G.O. Brown - Henry Darcy and the making of a law (796978), страница 2
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It includes,Prony, Henri de Pitot (1695 – 1771), Antoine Chézy(1718 – 1798), Louis Marie Henri Navier (1785 – 1836),Augustin Louis Cauchy (1789 – 1857), Jean-BaptisteBélanger (1790 – 1874), Gaspard Gustave de Coriolis(1792 – 1843), Jean Claude Barre de Saint-Venant (1797 –1886), Arsene Jules Emile Juvenal Dupuit (1804 – 1866)and Henri Emile Bazin (1829 – 1917) [Coronio, 1998].Coriolis was also teaching at L’Ecole Polytechnique duringDarcy’s residence.[10] When Darcy entered L’Ecole des Ponts et Chaussées,it was open to males from the whole of France, recruitmentwas by competitive examination, tuition was free, andstudents received a small fixed stipend.
The total enrollmentwas about 65 and there were seven regular faculty [Bradley,1998]. Some instructors were graduates of the school, whoafter a period of practice, had returned to pursue their ownstudies. The school’s curriculum and its instructors’ expertise are well known. First, following the tradition theycreated, every student had significant math instruction thatincluded calculus. Consistent with the school name, thestudents had training in solid mechanics, bridge design andconstruction that was relatively sophisticated even byBROWN: HENRY DARCY AND THE MAKING OF A LAWtoday’s standards.
Prony was the school’s longtime directorand Navier was an instructor, so we may be certain thestudents learned the state of the art in fluid flow. On hisdeath, Prony’s library contained lecture notebooks onhydrostatics, hydrodynamics, navigation, irrigation anddiversions [Bradley, 1998].3.2. Theorical Foundations[11] Hydrostatic and hydrodynamic theory had been welldefined by eighteenth century mathematicians and scientists.
First among them was Daniel Bernoulli (1700– 1782),who showed that energy was conserved along a streamlinein steady, incompressible, invisid flow, or in modern terms,V2þ h þ z ¼ const;2gð2Þwhere V is the velocity. Following Pierre Simon Laplace’s(1749 – 1827) earlier efforts, Navier [1823] presented adifferential relationship for pressure and velocity inunsteady three-dimensional viscous flow. While additionalwork was necessary for the development of what we call theNavier-Stokes equations, the mathematical basis of idealfluid flow was well developed and undoubtedly known toDarcy.[12] Conversely hydraulics, the science of real flows,was not as advanced. The fluid friction between two pointsin a pipe or channel could be quantified by the empiricalextension of equation (2) properly called the energyequation,hL ¼ 2 2V1V2þ h1 þ z1 þ h2 þ z22g2gffi ðh1 þ z1 Þ ðh2 þ z2 Þ;ð3Þwhere hL is the fluid friction or head loss between positions1 and 2.
Since they usually limited analysis to uniform(constant area) flow, the velocity terms would cancel, andthe RHS was used without explanation. For design however,there were no reliable relationships to predict hL in pipes,open channels or other flows. The most accepted relationship for pipe flow resistance was Prony’s,hL ¼LaV þ bV 2 ;Dð4Þwhere D is the pipe diameter, and a and b are empiricalfriction coefficients. A similar equation with differentcoefficients was used for open channel flow. At high flowvelocities, the first order term was often dropped forcomputational convenience. Prony’s equation was prone toerror since the recommendations for the coefficient valuesdid not account for the pipe roughness.
The only practicallink between hydrodynamics and hydraulics was theapplication of equation (2) to orifice and weir flow thatthe French called Torricelli’s theorem,pffiffiffiffiffiffiffiffiffiffiffiV ¼ 2 gH ;ð5Þ11 - 3where H and is the difference between a reservoir’s watersurface, z1 and the orifice elevation, z2. That relation wascombined with continuity to give the orifice discharge,pffiffiffiffiffiffiffiffiffiffiffiQ ¼ mA 2 gH ;ð6Þwhere Q is the volume flow rate, A is the orifice area and mis an empirical discharge coefficient that was calibrated foreach device. The vertical integration of equation (5) alsoprovided similar accurate relationships for weir flow andlow head orifices.[13] At that time in England, there was little if anyquantitative understanding of fluid flow.
