Jean Le Rond D'Alembert: A New Theory of the Resistance of Fluids

285 Pages·2018·4.875 MB·English

by  Julián Simón Calero (eds.)

Studies in History and Philosophy of Science 47
Julián Simón Calero Editor
Jean Le Rond
D’Alembert: A
New Theory of
the Resistance of
Fluids
Studies in History and Philosophy of Science
Volume 47
SeriesEditor
StephenGaukroger,UniversityofSydney,Australia
AdvisoryBoard
RachelAnkeny,UniversityofAdelaide,Australia
PeterAnstey,UniversityofSydney,Sydney,Australia
StevenFrench,UniversityofLeeds,UK
OferGal,UniversityofSydney,Australia
ClemencyMontelle,UniversityofCanterbury,NewZealand
NicholasRasmussen,UniversityofNewSouthWales,Australia
JohnSchuster,UniversityofSydney/CampionCollege,Australia
KoenVermeir,CentreNationaldelaRechercheScientifique,Paris,France
RichardYeo,GriffithUniversity,Australia
Moreinformationaboutthisseriesathttp://www.springer.com/series/5671
Julia´n Simo´n Calero
Editor
’
Jean Le Rond D Alembert:
A New Theory of the
Resistance of Fluids
Editor
Julia´nSimo´nCalero
DepartmentofLogic,Philosophy
andHistoryofScience
UNED
Madrid,Spain
Translators
Vero´nica H.A.Watson LarrieD.Ferreiro
INTA GeorgeMason University
Madrid,Spain Fairfax, VA,USA
ISSN0929-6425 ISSN2215-1958 (electronic)
StudiesinHistoryandPhilosophyofScience
ISBN978-3-319-67999-0 ISBN978-3-319-68000-2 (eBook)
https://doi.org/10.1007/978-3-319-68000-2
LibraryofCongressControlNumber:2017960828
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Abstract
ItisrecognisedthattheNewTheoryoftheResistanceofFluidswasaturningpoint
in the genesis of the Fluid Mechanics, for the first time the motion of a fluid was
reduced to two differential equations in partial derivatives relating the velocities
and positions. Therefore, the physical problem of the fluid motion was converted
intoamathematicalone.
However, the rapid evolution of the discipline, jointly with the difficulties
inherentintheworkovershadowedd’Alembert’scontributions,sothatthestudies
havebeencarriedoutuptonowareonlypartialonesandinsomecaseshisfindings
havebeenundervalued.Wethinkthatthebookdeservesanin-depthstudyinorder
tobringbothmeritsanddefectstolight.
Firstly,wepresentatranslationintoEnglishofd’Alembert’sbook,inwhichwe
havetriedtofollowhisoriginalwords,evenwhensometimesitresultsabitliteral
andunidiomatic.
Thesubsequentcommentariesaredividedintwoparts.Oneisdedicatedtothe
circumstancesinwhichthisbookwaswrittenandthestateoftheFluidDynamicsat
that time. D’Alembert’s ideas on basic concepts, such as forces, pressures, fluids
anddynamicsarealsoincluded.Finally,abriefanalysisoftheNewTheoryismade
inordertomakethenextstageeasier.
ThesecondpartisdedicatedtotheNewTheory.Inordertohighlightthegenuine
contributionofd’AlemberttoFluidMechanicsandtoextracthiscorecontribution,
we have preferred to analyse the book by subjects, giving preference to those
related with theresistanceover thoseotherwith little,ifany,relationwith it.The
reorganization of the articles and the use of his previous Latin Memoire, that
preceded the New Theory, contribute to mitigate the negative opinions about the
lengthinessandtortuositythatsometimeshavebeenattributedtoit.Wehavemade
an effort to show how he manages to find the differential equations ruling the
velocities around the body and the streamlines pattern. Also how he contrives to
jointhepressureforcesoverthebodywithitslossofmomentum,whichturnsoutto
betheresistance.
v
Contents
PartI ANewTheoryoftheResistanceofFluid
1 PrinciplesofDynamicsandHydrodynamicsNecessary
fortheUnderstandingoftheSubsequentPropositions. . . . . . . . . . 19
2 GeneralPrinciplesoftheEquilibriumofFluids. . . . . . . . . . . . . . . 25
3 GeneralPrinciplesofthePressureFluids,inMotion
oratRest. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4 OnthePressureThataFluidExertsonaBodyatRest
andImmersedinIt. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.1 ObservationsNecessaryfortheUnderstanding
oftheSubsequentPropositions. . . . . . . . . . . . . . . . . . . . . . . . 39
4.2 OntheFluidPressureattheFirstInstantoftheImpulse. . . . . . 52
4.3 MethodforDeterminingtheFluidVelocityatAnyPoint. . . . . 53
4.4 OnthePressureoftheFluidatEachMoment. . . . . . . . . . . . . . 57
4.5 TheResistanceofaPlaneFigure. . . . . . . . . . . . . . . . . . . . . . . 61
4.6 NotesonOurSolutiontotheProblemofFluidPressure. . . . . . 61
4.7 ReflectionsontheExperimentsThatHaveBeenMadeorThat
CanBeMadetoDeterminethePressureoftheFluids. . . . . . . . 62
5 OntheResistanceofFluidstotheBodiesMovingTherein. . . . . . . 67
5.1 GeneralObservationsontheVariousClassesofFluids. . . . . . . 67
5.2 TheResistanceofNon-elasticandIndefiniteFluids. . . . . . . . . 68
5.3 OntheUseofPendulumExperimentstoDetermine
theResistanceofFluidsWhoseVelocityIsVerySmall. . . . . . 77
5.4 ExaminationofanHypothesisWhichWouldLeadtoStrange
ParadoxesontheResistanceofFluids. . . . . . . . . . . . . . . . . . . 80
