Beverloo law for hopper flow derived from self-similar profiles

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 i...

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Bibliographic Details
Published in:Granular matter 2021-02, Vol.23 (1), Article 7
Main Authors: Alonso-Marroquin, Fernando, Mora, Peter
Format: Article
Language:English
Subjects:
Arches
Complex Fluids and Microfluidics
Density
Dependence
Diameters
Engineering Fluid Dynamics
Engineering Thermodynamics
Flow velocity
Foundations
Geoengineering
Heat and Mass Transfer
Hydraulics
Industrial Chemistry/Chemical Engineering
Mass flow
Materials Science
Original Paper
Particle size
Physics
Physics and Astronomy
Self-similarity
Soft and Granular Matter
Two dimensional analysis
Two dimensional flow
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Summary: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. Graphic abstract
ISSN:1434-5021
1434-7636
DOI:10.1007/s10035-020-01067-1