The benchmarkEnglish document of the period, Hydraulia [Matthews,1835], contains almost no quantitative analysis, with theexception of reporting French and English orifice and weirflow measurements. Matthews demonstrated that while theEnglish had already completed several successful largewater projects, they had little appreciation of hydraulicanalysis and design. Storrow [1835], an American whotrained at L’Ecole des Ponts et Chaussées, is credited forintroducing Britain to the French work [Straub, 1964].[14] Porous media and groundwater flow was even lesswell understood. Because of his familiarity with the American, English and French literature, Storrow’s thesis may beconsidered an authoritative reference on the contemporarystate of the art.
His discussion of the large water filters builtby the Chelsea and Greenock Waterworks Companiesincluded flow rates, bed areas and supply heads. However,no attempt was made to quantify the resistance to flow inthe sand. This is curious, considering he wrote at length onpipe friction. It appears that although water filtration wasbecoming standard practice, the notion of quantitativelyanalyzing the hydraulics of the systems had not occurredto the practitioners. This may have been due to their focuson the clogging and cleaning of the filters, which was themajor operational concern.[15] Groundwater research focused solely on artesianwells in carbonate aquifers, which is not surprising.Mechanical pumps were large, expensive and unsuitablefor deep down hole applications. Furthermore, the traditional shallow well drawn with a bucket was known to bevulnerable to pollution.
Thus only deep artesian wells wereconsidered appropriate for water supply systems. Upsloperecharge had been correctly identified by the AmericanLathrop in 1800 and the Frenchman Garnier [1822], asthe source of the water in artesian wells. Storrow [1835]cited the former and translated much of the latter in histhesis. Those and other accounts from France and Englandlead him to state:It is only in calcareous rocks, then, that we should seek for risingsprings. We have seen, that these springs may be found wherever astratum containing fissures sufficient to give passage of water, isenclosed between two others which are water-tight; and if theintermediate stratum comes to the surface in the more elevated spotsso as to receive water from rain, and from streams, and afterwardsdescends without there being any vent for the waters, we have only topierce through the upper bed and give to these a free passage, and theywill rise to the surface of the ground and sometimes even above it.That and other sections makes it clear that while theyunderstood the nature of confined aquifers, it was assumedsignificant volumes of water could only be transported over11 - 4BROWN: HENRY DARCY AND THE MAKING OF A LAWFigure 2.
Section of Rosoir Spring Inlet Structure, covered aqueduct on the right. Detail from Darcy[1856, Plate 3].long distances in relatively large, continuous open conduitswithin an aquifer.3.3. Water for Dijon[16] Darcy graduated in 1826 with a degree in CivilEngineering and was assigned by the Corps to the Department of Jura, but he was soon transferred home to Dijon.Dijon had perhaps the worst water in Europe [Darcy, 1957],and Darcy was quickly assisting in the drilling of a deep testwell.[17] Caudemberg [1858] provides an account of the effortmade by a society of subscribers and the Municipal Councilin hopes of repeating Molut’s successful artesian well inParis.
Beginning in March of 1829 they started drilling nearPlace Saint-Michel. ‘‘On August 6, 1830, the probe, thathad descended to 150.72 m, penetrated suddenly into void;or had reached a stream of undergroundwater, that flowedbriskly up the pipe, but without springing to the surface.’’Attempts made to pump the well were disappointing. ‘‘Mr.Darcy noted himself that the source gave a water ofexcellent quality, but that, even while lowering the levelto ten meters below the pavement of the square, it couldonly provide 500 liters per minute, a quantity insufficientfor the city of Dijon, . . .’’[18] Soon after the disappointment of the well, and underhis own initiative, Darcy set out to provide a clean, dependable water supply to the city from more conventionalsurface water sources [Dumay, 1845]. A number of proposals had been made in the past, but each had flaws.
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