5.5 AbouttheResistanceofNon-elasticandFiniteFluids. . . . . .. . 83
vii
viii Contents
5.6 OntheResistanceofElasticFluids. . . . . . . . . . . . . . . . . . . . . 85
5.7 PrinciplesNecessaryforDeterminingthePressure
ofanElasticFluid. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
6 OscillationsofaBodyFloatinginaFluid. . . . . . . . . . . . . . . . . . . . 91
6.1 RectilinearOscillations. . . . .. . . . . . . . . . . . . . . . . . . . . . . . . 91
6.2 CurvilinearOscillations. . . .. . . .. . . .. . . .. . . . .. . . .. . . .. 92
6.3 OscillationsofaBodyofIrregularShape. . . . . . . . . . . . . . . . . 97
7 OntheActionofaFluidStreamThatExitsfrom
aVesselandStrikesaPlane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
8 ApplicationofthePrinciplesOutlinedinThisEssay
intheResearchoftheMotionofaFluidinaVessel. . . . . . . . . . . . 113
9 ApplicationoftheSamePrinciplestoSomeResearch
onStreamsinRivers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
10 Appendix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
10.1 ReflectionsontheLawsoftheEquilibriumofFluid. . . . . . . . . 121
PartII IntroductiontotheEssay
11 GeneralConsiderations. . .. . . . . . .. . . . . . . .. . . . . . .. . . . . . . .. 135
11.1 TheManuscriptandtheEssay. . . . . . . . . . . . . . . . . . . . . . . . . 135
11.2 FluidMechanicsintheEighteenthCentury. . . . . . . . . . . . . . . 139
12 D’Alembert’sDynamicConceptions. . . . . . . . . . . . . . . . . . . . . . . . 147
13 ForcesandFluidsintheEssay. . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
13.1 ForcesandPressures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
13.2 ConceptionofFluids. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
13.3 ExperienceandExperiments. . . . . . . . . . . . . . . . . . . . . . . . . . 158
14 BriefAnalysisoftheContentsoftheEssay. . . . . . . . . . . . . . . . . . . 161
14.1 ThePreliminaries. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
14.2 BodyinaFluidStream. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
14.3 FluidImpulsiveVelocity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
14.4 BodyMovinginFluidatRest. . . . . . . . . . . . . . . . . . . . . . . . . 165
PartIII AnalysisoftheEssay
15 TheEssay’sIntroduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
16 ThePreliminaries. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
16.1 PrinciplesofDynamics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
16.2 GeneralPrinciplesoftheFluidEquilibrium. . . . . . . . . . . . . . . 176
16.3 PressureonSubmergedBodies. . . . . . . . . . . . . . . . . . . . . . . . 179
16.4 MotioninTubes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
Contents ix
17 ResistanceofaBodyMovinginaFluid. . . . . . . . . . . . . . . . . . . . . 187
17.1 FluidinMotion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
17.2 ImpulsiveMotion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
17.3 BodyinMotion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
18 OtherResistancesandFluids. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
18.1 FrictionandViscosity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
18.2 ResistanceinNon-elasticandFiniteFluids. . . . . . . . . . . . . . . 223
18.3 ResistanceofElasticFluids. . . . . . . . . . . . . . . . . . . . . . . . . . . 226
19 ExperimentsandTheories. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
19.1 ReflectionsonExperiments. . . . . . . . . . . . . . . . . . . . . . . . . . . 231
19.2 ExperimentwithPendulums. . . . . . . . . . . . . . . . . . . . . . . . . . 237
20 OtherMotions. .. . . . .. . . . .. . . .. . . . .. . . . .. . . .. . . . .. . . . .. 243
20.1 MotioninaVessel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
20.2 StreamsinRivers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
20.3 JetStreamAgainstaPlate. . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
20.4 HypothesisofthePlaneSections. . . . . . . . . . . . . . . . . . . . . . . 252
21 TheOscillationofFloatingBodies. . . . . . . . . . . . . . . . . . . . . . . . . 257
21.1 RectilinearOscillations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258
21.2 CurvilinearOscillations.. . . .. . . .. . . .. . . .. . . .. . . .. . . .. 259
21.3 IrregularBodies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
22 ReflectionsonFluidEquilibrium. . . . . . . . . . . . . . . . . . . . . . . . . . 265
Annexes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
NotesontheTranslationandManuscript. . . . . . . . . . . . . . . . . . . . . . . 283
Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
Part I
A New Theory of the Resistance of Fluid
Translated by
Vero´nica H. A. Watson, Larrie D. Ferreiro
Julia´nSimo´nCalero
ByM.D’ALEMBERT,oftheAcade´mieRoyaledeSciencesofParis,ofthePrussia,
andoftheRoyalSocietyofLondon.
INPARIS
ChezDAVIDtheelder,Libraire,rueS.Jacques,(cid:1)alaPlumed’or.
MDCCLII
WITHTHEKINGAPPROBATIONANDPRIVILEGE