History of fluid mechanics
The history of fluid mechanics is a fundamental strand of the history of physics and engineering. The study of the movement of fluids (liquids and gases) and the forces that act upon them dates back to pre-history. The field has undergone a continuous evolution, driven by human dependence on water, meteorological conditions and internal biological processes.
The success of early civilizations, can be attributed to developments in the understanding of water dynamics, allowing for the construction of canals and aqueducts for water distribution and farm irrigation, as well as maritime transport. Due to its conceptual complexity, most discoveries in this field relied almost entirely on experiments, at least until the development of advanced understanding of differential equations and computational methods. Significant theoretical contributions were made by notables figures like Archimedes, Johann Bernoulli and his son Daniel Bernoulli, Leonhard Euler, Claude-Louis Navier and Stokes, who developed the fundamental equations to describe fluid mechanics. Advancements in experimentation and computational methods have further propelled the field, leading to practical applications in more specialized industries ranging from aerospace to environmental engineering. Fluid mechanics has also been important for the study astronomical bodies and the dynamics of galaxies.
Antiquity
Pre-history
A pragmatic, if not scientific, knowledge of fluid flow was exhibited by ancient civilizations, such as in the design of arrows, spears, boats, and particularly hydraulic engineering projects for flood protection, irrigation, drainage, and water supply.
Ancient China
Observations of specific gravity and buoyancy were recorded by ancient Chinese philosophers. In the 4th century BCE Mencius describes the weight of the gold is equivalent to the feathers. In 3rd century CE, Cao Chong describes the story of weighing the elephant by observing displacement of the boats loaded with different weights.[2]
Archimedes
The fundamental principles of hydrostatics and dynamics were given by Archimedes in his work
The Alexandrian school
In the Greek school at
Sextus Julius Frontinus
Notwithstanding these inventions of the Alexandrian school, its attention does not seem to have been directed to the motion of fluids; and the first attempt to investigate this subject was made by
Middle Ages
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Islamicate physicists
Biruni introduced the method of
Al-Khazini, in The Book of the Balance of Wisdom (1121), invented a hydrostatic balance.[7]
Islamicate engineers
In the 9th century,
In 1206,
Sixteenth and seventeenth century
Leonardo da Vinci
During the Renaissance, Leonardo da Vinci was well known for his experimental skills. His notes provide precise depictions of various phenomena, including vessels, jets, hydraulic jumps, eddy formation, tides, as well as designs for both low drag (streamlined) and high drag (parachute) configurations. Da Vinci is also credited for formulating the conservation of mass in one-dimensional steady flow.[18]
Castelli and Torricelli
Blaise Pascal
In the hands of Blaise Pascal hydrostatics assumed the dignity of a science, and in a treatise on the equilibrium of liquids (Sur l’équilibre des liqueurs), found among his manuscripts after his death and published in 1663, the laws of the equilibrium of liquids were demonstrated in the most simple manner, and amply confirmed by experiments.[4]
Mariotte and Guglielmini
The theorem of Torricelli was employed by many succeeding writers, but particularly by
Eighteenth century
Studies by Isaac Newton
Friction and viscosity
The effects of friction and viscosity in diminishing the velocity of running water were noticed in the
Orifices
The attention of Newton was also directed to the discharge of water from orifices in the bottom of vessels. He supposed a cylindrical vessel full of water to be perforated in its bottom with a small hole by which the water escaped, and the vessel to be supplied with water in such a manner that it always remained full at the same height. He then supposed this cylindrical column of water to be divided into two parts – the first, which he called the "cataract," being an hyperboloid generated by the revolution of an hyperbola of the fifth degree around the axis of the cylinder which should pass through the orifice, and the second the remainder of the water in the cylindrical vessel. He considered the horizontal strata of this hyperboloid as always in motion, while the remainder of the water was in a state of rest, and imagined that there was a kind of cataract in the middle of the fluid.[4]
