R. W. (Jr.) Ritzi, P. Bobeck - Comprehensive principles of quantitative hydrogeology established by Darcy and Dupuit (796982)
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ClickHereWATER RESOURCES RESEARCH, VOL. 44, W10402, doi:10.1029/2008WR007002, 2008forFullArticleComprehensive principles of quantitative hydrogeology establishedby Darcy (1856) and Dupuit (1857)Robert W. Ritzi Jr.1 and Patricia Bobeck2Received 14 March 2008; revised 22 June 2008; accepted 8 July 2008; published 3 October 2008.[1] Henry Darcy and Jules Dupuit were born 1 year apart, were classmates during theirundergraduate and graduate education in civil engineering, and were colleagues in theFrench corps of civil engineers, with overlapping appointments as inspector general in theearly 1850s.
At that time Darcy turned over, to Dupuit, his position as Director of Waterand Bridges in Paris and the research on pipe flow he had begun there in 1849. In thesepipe flow experiments, Darcy discovered what he referred to as a ‘‘law’’ of fluidmechanics, which is that above a certain velocity threshold, the head loss is proportional tovelocity squared, and below that threshold, the head loss is linearly proportional tovelocity. During the remainder of their careers, Darcy and Dupuit applied this law withtheir collective, extensive, prior knowledge of fluid mechanics, geology, aquifers, wells,and springs to quantitative studies of fluid flow in the subsurface (and also in pipes,aqueducts, rivers, and sand filters).
Two monographs by Darcy (1856) and Dupuit (1857)are mutually cited retrospectives on much of this research, submitted at nearly the same time,to the same Corps des Ponts et Chaussées publisher, near the end of their careers. Betweenthese two monographs, many of the fundamentals of quantitative hydrogeology wereestablished, including the equation for groundwater motion, average linear velocity,average travel time, effective hydraulic conductivity for layered heterogeneity,conservation of mass in confined and unconfined flow, the nature of the regionalpieziometric surface, porous flow versus flow through discrete fractures and karstconduits, the equation for a cone of depression around flowing wells, superposition of theeffects of multiple wells, and capture zone geometries of wells within a regional flow field.Citation: Ritzi, R.
W., Jr., and P. Bobeck (2008), Comprehensive principles of quantitative hydrogeology established by Darcy(1856) and Dupuit (1857), Water Resour. Res., 44, W10402, doi:10.1029/2008WR007002.1. Introduction[2] In quantitative hydrogeology, the principles of fluidmechanics are combined with a geologic understanding ofthe occurrence and movement of groundwater.
This combination allows quantification of important attributes such asvolume flow rate, head loss, magnitude and direction ofvelocity, mass transport rate, and residence time in thesubsurface.[3] One paradigm for the history of quantitative hydrogeology is that it began with the introduction of an equationfor fluid motion through sand, determined empirically byHenry Darcy’s sand column experiments as described byDarcy [1856, Appendix D]. This thinking is clearly characterized by a statement by Freeze and Back [1983, p. 10]:‘‘the experiments carried out by Darcy with the help of hisassistant, Ritter, in Dijon, France in 1855 and 1856 represent the beginning of groundwater hydrology as a quantitative science.’’[4] In their view, Darcy’s sand column experiments were ascientific revolution.
The revolution sparked a subsequent1Department of Earth and Environmental Sciences, Wright StateUniversity, Dayton, Ohio, USA.2Geotechnical Translations, Austin, Texas, USA.Copyright 2008 by the American Geophysical Union.0043-1397/08/2008WR007002$09.00period of evolution (cf. the Kuhnian model for sciencehistory) as Darcy’s law was applied through the latter halfof the nineteenth and early twentieth centuries by severalEuropean hydraulic engineers including Boussinesq, Dupuit,Forchheimer and the two Thiems. Freeze and Back [1983]view the next revolution as occurring 79 years later withTheis’s [1935] introduction of transient well hydraulics.
Anunderstanding of who Henry Darcy was and how he conducted his sand column experiments first began to emerge inthe English literature from Freeze’s [1994] excellent scholarship and translations (from French) including Darcy’s[1856] Appendix D. Freeze [1994] concluded ‘‘I’m sure thatDarcy went to his grave without the realization that he hadunlocked one of nature’s basic laws,’’ bringing into questionDarcy’s awareness of the significance of his sand filterexperiments within the context of quantitative hydrogeologyand well hydraulics.
This conclusion, and the prevalent viewof the beginnings of quantitative hydrogeology, were biasedby the limited scope of what was translated, primarilyAppendix D along with Darcy necrologies and nontechnicalbiographies. Accessing the historical documents and translating from the antiquated French terminology is difficult.The scope of Dupuit’s contributions to quantitative hydrogeology had been similarly underrepresented.[5] However, a newer wave of scholarship emergedcoincident with the bicentennial commemorations of theW104021 of 14W10402RITZI AND BOBECK: QUANTITATIVE HYDROGEOLOGYbirths of Henry Philibert Gaspard Darcy (1803 – 1858) andArsene Jules Etienne Dupuit (1804 – 1866).
