R. W. (Jr.) Ritzi, P. Bobeck - Comprehensive principles of quantitative hydrogeology established by Darcy and Dupuit (796982), страница 5
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Then various configurations of sand-filled containersare considered, as aquifer analogs. Finally, these principlesare applied to understanding flow in confined and inunconfined aquifers.[41] Despite the disparate styles, both Darcy [1856] andDupuit [1857] are clear and consistent on the use of the lawof how head loss changes from linear to parabolic depending on the magnitude of the velocity. They both use it todifferentiate aquifer head loss from head loss in well riserpipe. They have the same conceptual model for hydrogeology, spring flow, and artesian wells in the Paris basin.They both have considerable focus on the artesian well atGrenelle and on reciprocal effects of wells when more thanone produces from the same layer. In general, both focus onapplying fluid mechanics to quantitatively describe subsurface fluid flow.
Freeze and Back [1983] described Darcyand Dupuit’s focus as at the scale of a laboratory column orwell. However, our review of Darcy and Dupuit’s completecontributions illustrates that they understood hydrogeologyat a regional scale, and they developed a quantification ofprocesses at the scale of a geologic stratum tapped by one ormore wells.
The discussion of regional hydrogeology at thescale of systems of multiple strata and aquifers (e.g., all ofthe strata in Figures 1 or 7) would remain mostly qualitativeup until the quantitative studies of equipotential lines andflow lines at that scale by Tóth [1963] and Freeze andWitherspoon [1967].[42] Darcy’s sand column experiments were not completedby Darcy and Ritter until February of 1856. ‘‘Les Fontaines’’was completed in August 1856 (6 months later). The linearlaw for head loss in flow through sands examined inAppendix D is used throughout ‘‘Les Fontaines,’’ including12 of 14RITZI AND BOBECK: QUANTITATIVE HYDROGEOLOGYW10402W10402Table 1. Timeline of the Education and the Career Contributions of Darcy and Dupuit and Related EventsYearEvent18031804182118221823 – 182418261827Darcy is born on 10 JuneDupuit is born on 18 MayDarcy enters L’Ecole PolytechniqueDupuit enters L’Ecole PolytechniqueDarcy and Dupuit enter L’Ecole des Ponts et ChausséesDarcy graduates, enters Corps des Ponts et Chaussées and is assigned to JuraDarcy assigned to DijonDupuit graduates, enters Corps de Ponts et Chaussées and is assigned to SartheDrilling of artesian well at Place Saint-Michel started in Dijon in MarchDarcy gauges the Rosoir springDupuit conducts experiments on wheels and road frictionDarcy issues report with Dijon water supply plan that contains data showing aquiferhead loss with flow to artesian wellsDarcy severely injured in a railcar accidentRosoir to Dijon aqueduct construction started on 21 MarchFirst arrival of water in Dijon on 6 SeptemberDupuit transferred to MarneDarcy receives Legion of HonorDarcy receives gold medal from Dijon municipal councilDupuit receives Legion of Honor for research on roads and pavementsExperiments of head loss versus riser pipe height at Grenelle conductedDupuit, as Chief Engineer of Maine-et-Loire, publishes ‘‘De la Mesure de l’Utilitédes Travaux Publics,’’ starting the foundation of microeconomicsDarcy’s plan for bringing the Paris to Lyon rail through Dijon acceptedDupuit witnesses floods of River LoireDarcy channelizes the Suzon through DijonExperiments of head loss versus riser pipe height at Tours conductedFebruary Revolution; Darcy removed from DijonAfter temporary appointment to Bourges, Louis Napoleon takes office, and Darcy istransferred to Paris and is appointed Chief Director for Water and PavementsDarcy’s pipe flow experiments started at Chaillot on 31 AugustJohn Snow and William Bud publish articles linking cholera to public water suppliesDarcy promoted to inspector general, 2nd class, in ParisDupuit called to Paris in May and groomed to succeed Darcy as Chief Director forWater and PavementsDarcy’s experiments at Chaillot completed on 27 OctoberCouncil on Public Health held in Brussels connects public health with water supply(discussed by Darcy [1856])As a sign of failing health, Darcy passes out in the streetDarcy completes report on pipe flow experiments at Chaillot; report goes into 3-year reviewDupuit publishes book on theory of pipe flow, Paris supply wells, and sewer improvementsJohn Snow removes pump handle from Broad St.
wellDarcy released of duties except for researchDarcy starts permeameter experiments at the Dijon HospitalDarcy publishes ‘‘Les Fontaines Publiques de la Ville de Dijon’’Dupuit completes ‘‘Mouvement de l’Eau à Travers les Terrains Perméables,’’ whichgoes into review by the Academy of SciencesDarcy’s death on 3 JanuaryExperiments of head loss versus riser pipe height at Passy conductedDupuit publishes ‘‘Mouvement de l’Eau à Travers les Terrains Perméables’’as chapter 8 in larger book on hydraulicsPasteur lectures on the germ theory of diseaseDupuit’s death on 5 September18291832 – 18331833 – 1834183718391840184218431844184518461847184818491850185118521853185418551856185718581861186318641866analyses of data on artesian wells and springs collected adecade earlier.