When the results of this theory were compared with the quantity of water actually discharged, Newton concluded that the velocity with which the water issued from the orifice was equal to that which a falling body would receive by descending through half the height of water in the reservoir. This conclusion, however, is absolutely irreconcilable with the known fact that jets of water rise nearly to the same height as their reservoirs, and Newton seems to have been aware of this objection. Accordingly, in the second edition of his Principia, which appeared in 1713, he reconsidered his theory. He had discovered a contraction in the vein of fluid (vena contracta) which issued from the orifice, and found that, at the distance of about a diameter of the aperture, the section of the vein was contracted in the subduplicate ratio of two to one. He regarded, therefore, the section of the contracted vein as the true orifice from which the discharge of water ought to be deduced, and the velocity of the effluent water as due to the whole height of water in the reservoir; and by this means his theory became more conformable to the results of experience, though still open to serious objections.[4]
Waves
Newton was also the first to investigate the difficult subject of the motion of waves.[4]
Daniel Bernoulli
In 1738 Daniel Bernoulli published his Hydrodynamica seu de viribus et motibus fluidorum commentarii. His theory of the motion of fluids, the germ of which was first published in his memoir entitled Theoria nova de motu aquarum per canales quocunque fluentes, communicated to the academy of
Jean le Rond d'Alembert
The theory of Daniel Bernoulli was opposed also by Jean le Rond d'Alembert. When generalizing the theory of pendulums of Jacob Bernoulli he discovered a principle of dynamics so simple and general that it reduced the laws of the motions of bodies to that of their equilibrium. He applied this principle to the motion of fluids, and gave a specimen of its application at the end of his Dynamics in 1743. It was more fully developed in his Traité des fluides, published in 1744, in which he gave simple and elegant solutions of problems relating to the equilibrium and motion of fluids. He made use of the same suppositions as Daniel Bernoulli, though his calculus was established in a very different manner. He considered, at every instant, the actual motion of a stratum as composed of a motion which it had in the preceding instant and of a motion which it had lost; and the laws of equilibrium between the motions lost furnished him with equations representing the motion of the fluid. It remained a desideratum to express by equations the motion of a particle of the fluid in any assigned direction. These equations were found by d'Alembert from two principles – that a rectangular canal, taken in a mass of fluid in equilibrium, is itself in equilibrium, and that a portion of the fluid, in passing from one place to another, preserves the same volume when the fluid is incompressible, or dilates itself according to a given law when the fluid is elastic. His ingenious method, published in 1752, in his Essai sur la résistance des fluides, was brought to perfection in his Opuscules mathématiques, and was adopted by Leonhard Euler.[4]
Leonhard Euler
The resolution of the questions concerning the motion of fluids was effected by means of Leonhard Euler's partial differential coefficients. This calculus was first applied to the motion of water by d'Alembert, and enabled both him and Euler to represent the theory of fluids in formulae restricted by no particular hypothesis.[4]
Pierre Louis Georges Dubuat
One of the most successful labourers in the science of hydrodynamics at this period was Pierre-Louis-Georges du Buat. Following in the steps of the Abbé Charles Bossut (Nouvelles Experiences sur la résistance des fluides, 1777), he published, in 1786, a revised edition of his Principes d'hydraulique, which contains a satisfactory theory of the motion of fluids, founded solely upon experiments. Dubuat considered that if water were a perfect fluid, and the channels in which it flowed infinitely smooth, its motion would be continually accelerated, like that of bodies descending in an inclined plane. But as the motion of rivers is not continually accelerated, and soon arrives at a state of uniformity, it is evident that the viscosity of the water, and the friction of the channel in which it descends, must equal the accelerating force. Dubuat, therefore, assumed it as a proposition of fundamental importance that, when water flows in any channel or bed, the accelerating force which obliges it to move is equal to the sum of all the resistances which it meets with, whether they arise from its own viscosity or from the friction of its bed. This principle was employed by him in the first edition of his work, which appeared in 1779. The theory contained in that edition was founded on the experiments of others, but he soon saw that a theory so new, and leading to results so different from the ordinary theory, should be founded on new experiments more direct than the former, and he was employed in the performance of these from 1780 to 1783. The experiments of Bossut were made only on pipes of a moderate declivity, but Dubuat used declivities of every kind, and made his experiments upon channels of various sizes.[4]
Nineteenth century
