Abstract
A theoretical calculation method for the flow rate of granular matter from an inclined orifice is discussed in this article and for the inclination angles at \(\theta \le 90^{\circ }\), a theoretical relation between the flow rate \(Q\) and inclination angle \(\theta \) is derived; and for the inclination angles at \(\theta >90^{\circ }\), a semi-theoretical relation is established. From the relations, we found that the ratio of the flow rate from a vertical orifice, \(Q_{90}\), to that from a horizontal orifice, \(Q_{0}\), is equal to the sine of the angle of repose \(\theta _{\mathrm{r}}\), i.e., \(Q_{90} /Q_0 =\sin \theta _{\mathrm{r}} \). The theoretical relations are tested by means of the experimental data and the results indicate that the theoretical calculating values are in good agreement with the experimental data over a wide range of the inclination angles. Therefore, the formula proposed in this article can be used for the theoretical calculation of the flow rate of granular matter from an inclined orifice. The relation \(Q_{90} /Q_0 =\sin \theta _{\mathrm{r}}\) may be used as an alternative approach to obtaining \(\theta _{\mathrm{r}}\): measuring \(Q_{90}\) and \(Q_{0}\), and then calculating \(\theta _{\mathrm{r}} \) by using formula \(\theta _{\mathrm{r}} =\arcsin (Q_{90} /Q_0 )\).
Similar content being viewed by others
References
Beverloo, W.A., Leniger, H.A., van de Velde, J.: The flow of granular solids through orifices. Chem. Eng. Sci. 15, 260–269 (1961)
Nedderman, R.M., Tuzun, U., Savage, S.B., Houlsby, G.T.: The flow of granular materials(I): discharge rates from hoppers. Chem. Eng. Sci. 37, 1597 (1982)
Mankoc, C., Janda, A., Arévalo, R., Pastor, J.M., Zuriguel, I., Garcimartin, A., Maza, D.: The flow rate of granular materials through an orifice. Granul. Matter 9, 407–414 (2007)
Tuzun, U., Houlsby, G.T., Nedderman, R.M., Savage, S.B.: The flow of granular materials(II): velocity distribution in slow flow. Chem. Eng. Sci. 37, 1691 (1982)
Ahn, H., Basaranoglu, Z., Yilmaz, M., Bugutekin, A., Zafer Gül, M.: Experimental investigation of granular flow through an orifice. Powder Technol. 186, 65–71 (2008)
Choi, J., Kudrolli, A., Bazant, M.Z.: Velocity profile of granular flows inside silos and hoppers. J. Phys. Condens. Matter 17, S2533–S2548 (2005)
Oldal, I., Csizmadia, B.M.: Determination of velocity distribution at silo outlet. In: 7th International Multidisciplinary Conference. Baia Mare, Romania (2007)
Cǎsǎndroiu, T., Mieilǎ, C.: Theoretical development of mathematic model to evaluate gravimetrical flow rate of seeds through an orifices. Universitatea Politehnica din Bucuresti, Scientific Bulletin, Series D 72, 269 (2010)
Evesque, P., Meftah, W.: Mean flow of a vertically vibrated hourglass. Int. J. Mod. Phys. B 7, 1799 (1993)
Hunt, M.L., Weathers, R.C., Lee, A.T., Brennen, C.E., Wassgren, C.R.: Effects of horizontal vibration on hopper flows of granular materials. Phys. Fluids 11, 68 (1999)
Wassgren, C.R., Hunt, M.L., Freese, P.J., Palamara, J., Brennen, C.E.: Effects of vertical vibration on hopper flows of granular materials. Phys. Fluids 14, 3439 (2002)
Chen, K., Stone, M.B., Barry, R., Lohr, M., McConville, W., Klein, K., Sheu, B.L., Morss, A.J., Scheidemantel, T., Schiffer, P.: Flux through a hole from a shaken granular medium. Phys. Rev. E 74, 011306 (2006)
Franklin, F.C., Johanson, L.N.: Flow of granular material through a circular orifice. Chem. Eng. Sci. 4, 119 (1955)
Davies, C.E., Foye, J.: Flow of granular material through vertical slots. Trans. Inst. Chem. Eng. Sci. 69, 369 (1991)
Sheldon, H.G., Durian, D.J.: Granular discharge and clogging for tilted hoppers. Granul. Matter 12, 579 (2010)
Chang, C.S., Converse, H.H., Steele, J.L.: Flow rates of grain through vertical orifices. Trans. ASAE 33, 601 (1990)
Chang, C.S., Converse, H.H., Steele, J.L.: Flow rates of grain through various shapes of vertical and horizontal orifices. Trans. Am. Soc. Agric. Eng. 34, 1789 (1991)
Thomas, C.C., Durian, D.J.: Geometry dependence of the clogging transition in tilted hoppers. arXiv:1206.7052 [cond-mat.soft] (2012)
Peng, Z., Jiang, Y.M.: Maximum ceasing angle of inclination and flux formula for granular orifice flow. Acta Phys. Sin. 60, 054501 (2011)
Lu, K.Q., Liu, J.X.: Static and dynamic properties of granular matter(I). Physics 33, 629 (2004)
Wilcke, W., Wyatt, G.: Grain Storage Tips: Factors and Formulas for Crop Drying, Storage and Handling. Available on line at http://www.extension.umn.edu/distribution/cropsystems/M1080-FS.pdf
Wikipedia. Angle of repose of various materials. Available on line at http://en.wikipedia.org/wiki/Angle_of_repose
Agridry. Bulk density and angle of repose of grain and seed. Available on line at http://www.agridry.com.au/pdf/bulk_density.pdf
Leoncooksilos. Typical grain bulk densities and angles of repose. Available on line at http://www.leoncooksilos.com.au/TypicalGrainBulkDensitiesandAnglesofRepose.pdf
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Liu, Y. The theoretical calculation of the flow rate of granular matter from an inclined orifice. Granular Matter 16, 133–139 (2014). https://doi.org/10.1007/s10035-013-0473-1
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10035-013-0473-1