G.O. Brown - Henry Darcy and the making of a law (796978), страница 3
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Darcyreviewed the previous designs and proceeded to develop abetter solution. In 1834, he published Rapport à M. le Maireet au Conseil Municipal de Dijon sur les Moyens de Fournirl’Eau Nécessaire à cette Ville (Report to the Mayor andMunicipal Council of Dijon on the Means to Supply WaterNecessary to this City) [Darcy, 1834]. His recommendeddesign provided for the collection of 8 m3/min at the RosoirSpring, which required digging out the spring to improve itsflow.
The water was then carried 12.7 km in a coveredaqueduct to an enclosed 5700 m3 reservoir located near thePorte Guillaume and another reservoir at Montmusard.Pressurized distribution lines totaling 28,000 m were laidin underground galleries and delivered water to majorbuildings and 142 public street hydrants spaced 100 mapart throughout the city.
The entire system was gravitydriven and required no pumps. The completely enclosedspring shown in Figure 2 allowed direct distribution withoutfiltration or treatment. One of the elegant reservoir entrances, or ‘‘Chateau d’Eau’’ is shown in Figure 3. It indicatesthe importance placed on the system by the community (andthe French flair for monumental architecture).[19] The 1834 work provides a glimpse of Darcy’s professional ability and technical knowledge.
In the first part, thereader is impressed by the thoroughness of his review ofprevious proposals and existing systems. Darcy clearly didhis time in the library as he described efforts back to thefifteenth century. Similarly, he reported correspondence withFrench and English engineers that helped him determinesystem feasibility and design standards. In the second partof the report, he provided a comprehensive analysis of fourproject alternatives with cost estimates for construction andoperation. Two options utilized spring sources, the third usedfiltered water from the Ouche, and the fourth the Saint-Michelwell.
Prony’s relationships equation (4) were used to sizepipes and channels, typically using a design flow 50% greaterthan required, while numerous flow rates were quantifiedusing the appropriate orifice and weir flow equations.11 - 5BROWN: HENRY DARCY AND THE MAKING OF A LAW1.8, 3.8 and 5.8 m for flows of 125, 272 and 575 L/minrespectively. No mention was made of pumping duration ortemporal variations, so it appears he believed them to besteady state values. Darcy deduced that significant resistance to flow was occurring in the aquifer, an apparently newdiscovery. He showed this by quantifying what the flow ratewould have been if the drawdown was only result of thepipe friction in the pump intake pipe using the relation,rffiffiffiffiffiffiffiffiffiHD5;LQ ¼ 20:73Figure 3.
Chateau d’Eau, entrance to Porte GuillaumeReservoir. Detail from Darcy [1856, Plate 9].[20] The discussions on filtering river water and the SaintMichel well pump test reveal Darcy’s understanding ofporous media flow at that time. Both ‘‘natural’’ and ‘‘artificial’’ filters were in use elsewhere for clarifying surface water.Natural filters used large galleries constructed in alluvialdeposits next to streams, while artificial filters were smaller,fully enclosed basins of various designs. Both types wouldnormally use steam engines and pumps to overcome elevation differences between the supply and delivery points. Allcontemporary filters had problems with clogging and Darcywas clearly hesitant to use them in any design. He writes, ‘‘Ihad to go through the preceding details to show how delicatethe water purification operation is; English engineers are sothoroughly convinced of this, that if at any time that they canresort to spring waters, they advise companies to employthem, even with an increase in expenditure.’’[21] While Darcy computed pump horsepower and coalrequirements for one alternative design using a natural filter,he made no explicit estimation of filter head losses.
Instead,the required filter area was estimated based a rule of thumbwith a fixed supply head. Similar to Matthews [1835], thefilter operation was never decomposed into its variouscomponents. Thus the concept of fluid friction within thesand was never directly distinguished.[22] Details of the Saint-Michel well construction werenot explicitly reported. However, by piecing together various comments, it is believed that the well had solid casingwith a short length of open hole at the bottom. A 0.11 minside diameter pipe was dropped down 152 m and used asthe intake of a steam powered piston pump.
Well drawdowncould have been measured in the annulus between thecasing and the pump pipe. Darcy reported drawdowns ofð7ÞWhile not explicitly explained in the text, equation (7)combines continuity with a simplified version of equation(4) where the first order term has been dropped. Head loss isassumed equal to the well drawdown,(hL = H ).