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Hermann von Helmholtz
In 1858
For the next century or so vortex dynamics matured as a subfield of fluid mechanics, always commanding at least a major chapter in treatises on the subject. Thus,
The range of applicability of Helmholtz's work grew to encompass
Gaspard Riche de Prony
The theory of running water was greatly advanced by the researches of
Johann Albert Eytelwein
J. A. Eytelwein of Berlin, who published in 1801 a valuable compendium of hydraulics entitled Handbuch der Mechanik und der Hydraulik, investigated the subject of the discharge of water by compound pipes, the motions of jets and their impulses against plane and oblique surfaces; and he showed theoretically that a water-wheel will have its maximum effect when its circumference moves with half the velocity of the stream.[4]
Jean Nicolas Pierre Hachette and others
JNP Hachette in 1816–1817 published memoirs containing the results of experiments on the spouting of fluids and the discharge of vessels. His object was to measure the contracted part of a fluid vein, to examine the phenomena attendant on additional tubes, and to investigate the form of the fluid vein and the results obtained when different forms of orifices are employed. Extensive experiments on the discharge of water from orifices (Expériences hydrauliques, Paris, 1832) were conducted under the direction of the French government by J. V. Poncelet (1788–1867) and J. A. Lesbros (1790–1860).[4]
P. P. Boileau (1811–1891) discussed their results and added experiments of his own (Traité de la mesure des eaux courantes, Paris, 1854). K. R. Bornemann re-examined all these results with great care, and gave formulae expressing the variation of the coefficients of discharge in different conditions (Civil Ingénieur, 1880). Julius Weisbach (1806–1871) also made many experimental investigations on the discharge of fluids.[4]
The experiments of
Andreas Rudolf Harlacher and others
German engineers have also devoted special attention to the measurement of the flow in rivers; the Beiträge zur Hydrographie des Königreiches Böhmen (Prague, 1872–1875) of
Twentieth century
Ludwig Prandtl
In 1904, German scientist Ludwig Prandtl pioneered boundary layer theory. He pointed out that fluids with small viscosity can be divided into a thin viscous layer (boundary layer) near solid surfaces and interfaces, and an outer layer where Bernoulli's principle and Euler equations apply.[18]
Developments in vortex dynamics
Vortex dynamics is a vibrant subfield of fluid dynamics, commanding attention at major scientific conferences and precipitating workshops and symposia that focus fully on the subject.
A curious diversion in the history of vortex dynamics was the
The history of vortex dynamics seems particularly rich in discoveries and re-discoveries of important results, because results obtained were entirely forgotten after their discovery and then were re-discovered decades later. Thus, the integrability of the problem of three point vortices on the plane was solved in the 1877 thesis of a young Swiss applied mathematician named
Another example of this kind is the so-called "localized induction approximation" (LIA) for three-dimensional vortex filament motion, which gained favor in the mid-1960s through the work of Arms, Hama, Betchov and others, but turns out to date from the early years of the 20th century in the work of Da Rios, a gifted student of the noted Italian mathematician T. Levi-Civita. Da Rios published his results in several forms but they were never assimilated into the fluid mechanics literature of his time. In 1972 H. Hasimoto used Da Rios' "intrinsic equations" (later re-discovered independently by R. Betchov) to show how the motion of a vortex filament under LIA could be related to the non-linear Schrödinger equation. This immediately made the problem part of "modern science" since it was then realized that vortex filaments can support solitary twist waves of large amplitude.
See also
Further reading
- J. D. Anderson Jr. (1997). A History of Aerodynamics (Cambridge University Press). ISBN 0-521-45435-2
- J. D. Anderson Jr. (1998). Some Reflections on the History of Fluid Dynamics, in The Handbook of Fluid Dynamics (ed. by R.W. Johnson, CRC Press) Ch. 2.
- J. S. Calero (2008). The Genesis of Fluid Mechanics, 1640–1780 (Springer). ISBN 978-1-4020-6414-2
- O. Darrigol (2005). Worlds of Flow: A History of Hydrodynamics from the Bernoullis to Prandtl (Oxford University Press). ISBN 0-19-856843-6
- P. A. Davidson, Y. Kaneda, K. Moffatt, and K. R. Sreenivasan (eds, 2011). A Voyage Through Turbulence (Cambridge University Press). ISBN 978-0-521-19868-4
- M. Eckert (2006). The Dawn of Fluid Dynamics: A Discipline Between Science and Technology (Wiley-VCH). ISBN 978-3-527-40513-8
- G. Garbrecht (ed., 1987). Hydraulics and Hydraulic Research: A Historical Review (A.A. Balkema). ISBN 90-6191-621-6
- M. J. Lighthill (1995). Fluid mechanics, in Twentieth Century Physics ed. by L.M. Brown, A. Pais, and B. Pippard (IOP/AIP), Vol. 2, pp. 795–912.
