G.O. Brown - Henry Darcy and the making of a law (796978), страница 4
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Another very popular project was hiscovering 1.3 km of the Suzon; a small stream that acted asan open sewer through the center of Dijon [Caudemberg,1858]. His most difficult and controversial project was thedesign, approval and initiation of the segment of the ParisLyon railroad passing though the Côte-d’Or [Darcy, 1957].As in the water project, Darcy reviewed several previousproposals and came up with his own improved design thatrelied on the construction of a four-km tunnel at Blaizy.The bore equaled the longest existing tunnel at the time andwas proposed only after test excavations and consultationswith the noted geologist Elie de Beaumont (1798 – 1874).After a difficult and politically charged approval process,Darcy began construction in January of 1845 and completed about one third of the tunnel before a privatecorporation assumed the project in April of 1846.
Darcyleft no known record of his experiences. However, thetunnel must have provided him direct observations ofgeology and water seepage processes that few of hiscontemporaries had experienced.[29] Several researchers were advancing hydraulic theoryduring this period. Of particular interest was the work doneby Jean Louis Poiseuille (1799 – 1869).
He measured friction losses in 0.029 to 0.142 mm capillary tubes over arange of conditions and developed an empirical relationshipfor flow,Q ¼ kD4hL;Lð9Þwhere k is an empirical coefficient that lumps constants witha second order equation for the viscosity as a function of thetemperature [Poiseuille, 1841]. The most important aspectof Poiseuille’s results was the accuracy of equation (9).While the restriction to small tubes and low velocities wasrealized, it was the first fluid-friction equation to achievedmodern precision. An analytical derivation of Poiseuilleflow based on Newton’s viscosity law was not accomplished until 1860 [Rouse and Ince, 1957].[30] However, the understanding of porous media flowwas not progressing, which is best demonstrated by Dupuit[1854]. He discussed the natural filters at Toulouse anddescribed several small household artificial filters.
Similarto Darcy [1834], he carried out no explicit calculation onthe natural filter losses. He also calculated artificial filterflow using an orifice discharge analogy based on equation(6). In the analysis, A and m were always kept lumpedtogether. Again, the use of an orifice equation in filter flowwas not justified by reference or experiment. More important to note is that the lumping of the area and resistanceterms indicates that Dupuit was not applying continuumconcepts. That is, he was only thinking of a discrete filterand not the flow within the porous media. Darcy’s contemporary biographers have attributed the use of orificeequations such as equations (6) and (8) in the description offilter flow to English engineers [Marsaines, 1858; Caudemberg, 1858].
That may well be the case, but Darcy [1834]and Dupuit [1854] are the only known published examplesof their use.3.5. A Shift to Research[31] In February of 1848, the Government of LouisPhillipe collapsed under the pressure of a failing economy.The constitutional monarchy was replaced by a provisionalrepublican government that was a mix of monarchists,bourgeois republicans and socialists.
Darcy was soon suspended from duties, since he was considered ‘‘dangerous forthe new state of things’’ [Darcy, 1957]. Apparently, he hadtoo much influence in Dijon for the new Commissioner’scomfort. The Dijon Municipal Council, the Corps, andL’Ecole Polytechnique protested his removal, but all itBROWN: HENRY DARCY AND THE MAKING OF A LAWaccomplished was an appointment to Bourges to work onthe Berry Canal. At his new assignment, Darcy proceededto prepare a draft plan for a massive new project to providedrainage and irrigation over the Sologne region [Caudemberg, 1858]. However, after the formation of the SecondRepublic and the election of Louis Napoleon, Darcy wastransferred to Paris and appointed Chief Director for Waterand Pavements.[32] He soon traveled to England to interview engineersand gather data on street pavements; a topic he apparentlyhad been working on since at least 1847.
(Darcy’s Englishwas probably very good since he had required Englishclasses at L’Ecole des Ponts et Chaussées and his wife,Henriette Carey (1808 – 1875) was Anglo.) It is reasonableto expect that Darcy also took the time to visit the Britishwater-supply engineers he had previously correspondedwith and view their facilities. On his return, he quicklypublished a lengthy and highly regarded paper on Englishroad construction practice [Darcy, 1850] and was promptlypromoted to the rank of Inspector General, 2nd Class, inApril of 1850.
