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The statistical mechanical theory of groundwater flow
Author(s) -
Sposito Garrison,
Chu ShuYuan
Publication year - 1981
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/wr017i004p00885
Subject(s) - groundwater flow , groundwater , balance equation , mechanics , energy balance , groundwater flow equation , internal energy , partial differential equation , flow (mathematics) , mathematics , physics , geology , aquifer , geotechnical engineering , thermodynamics , mathematical analysis , statistics , markov model , markov chain
The macroscopic differential equations of mass, linear momentum, and energy balance for groundwater are derived from first principles by using the methods of statistical mechanics. The resulting macroscopic equations agree with those derived recently on the basis of fluid mechanics and local volume averaging, except in the case of energy balance. The balance equations for total and internal energy in groundwater are analyzed in detail. It is shown that the groundwater internal energy is actually a partial specific internal energy and that its time development is affected by a gravitational field, whereas the time development of the total energy of groundwater is not. Finally, it is shown that the standard equation of groundwater flow is a special case of the macroscopic equation of internal energy balance. An appeal to the macroscopic equation of mass balance is not required in order to derive the flow equation.