The many questions about linear versusparabolic flow in aquifers and springs would probably nothave come up, been answered, and written into so manydifferent parts of the text within such a short 6-monthinterval. Rather, many of the ideas had probably begun tocrystallize in Darcy’s thinking for years prior to 1856.Indeed, as discussed by Brown [2002], Darcy’s interest inquantifying groundwater processes was sparked at thebeginning of his career, and he would have ruminated overquestions about head loss in aquifers for decades (Table 1).The basic law of linear versus parabolic head loss discovered at Chaillot provided a foundation with which to addressmany of these questions.
Between 1851 and 1857, Darcywould have had 6 years to apply this law to his thinkingabout the linear data from artesian wells (Figure 3), and hiswealth of early experience with spring flows. In a similarvein, Dupuit [1857] was submitted 1 year after the sandcolumn experiments. It is not likely that all his ideas,derivations, and writing, and figure production would haveoccurred in just 1 year.
More likely, Dupuit and Darcy,while together in Paris in the highest circles of theInspector General’s office and Ponts et Chaussées Council, thought about and discussed the ramifications of theircollective pipe flow experiments at the Chaillot facility, andthe linear law of low-velocity flows which came out ofthose experiments, starting in 1851, well before the sandcolumn experiments. Furthermore, Dupuit was in charge,13 of 14W10402RITZI AND BOBECK: QUANTITATIVE HYDROGEOLOGYunder Haussmann, of the expansion of water supply andsewer service in Paris.
This included upgrades of theartesian well at Grenelle [Mahyer, 1866]. It seems verylikely that Darcy and Dupuit would have carefully considered and discussed the linear data from the riser pipeexperiments conducted some 10 years earlier at Grenelle(in 1844, as plotted in Figure 3), and would have started torealize the significance of the 1849 – 1851 pipe flow experiments in explaining those 1844 results. Indeed, as stated byBrown [2002], the sand column experiments probablyconfirmed a hypothesis they would have held with greatconfidence.[43] In closing, clearly Darcy’s linear law of fluid mechanics is widely applied to quantifying various aspects ofgroundwater flow by both Darcy [1856] and Dupuit [1857].The range of groundwater processes or attributes which arequantified and elucidated include: groundwater flow rate asa linear function of driving force, average linear velocity,average travel time, effective hydraulic conductivity forlayered heterogeneity, conservation of mass in confinedand unconfined flow, the nature of the regional piezometricsurface, porous flow versus flow through discrete fracturesand karst conduits, the concept and equation for a cone ofdepression around flowing wells, superposition of theeffects of multiple wells, and capture zone geometries ofwells within a regional flow field.
This review of thecomprehensive contributions to quantitative hydrogeologyby Darcy [1856] and Dupuit [1857] shows that many, if nota majority, of the principles of steady state quantitativehydrogeology which are commonly introduced in the beginning chapters of hydrogeology textbooks were established with the nearly simultaneous publication of thesedocuments.[44] Acknowledgments.
The first author was introduced to the history of hydrogeology by Stanley Davis and found continual enthusiasm andencouragement for its study through William Back. Catherine Masteau atthe Ecole Nationale des Ponts et Chaussées, la Section Historique, andDiana Kaylor in the Paul Lawrence Dunbar Library at Wright StateUniversity facilitated access to historical documents. The manuscript wasimproved from helpful suggestions in reviews by Glenn Brown, Ghislain deMarsily, and T. N. Narasimhan.ReferencesBobeck, P. (2004), The Public Fountains of the City of Dijon, Henry Darcy,1856, translated from French, Geotech. Transl., Austin, Tex.Brown, G.
O. (2002), Henry Darcy and the making of a law, Water Resour.Res., 38(7), 1106, doi:10.1029/2001WR000727.Brown, G. O. (2003), Henry Darcy’s perfection of the pitot tube, in HenryP. G. Darcy and Other Pioneers in Hydraulics, edited by G. O. Brown,J. D. Garbrecht, and W. H. Hager, pp. 14 – 23, Am. Soc. of Civ.
Eng.,Reston, Va.Brown, G. O. (2004), Jules Dupuit’s contributions in water resources,in Water Resources and Environmental History, edited by J. R. Rogers,G. O. Brown, and J. D. Garbrecht, pp. 104 – 110, Am. Soc. of Civ. Eng.,Reston, Va.Caudemberg, G. (1858), Notice sur M. Henri Darcy, in Mémoires de l’Académie de Dijon, Loireau-Feuchot, Dijon, France.Darcy, H.
(1834), Rappport à le maire et au conseil municipal de Dijon, surles moyens de fournir l’eau nécessaire à cette bille, Douillier, Dijon,France.Darcy, H. (1856), Les Fontaines Publiques de la ville de Dijon, Dalmont,Paris.Darcy, H. (1857), Recherches Experimentales Relatives au Mouvement del’Eau dans les Tuyaux, Mallet-Bachelier, Paris.W10402Darcy, H.
(1858), Recherches experimentales relatives au mouvement del’eau dans les tuyaux, in Mémoires Présentés par Divers Savants àl’Académie des Sciences de l’Institut Impérial de France, Paris, vol.15, 14 – 401, Acad. Des Sci. de l’Inst. Imp. de France, Paris.Driscoll, F. G. (1986), Groundwater and Wells, 1089 pp., Johnson Div., St.Paul, Minn.Dupuit, J. (1854), Traite Theorique et Pratique de la Conduite et de laDistribution des Eaux, Carilian-Goeury et Dalmont, Paris.Dupuit, J.
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