Thepffiffiffinumerical coefficient is equal to p=4 b and L was set as thepipe length less the drawdown (152.3 - H ). Theoreticalflows of 534, 810 and 984 L/s were computed when thehead loss was set equal to the measured drawdowns. Herightly concluded, ‘‘The comparison of these figures showsthat the source did not provide to the pump what the headand the diameter of pipe made it possible to provide, or inthe least, the difference was absorbed by filtration.’’ Darcy’scalculations are reasonable when compared to the DarcyWeisbach equation (discussed latter) and showed that onlyabout one half of the drawdown was friction in the pumppipe.[23] Darcy’s analysis of the well was correct up to thispoint, but he then displays the contemporary theoreticallimitations.
He refers to the source of the water as areservoir and states, ‘‘. . . it seems to me that the reservoiris separated from the artesian well by natural conduits thatoffer resistance to the flowing water, . . .’’. The resistance islater quantified, ‘‘By calling d the diameter of the openingof the natural conduit, the volume of water that enters theartesian well is given by the equation,pffiffiffiffiQ ¼ 3:48 d 2 H ;ð8Þwhere H represents the height due to the velocity withwhich the fluid enters the well.’’ Again, while not explicitlystated, the reference to ‘‘height due to the velocity’’ clearlyshows equation (8) is simply the orifice equation, equation(6) with m = 1, and the numerical constants combine toproduce the coefficient shown, for which Darcy provided nojustification or reference.
Finally, using equation (7),equation (8), and inelegant but reasonable logic, Darcyconcluded that even if the well were enlarged, the aquiferresistance would not allow the required flow at a practicaldrawdown.[24] Darcy’s use of equation (8) left an important factunstated, which is demonstrated by one simple observation.The drawdown data along with the zero point fits the linearregression Q = 79 H, with a correlation coefficient, R2 =0.99. I believe he was too thorough not to have observed thelinear trend of his data, but can only speculate on hisreasons to disregard it. Given that he only used the highestflow rate data to evaluate the system, he may have chosen toignore the low flow data thinking that it wasn’t in the regionwhere the second order term of equation (4) dominates.Similarly, he may have doubted limited observations when11 - 6BROWN: HENRY DARCY AND THE MAKING OF A LAWthey diametrically opposed the established theory.
Possibly,the most pragmatic reason is he may not have wanted tostart an argument on a side issue of a nonviable alternativewhen his first priority was to win project approval for theRosoir Spring option. The negative assessment of the well’spotential output was already in direct conflict of an earlierreport by Arnollet (?-1856), the Chief Engineer of theDepartment of Côte-d’Or [Dumay, 1845].
In any case, thelinear relationship is problematic. Steady state well drawdown is a function of both the linear loss in the aquifer andthe second order turbulent losses near the well casing and inthis case, up the pump pipe. For the three flows, Reynoldsnumbers ranged from 16,000 to 74,000 indicating turbulentflow in the pipe. It can be concluded that either the data wasin error, flow was not steady state, or a variable such as thepump intake pressure ignored.[25] A final observation can be made on the 1834 report.While not intended to be a thesis in the style of the day, itcompares well against both Matthew’s and Storrow’s worksthat were published a year later. The Dijon MunicipalCouncil published 400 copies, and undoubtedly manyended up in the hands of practicing engineers.3.4.
Rise to Prominence[26] From 1834 to 1848 Darcy advanced professionallyas he carried out a number of significant projects. Hispreferred plan for Dijon’s water supply was approved bythe Municipal Council with no revision on March 5, 1835.On December 31, 1835, a Royal ordinance declared theDijon water project a public utility, which allowed for landacquisition. Work began in March of 1838, and on 6September 1840, water was delivered to the reservoir atPorte Guillaume, 535 days later. The construction of thecovered aqueduct in that period implies an impressiveaverage daily rate of 24 m/d. Work on water distributionand delivery components continued until 1844, when theproject was substantially completed.[27] Honors were soon to follow. In 1836, his work waspraised in a letter from the Under Secretary of State andDirector of Public Works [Dumay, 1845].
On 7 May 1840Darcy was appointed Chief Engineer for the Department ofCôte-d’Or, which carried with it a seat on the MunicipalCouncil. After recommendation by the Prefect of Côte-d’Orand the Minister of the Interior, on 31 August 1842 he wasawarded the Legion of Honor by King Louis Philippe.Perhaps he took his greatest satisfaction at the projectcompletion when he accepted a gold medal from theMunicipal Council and a laurel wreath from the workmen.Finally in 1845, he was admitted to the Dijon Society ofScience, Art and Letters.[28] During this time, Darcy was also supervising theconstruction of road projects, navigation works and severalbridges, including two major structures over the Saône[Marsaines, 1858].
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