A Conductivity Relationship for Steady-state Unsaturated Flow Processes under Optimal Flow Conditions

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Optimality principles have been used for investigating physical processes in different areas. This work attempts to apply an optimal principle (that water flow resistance is minimized on global scale) to steady-state unsaturated flow processes. Based on the calculus of variations, we show that under optimal conditions, hydraulic conductivity for steady-state unsaturated flow is proportional to a power function of the magnitude of water flux. This relationship is consistent with an intuitive expectation that for an optimal water flow system, locations where relatively large water fluxes occur should correspond to relatively small resistance (or large conductance). Similar results were also obtained ... continued below

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Liu, H. H. September 15, 2010.

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Optimality principles have been used for investigating physical processes in different areas. This work attempts to apply an optimal principle (that water flow resistance is minimized on global scale) to steady-state unsaturated flow processes. Based on the calculus of variations, we show that under optimal conditions, hydraulic conductivity for steady-state unsaturated flow is proportional to a power function of the magnitude of water flux. This relationship is consistent with an intuitive expectation that for an optimal water flow system, locations where relatively large water fluxes occur should correspond to relatively small resistance (or large conductance). Similar results were also obtained for hydraulic structures in river basins and tree leaves, as reported in other studies. Consistence of this theoretical result with observed fingering-flow behavior in unsaturated soils and an existing model is also demonstrated.

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  • Report No.: LBNL-3977E
  • Grant Number: DE-AC02-05CH11231
  • DOI: 10.2172/991746 | External Link
  • Office of Scientific & Technical Information Report Number: 991746
  • Archival Resource Key: ark:/67531/metadc1013400

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  • September 15, 2010

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  • Oct. 14, 2017, 8:36 a.m.

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  • Oct. 17, 2017, 6:11 p.m.

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Liu, H. H. A Conductivity Relationship for Steady-state Unsaturated Flow Processes under Optimal Flow Conditions, report, September 15, 2010; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc1013400/: accessed December 11, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.