128 research outputs found
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Ohm's Law, Fick's Law, Joule's Law, and Ground Water Flow
Starting from the contributions of Ohm, Fick and Joule during the nineteenth century, an integral expression is derived for a steady-state groundwater flow system. In general, this integral statement gives expression to the fact that the steady-state groundwater system is characterized by two dependent variables, namely, flow geometry and fluid potential. As a consequence, solving the steady-state flow problem implies the finding of optimal conditions under which flow geometry and the distribution of potentials are compatible with each other, subject to the constraint of least action. With the availability of the digital computer and powerful graphics software, this perspective opens up possibilities of understanding the groundwater flow process without resorting to the traditional differential equation. Conceptual difficulties arise in extending the integral expression to a transient groundwater flow system. These difficulties suggest that the foundations of groundwater hydraulics deserve to be reexamined
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Water, law, science
In a world with water resources severely impacted bytechnology, science must actively contribute to water law. To this end,this paper is an earth scientist s attempt to comprehend essentialelements of water law, and to examine their connections to science.Science and law share a common logical framework of starting with apriori prescribed tenets, and drawing consistent inferences. In science,observationally established physical laws constitute the tenets, while inlaw, they stem from social values. The foundations of modern water law inEurope and the New World were formulated nearly two thousand years ago byRoman jurists who were inspired by Greek philosophy of reason.Recognizing that vital natural elements such as water, air, and the seawere governed by immutable natural laws, they reasoned that theseelements belonged to all humans, and therefore cannot be owned as privateproperty. Legally, such public property was to be governed by jusgentium, the law of all people or the law of all nations. In contrast,jus civile or civil law governed private property. Remarkably, jusgentium continues to be relevant in our contemporary society in whichscience plays a pivotal role in exploiting vital resources common to all.This paper examines the historical roots of modern water law, followstheir evolution through the centuries, and examines how the spirit ofscience inherent in jus gentium is profoundly influencing evolving waterand environmental laws in Europe, the United States and elsewhere. In atechnological world, scientific knowledge has to lie at the core of waterlaw. Yet, science cannot formulate law. It is hoped that a philosophicalunderstanding of the relationships between science and law willcontribute to their constructively coming together in the service ofsociety
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Fick's Insights on Liquid Diffusion
In 1855, Adolph Fick published ''On Liquid Diffusion'', mathematically treating salt movements in liquids as a diffusion process, analogous to heat diffusion. Less recognized is the fact that Fick also provided a detailed account of the implications of salt diffusion to transport through membranes. A careful look at Fick (1855) shows that his conceptualization of molecular diffusion was more comprehensive than could be captured with the mathematical methods available to him, and therefore his expression, referred to as Fick's Law, dealt only with salt flux. He viewed salt diffusion in liquids as a binary process, with salt moving in one way and water moving in the other. Fick's analysis of the consequences of such a binary process operating in a hydrophilic pore in a membrane offers insights that are relevant to earth systems. This paper draws attention to Fick's rationale, and its implications to hydrogeological systems. Fick (1829-1901; Figure 1), a gifted scientist, published the first book on medical physics (Fick, 1858), discussing the application of optics, solid mechanics, gas diffusion, and heat budget to biological systems. Fick's paper is divisible into two parts. The first describes his experimental verification of the applicability of Fourier's equation to liquid diffusion. The second is a detailed discussion of diffusion through a membrane. Although Fick's Law specifically quantifies solute flux, Fick visualized a simultaneous movement of water and stated, ''It is evident that a volume of water equal to that of the salt passes simultaneously out of the upper stratum into the lower.'' (Fick, 1855, p.30). Fick drew upon Fourier's model purely by analogy. He assumed that concentration gradient impelled salt movement, without inquiring why concentration gradient should constitute a driving force. As for water movement, he stated intuitively, ''a force of suction comes into play on each side of the membrane, proportional to the difference of concentration, consequently a stronger force at the upper side corresponding to the saturated solution'' (Fick, 1855, p.38)
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Agriculture, Irrigation and Drainage on the West Side of the San Joaquin Valley, California: Unified Perspective on Hydrogeology, Geochemistry and Management
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PHYSICAL ASPECTS OF THE INTERFACE BETWEEN THE SATURATED AND THE UNSATURATED REGIMES
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