On a general correlation for the discharge rate of grains through slots in sidewalls of silos due to gravity

G. M. Brito-Licea, A. López-Villa, A. Zacarias-Santiago, A. Medina


In this work we discuss the general validity of a phenomenological correlation for the mass flow rate of dry non cohesive granular material that outflows, due to the gravity, from slots in very thin vertical sidewalls of bins. The correctness of such a formula is analyzed by comparing it to other correlations published elsewhere which reports cases of very large, similar and very small channel width W relative to its length D.


Granular media; Hagen formula; Berverloo formula.

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P. P. Ong, Eur. J. Phys. 11 (1990) 188.

T. Le Pennec, M. Ammi, J. C. Messager, B. Truffin, D. Bideau, 85J. Ganier, Powder Tech. 85 (1995) 279.

A. A. Mills, S. Day, and S. Parkes, Eur. J. Phys. 17 (1996) 97.

G. H. L. Hagen, A˜oeber den Druck und die Bewegung des trocknen Sandes, Bericht Aber die zur Bekanntmachung geeigneten Verhandlungen der Koniglich Preussischen Akademie der Wissenschaften zu Berlin 35 (1852) 35.

K. Wieghardt, Ann. Rev. Fluid Mech. 7 (1975) 89.

D. A. Serrano, G. Ruiz-Chavarr´ıa, M. Pliego, C. A. Vargas, and A. Medina, Rev. Mex. F´ıs. 65 (2019) 139.

C. E. Davies, and J. Foye, Trans. Inst. Chem. Engrs. 69 (1991) 369.

C. J. Coberly, Selection of Screen Openings for Unconsolidated Sands, Paper API-37-189 American Petroleum Institute. Drilling and Production Practice, New York, USA (1937).

V. Fattahpour, M. Mahmoudi, A. Nouri, and M. Leitch, A critical review of sand control design for SAGD wells, Paper

WHOC16-613. 2016 World Heavy Oil Congress, (2016) Calgary, Alberta Canada.

R. L. Brown and J. C. Richards, Trans. Instn. Chem. Eng., 38 (1960) 243.

W. A. Beverloo, H. A. Leniger and J. van de Velde, Chem. Eng. Sci. 15 (1961) 260-.

R. L. Brown and J. C. Richards, Principles of Powder Mechanics, Pergamon Press, Oxford, England (1970).

F. M. White, Viscous Fluid Flow, Third edition McGraw-Hill,

New York, USA (2006).

Y. Zhou, P.-Y. Lagr´ee, S. Popinet, P. Ruyer, and P. Aussillous, J. Fluid Mech. 829 (2017) 459.

A. Medina, D. Cabrera, A. L´opez-Villa, and M. Pliego, Powder Tech. 253 (2014) 270.


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