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More applicable form of Beverloo’s equation: Correction of coefficient k

Lookup NU author(s): Dr Vladimir ZivkovicORCiD

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This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).


Abstract

Mass discharge rate, as an important characteristic quantity reflecting the fluidity of particulate materials. And it is crucial to accurately measure and calculate the mass discharge rate. There are two issues with the existing Beverloo’s equation: the inability to accurately fit the experiment points within the wide range outlet, and the lack of physical significance for the coefficient k. In this work, the fitting equations and relevant variation law of mass discharge rate were explored for eccentric silos with different sidewall frictional coefficients. The intrinsic connection between coefficient k and diameter D, frictional coefficient μ was revealed for the first time. And the frictional coefficient μ was successfully introduced into Beverloo’s equation, completing the correction and improvement of the equation. By establishing a quantitative relationship between the outlet diameter, frictional coefficient, and coefficient k, the coefficient k is given a relevant physical significance, making the equation more widely applicable. In addition, by comparing different models, it was found that the modified model has high accuracy, and the mean relative error (MRE) is only 1.3%. Meanwhile, different particle size and frictional coefficient were used to validate the modified model, demonstrating its wide applicability. This work provides new insights into coefficient calibration of the Beverloo’s equation.


Publication metadata

Author(s): Sun G, Chen Q, Li R, Mu T, Xu Y, Li Z, Zivkovic V, Yang H

Publication type: Article

Publication status: Published

Journal: Chemical Engineering Science

Year: 2027

Volume: 338

Issue: Part A

Print publication date: 01/02/2027

Online publication date: 20/07/2026

Acceptance date: 19/07/2026

Date deposited: 10/08/2026

ISSN (print): 0009-2509

ISSN (electronic): 1873-4405

Publisher: Elsevier Ltd

URL: https://doi.org/10.1016/j.ces.2026.124723

DOI: 10.1016/j.ces.2026.124723

ePrints DOI: 10.57711/xdwn-5g45

Data Access Statement: Data will be made available on request.


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Funding

Funder referenceFunder name
National Natural Science Foundation of China (12372384)
National Key Research and Development Program of China (2022YFF0607701)

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