As Inspector General, he reviewed andreported on Corps projects being carried out throughoutthe country. Somehow during this period he also consultedon the Brussels, Belgium municipal water system, for whichhe received the Order of Leopold.[33] Darcy’s new position brought with it command ofthe large hydraulic installation at Chaillot, which provided amajor research opportunity. He initiated and completed acomprehensive experimental program intended to improvethe estimation of the Prony pipe friction coefficients [Darcy,1857]. (His interest in pipe flow originated during theconstruction of the Dijon water system and he had carriedout limited experiments in the 1840s.) The pipe hydraulicsresults are a topic unto itself that cannot be done full justicehere.
In short, he ran tests on various types of pipes from0.012 to 0.50 m diameter over a large velocity range. Theresults greatly improved friction estimates by showing thewall roughness influenced the friction loss. He also provided the first accurate measurement of turbulent pipevelocity distributions and furnished the first evidence forthe existence of the fluid boundary layer. His contribution isacknowledged in the co-naming of the Darcy-Weisbachpipe friction formula given by,hL ¼fL V 2;D 2gð10Þwhere f is usually called the Darcy friction factor and is acomplex function of the relative roughness and Reynoldsnumber.
Some references will name equation (10) simply‘‘Darcy’s equation’’. In all fairness, it was Julius Weisbach(1806 – 1871) who first proposed the exact form ofequation (10) in 1845 [Rouse and Ince, 1957]. Darcyproposed an equation similar to (4) with friction coefficients that were functions of D, and showed it reduced to adimensionally inhomogeneous form of equation (10) athigh velocities.[34] Darcy completed the pipe flow report in 1854. Sinceit contained significant new theoretical material, it wassubmitted to the French Academy of Sciences for reviewand publication, which took 3 years. The report shows he11 - 7clearly appreciated that fluid friction is a function of boththe fluid velocity and the conduit size.
Of even greaterrelevance is his observation that in small pipes and lowvelocities the hydraulic gradient (hL/L) is proportional to theflow rate. He wrote, ‘‘Before seeking the law for pipes thatrelates the gradient to the velocity, we will make anobservation: it appears that at very-low velocity, in pipesof small diameter that the velocity increases proportionallyto the gradient.’’ Later he showed explicitly that his newlyproposed pipe friction formula would reduce to equation (9)at low flow and small diameters. He noted that this was a‘‘. .
. rather remarkable result, since we arrived, Mr. Poiseuille and I, with this expression, by means of experimentsmade under completely different circumstances.’’ It wouldremain for Osborne Reynolds (1842 – 1912) [Reynolds,1883] to fully quantify the occurrence and differencesbetween laminar and turbulent flow.
However by 1854,Darcy had discovered the kernel of the truth, and heprobably had made the connection to flow in sands. In fact,a footnote that appears to have been added just beforeprinting cites the similarity to his 1856 sand column results.[35] During this period, Darcy’s strength was failing. Hehad chronic poor health that Caudemberg [1858] attributedto injuries resulting from a railcar accident during the Blaisytunnel construction.
In 1855, he was granted release from allduties except research, after which he returned to Dijon forrecuperation, writing and the initiation of an open-channelhydraulics study.3.6. Fontaines[36] During the time between the submission of the pipereport and its publication, he completed his most famoustext, Les Fontaines Publiques de la Ville de Dijon [Darcy,1856]. Fontaines weighs in with 680 pages and 28 plates ofillustrations, and is clearly a compilation of years of work.While much of the material directly addresses the Dijonwater supply, Darcy also discussed several unrelated topicsincluding groundwater, sand filters and pipe manufacture.Due to his deteriorating health, he probably decided to makeit his final thesis on water supply.[37] Chapter III of Part 1 is devoted entirely to artesianwells and shows Darcy had again been consulting Frenchand English experts in the field, in addition to gathering hisown data.
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