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Thermodynamics of the hydraulic head, pressure head, and gravitational head in subsurface hydrology, and principles for their spatial averaging
Wageningen University, Centre for Water and Climate, Soil Physics, Ecohydrology and Groundwater Management, Wageningen, The Netherlands
Abstract. In order to establish a thermodynamic justification of the theoretical relationship between the hydraulic, pressure/matric, and gravitational head in subsurface hydrology, the thermodynamic literature pertaining to subsurface flow processes is reviewed. The incompressibility of liquids negates a thermodynamic definition of pressure, which gives rise to several inconsistencies in pore scale theories. At larger scales, the gravitational potential and fluid pressure are treated as additive potentials. This superposition principle is replicated in the well-established relationship between the various heads according to subsurface hydrological theory. The necessary requirement that the superposition be maintained across scales is combined with conservation of energy during volume integration to establish consistent upscaling equations for the various heads. The power of these upscaling equations is demonstrated by the derivation of an upscaled water content-matric head relationship and the resolution of an apparent paradox reported in the literature that is shown to have arisen from a violation of the superposition principle.
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Citation: de Rooij, G. H.: Thermodynamics of the hydraulic head, pressure head, and gravitational head in subsurface hydrology, and principles for their spatial averaging, Hydrol. Earth Syst. Sci. Discuss., 5, 1137-1157, 2008. Bibtex EndNote Reference Manager