- H. Rouse and S. Ince (1957). History of Hydraulics (Iowa Institute of Hydraulic Research, State University of Iowa).
- G. A. Tokaty (1994). A History and Philosophy of Fluid Mechanics (Dover). ISBN 0-486-68103-3
References
- ^ G. Garbrecht (1987). Hydrologic and hydraulic concepts in antiquity in Hydraulics and Hydraulic Research: A Historical Review (A.A. Balkema).
- ^ Needham, Joseph (1978). "Science and civilization in china". Cambridge University Press. 2 (336): 476 – via Internet Archive.
- ^ Carroll, Bradley W. "Archimedes' Principle". Weber State University. Retrieved 2007-07-23.
- ^ a b c d e f g h i j k l m n o p q r s t public domain: Greenhill, Alfred George (1911). "Hydromechanics". In Chisholm, Hugh (ed.). Encyclopædia Britannica. Vol. 14 (11th ed.). Cambridge University Press. pp. 115–116. One or more of the preceding sentences incorporates text from a publication now in the
- ^ Mariam Rozhanskaya and I. S. Levinova (1996), "Statics", p. 642, in (Rashed & Morelon 1996, pp. 614–642):
Using a whole body of mathematical methods (not only those inherited from the antique theory of ratios and infinitesimal techniques, but also the methods of the contemporary algebra and fine calculation techniques), Arabic scientists raised statics to a new, higher level. The classical results of Archimedes in the theory of the centre of gravity were generalized and applied to three-dimensional bodies, the theory of ponderable lever was founded and the 'science of gravity' was created and later further developed in medieval Europe. The phenomena of statics were studied by using the dynamic approach so that two trends – statics and dynamics – turned out to be inter-related within a single science, mechanics. The combination of the dynamic approach with Archimedean hydrostatics gave birth to a direction in science which may be called medieval hydrodynamics. Archimedean statics formed the basis for creating the fundamentals of the science on specific weight. Numerous fine experimental methods were developed for determining the specific weight, which were based, in particular, on the theory of balances and weighing. The classical works of al-Biruni and al-Khazini can by right be considered as the beginning of the application of experimental methods in medieval science. Arabic statics was an essential link in the progress of world science. It played an important part in the prehistory of classical mechanics in medieval Europe. Without it classical mechanics proper could probably not have been created.
- ^ Marshall Clagett (1961), The Science of Mechanics in the Middle Ages, p. 64, University of Wisconsin Press
- ^ Robert E. Hall (1973), "Al-Biruni", Dictionary of Scientific Biography, Vol. VII, p. 336
- ^ Ahmad Y Hassan, Transfer Of Islamic Technology To The West, Part II: Transmission Of Islamic Engineering Archived 2008-02-18 at the Wayback Machine
- ^ a b c Otto Mayr (1970). The Origins of Feedback Control, MIT Press.
- ^ Donald Routledge Hill, "Mechanical Engineering in the Medieval Near East", Scientific American, May 1991, pp. 64–69. (cf. Donald Routledge Hill, Mechanical Engineering Archived 2007-12-25 at the Wayback Machine)
- ^ ISBN 90-277-0833-9
- History Channel, archivedfrom the original on 2021-12-21, retrieved 2008-09-06
- Donald Routledge Hill, "Engineering", in Roshdi Rashed, ed., Encyclopedia of the History of Arabic Science, Vol. 2, pp. 751–795 [776]. Routledge, London and New York.
- )
- Ahmad Y Hassan. "The Origin of the Suction Pump: Al-Jazari 1206 A.D." Archived from the originalon 2008-02-26. Retrieved 2008-07-16.
- Donald Routledge Hill (1996), A History of Engineering in Classical and Medieval Times, Routledge, pp. 143, 150–152
- ^ ISBN 978-0-07-116848-9.
- )
- Rashed, Roshdi; Morelon, Régis, eds. (1996). Encyclopedia of the History of Arabic Science.