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Geometry‐Imbedded Darcy's Law and Transient Subsurface Flow
Author(s) -
Narasimhan T. N.
Publication year - 1985
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr021i008p01285
Subject(s) - darcy's law , partial differential equation , darcy–weisbach equation , transient (computer programming) , mathematics , fluid dynamics , flow (mathematics) , groundwater flow equation , work (physics) , fluid mechanics , calculus (dental) , mechanics , mathematical analysis , geometry , physics , porous medium , geology , computer science , groundwater flow , geotechnical engineering , thermodynamics , aquifer , groundwater , medicine , dentistry , porosity , operating system
The traditional interpretation of Darcy's experiment views it as a valuable means for setting up the partial differential equation of transient or steady state subsurface fluid flow. In the present work, Darcy's observations are viewed from a different perspective, enabling the statement of transient subsurface fluid flow in terms of an equation defined over finite domains of space and time. Two new notions, namely, geometry imbedding and location of average, are introduced. The equation describes transient flow along a flow tube with arbitrarily varying cross section, consisting of materials with properties dependent on fluid potential. This equation, based on its own postulates, is fully consistent within itself and exists independently of the classical partial differential equation. This technical note presents preliminary ideas on what appears to be a promising new line of inquiry that departs from the traditional approach based on continuum mechanics. Further work is in progress.