Abstract
An entry length is always observed before laminar flow is achieved in fluid flowing in a conduit. This depends on the Reynolds number of the flow and the degree of smoothness of the conduit. This work examined this region and the point where laminar flow commences in the context of flow through conduit packed with porous material like beads, of known porosity. Using some theoretical assumptions, it is demonstrated that permeability varies from zero at wall-fluid boundary to maximum at mid-stream, creating a permeability profile similar to the velocity profile. An equation was obtained to establish this. We also found that peak values of permeability increase with increasing porosity, and therefore entry length increases with increasing porosity with all other parameters kept constant. A plot of peak permeability versus porosity revealed that they are linearly related.
Similar content being viewed by others
References
J A Adegoke, The effects of porosity, angle of hydrostatic equilibrium, volume flux and rate on groundwater flow through riverbed sand, Ph.D. thesis (University of Ibadan, Ibadan, 2005)
H L Langhaar, J. Appl. Mech. 9, 55 (1942) as in Sreeter and Wylie 1983
D J Tritton, Physical fluid dynamics (Van Nostrand Reinhold Company, 1977), twhipple@spelink.spe.org, retrieved on 7 October 2004
T C Frick and R W Taylor, Petroleum production handbook, vol. II; vol. 23 (1978)
Victor L Sreeter and E B Wylie, Fluid mechanics (McGraw-Hill International Book Company, Japan, 1983)
O O Glenn, The history of the Darcy-Weisbach equation for pipe flow resistance, as in http://biosystems.okstate.edu/darcy/DarcyWeisbach/HistoryoftheDarcyWeisbachEq.pdf (2004)
R T Flekky, U Oxaal and J Feder, Hydrodynamic irreversibility in creeping flow (University of Oslo, Blindern, 0316 Oslo 3 Norway, 1997), http://www.fys.uio.no/?trage/thesis/node14.html, Retrieved 14 July 2002
B P Ghildyal and R P Tripathi, Soil physics (Wiley Eastern Limited, New Delhi, 1987)
M K Cham and J R Blake, Math. Scientist 16, 15 (1991)
Glean Brown, Biosystems and agricultural engineering (Oklahoma State University, 2004), http://biosystems.okstate.edu/darcy/DarcyWesbach/Darcy-Weisbachhistory.htm, Retrieved on 23 July 2004
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Adegoke, J.A., Olowofela, J.A. Variability of permeability with diameter of conduit. Pramana - J Phys 70, 901–909 (2008). https://doi.org/10.1007/s12043-008-0098-9
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12043-008-0098-9