marroquin, F., Mora, P. Beverloo law for hopper flow derived from self-similar profiles. Granular Matter 23, 7 (2021). https://doi.org/10.1007/s10035-020-01067-1

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