This workincludes new reviews of their career contributions [Brown,2002, 2004, 2003; Gisonni, 2003; Rat, 2003; Hager, 2004;Simmons, 2007], a new perspective on the discovery ofDarcy’s law [Brown 2002], and the complete Englishtranslation of Darcy [1856] by Bobeck [2004]. From thiscollective work, the paradigm for the history of quantitativehydrogeology shifts.
Darcy’s sand filter experiments confirmed a linear law of fluid mechanics which he haddiscovered in an earlier phase of his career. From thebeginning of his career, Darcy had endeavored to quantifyand understand attributes of groundwater flow to wells andsprings, and Darcy [1856] clearly shows that he understoodthe significance of his linear law to well hydraulics (asdiscussed by Brown [2002]) and applied it in quantifyinggroundwater flow to artesian wells.[6] In this new view, the ‘‘revolution’’ occurred earlier withthe results of pipe flow experiments that Darcy began in Parisin 1849, which continued in the early 1850s with Dupuit.
Inthese experiments, a basic law of fluid mechanics wasdiscovered: head loss is proportional to velocity if velocityis below a threshold, and proportional to the square of velocitywhen the threshold is exceeded. In the remainder of theircareers, Darcy and Dupuit applied this law to understandingpipe flow, sand filters, regional groundwater flow in aquifers,well hydraulics, spring flow, and open-channel flow.[7] Darcy [1856] and Dupuit [1857] are mutually citedretrospectives, published near the end of their careers, boththrough their Corps des Ponts et Chaussées publisher. Thethesis of this article is that a fairly comprehensive development of quantitative hydrogeology was created by thesenear-simultaneous publications of Darcy [1856] and Dupuit[1857]. To support this thesis, we review these documentstogether with a focus on the comprehensive application offluid mechanics to the geologic understanding of groundwater flow.[8] We will not repeat all of the biographical information,already somewhat redundant, in the collective body of priorliterature cited above, but rather only the most relevantfacts.
These include the following.[9] Darcy and Dupuit began university studies 1 yearapart, and overlapped as classmates through most of theirundergraduate and graduate education at Ecole Polytechnique and Ecole des Ponts et Chaussées, from 1822 to 1826.Their schooling included the very best of education in fluidmechanics, from instructors including Navier, Cauchy,Coriolis, Barre de Saint-Venant, and de Prony [Rouse andInce, 1957; Freeze, 1994; Phillip, 1995; Brown, 2002, 2003;Hager, 2004].[10] Their subsequent careers as civil engineers in theCorps des Ponts et Chaussées included developing publicwater utilities.
At the time, the conventional focus was ondeveloping municipal supplies from among three possiblesources: springs, wells, or filtered river water. The principlesof hydrodynamics in which they were schooled wereapplied ubiquitously to understanding all three of thesepotential sources of municipal supply, and to understandingmunicipal delivery systems including flow through pipesand aqueducts [Darcy, 1834, 1856, 1857; Dupuit, 1854,1857, 1863].
For Darcy, the application began immediately.His first major public project was to find a public waterW10402supply for Dijon. All three potential sources were rigorouslyevaluated starting in the late 1820s. As he drilled andassessed flow versus head loss in an artesian well, and ashe quantified spring flows via weirs, he assiduously assimilated the understanding and methodologies of the time, andhe found ways to expand them through the rest of his career[Brown, 2002]. The understanding of groundwater andsurface water contamination from surface sources came intoawareness during Darcy’s time, as discussed extensively byDarcy [1856], and further motivated the need to quantifyattributes of groundwater flow.[11] As reviewed by Brown [2002], the convention at thetime of Darcy and Dupuit’s education would have focusedon hydrodynamic theory from the perspective of predictinghead loss.
They were taught the Bernoulli equation whichresults from conservation of energy along a streamline:hL ¼! 2" ! 2"V2 P2V1 P1þ þ z2 #þ þ z12gg2ggð1Þwhere hL is head loss, V is velocity, P is fluid pressure, z iselevation, g is gravitational acceleration, and g is specificweight. In the hydraulics of pipe flow, they were taught thathead loss was given by de Prony’s equation:hL ¼$L#aV þ bV 2Dð2Þwhere L is length, D is pipe diameter, and a and b areempirical coefficients of proportionality, and were as yetimperfectly known.[12] The structural geology and stratigraphy of theregions in which Darcy worked were already well knownin his time, as was the conceptual hydrogeology, and Darcyhad a sophisticated understanding of that knowledge [Rat,2003].
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