Fluid Mechanics and the History of Physics
“A fluid is any body whose parts yield to any force applied to it and yielding are moved easily with respect to one another.”
– Sir Isaac Newton, Principia Mathematica (1687), Book 2, Section 5.
“The resistance arising from the want of lubricity in the parts of a fluid is, other things being equal, proportional to the velocity with which the parts of the fluid are separated from one another.”
– Sir Isaac Newton, Principia Mathematica (1687), Book 2, Section 9.
“A fluid is a body the contiguous parts of which act on one another with a pressure which is perpendicular to the interface which separates those parts….A great many substances may be found which perfectly fulfil this definition of a fluid when they are at rest, and they are therefore called fluids. But no existing fluid fulfils the definition when it is in motion. In a fluid in motion the pressures at a point may be greater in one direction than in another, or, what is the same thing, the force between two parts may not be perpendicular to the interface which separates those parts. If a fluid could be found which fulfilled the defintion when in motion as well as when at rest, it would be called a Perfect Fluid. All actual fluids are imperfect, and exhibit the phenomenon of internal friction or viscosity, by which their motion after being stirred about in a vessel is gradually stopped, and the energy of the motion is converted into heat.”
– James Clerk Maxwell. Theory of Heat, 2d edition (Longmans, Green, 1888), Chapter V.
“Now I think hydrodynamics is to be the root of all physical science, and is at present second to none in the beauty of its mathematics.”
– William Thomson (Lord Kelvin), letter to Sir George Gabriel Stokes, 20 Dec 1857.
“Werner Heisenberg’s dissertation was ‘On the Stability and Turbulence of Fluid Flow’. He was disappointed with his progress and was glad to change to a more tractable problem.”
– Kip S. Thorne and Roger D. Blandford, Modern Classical Physics (2017), Sec. 15.1.
”[Ludwig] Prandtl created a revolution in fluid mechanics that was very similar to the revolution in quantum mechanics. He developed, just after the turn of the century, a mathematical ability to understand fluid mechanics. And once he did this, man, he and his students just solved all the outstanding problems. The same thing happened in quantum mechanics. Once the mathematical structure was developed, very quickly all the problems got solved.”
– John F. Clauser, 2022 Nobel Laureate in Physics, oral history interview with Joan Bromberg, May 2002.
Welcome. In the following, I present some thoughts about fluid mechanics and the history of physics, pointing in particular to some names that physicists may recognize, and others that they should. This is a work in progress. If you know of any errors or omissions, please contact me at (remove spaces) c t o n g “at” m a i l a p s . o r g.
– Christopher Tong, Ph.D. (physics).
Introduction
Most physicists attribute the beginning of field theory to Michael Faraday and James Clerk Maxwell in the 19th century. It is true that theirs was the first force field theory; however it borrows a great deal of its mathematics from mechanical field theories that originated in the 18th century with Jean le Rond D’Alembert and Leonhard Euler. Consequently much of the vector calculus of electromagnetism retains a distinctly hydrodynamic character, as illustrated in this video lecture from The Mechanical Universe and Beyond, by Prof. David Goodstein (Caltech). (However, the modern vector notation is a more direct consequence of electromagnetism rather than continuum mechanics.) Moreover, much of the mathematics of waves was developed in hydrodynamics, solid mechanics, and acoustics in the 18th and especially 19th centuries, beginning with D’Alembert’s 1747 wave equation for a vibrating string. Having said that, the unknown author of a book review of W. H. Besant’s A Treatise on Hydromechanics, Part 1: Hydrostatics, 4th ed. (Deighton Bell, 1883) exaggerated when he or she wrote, “It is perhaps superfluous to speak of the important place which the subject of hydromechanics has occupied in modern mathematical physics since the labors of Helmholtz, Maxwell, and Thomson, in reducing the mathematical treatment of electricity and magnetism to that of the motion of incompressible fluids” in Science, 3 (50): 78 (18 Jan 1884).
The greatest classical physicists of all time, Galileo, Newton, Faraday, and Maxwell, all investigated fluid mechanics, though (except for Newton) their primary influence on the subject is indirect, through their laying of the foundations of classical mechanics, electromagnetism, and kinetic theory. At least two of the principal founders of classical thermodynamics, Helmholtz and Kelvin, made more direct and profound contributions to hydrodynamics. Albert Einstein’s foray into aerodynamics is more questionable, but several of the other founders of quantum theory made contributions to hydrodynamics. Finally, while only one Nobel Prize in Physics has been awarded for classical hydrodynamics (Hannes Alfven, 1970), many have been awarded for work in superfluids, and many Nobel Laureates honored for other fields have been involved in a greater or lesser extent in the physics of fluids. (For the latter, please see the Appendix at the bottom of this page. I discuss some of these pesonalities elsewhere on this site - notably Lev Landau, Hannes Alfven, S. Chandrasekhar, and Kip Thorne; and here for more on Landau and Thorne, plus Richard Feynman, Steven Weinberg, and Edward M. Purcell.)
Galileo
Galileo Galilei (1564-1642) wrote a Discourse on Floating Bodies (1612), controversial at the time for its quarrelsome, pro-Archimedian, anti-Aristotelian arguments, but is mostly forgotten today. Stillman Drake believes this obscurity is undeserved, for “The Discourse is distinguished among other works of its time by its repeated recourse to observational and experimental data in opposition to philosophical doctrines. Moreover, the experiments proposed require no elaborate equipment and no technique beyond reasonable patience and care.” However Galileo’s account of air resistance encountered by a pendulum, in his Dialogues Concerning Two New Sciences (1638), was challenged almost immediately by Marin Mersenne’s experimental results. Galileo claimed that air resistance was directly proportional to both the speed of the moving object and the density of the fluid medium; today the former is considered incorrect, though the latter is considered correct. In this connection, later writers speculate that Galileo reported on air resistance experiments that he never actually did. Galileo had a mix of correct and incorrect views about hydrostatic pressure, and he provided scientific consulting to the Venetian state arsenal (a shipbuilding facility praised as the beginning of Two New Sciences) and much later, by opponents of a plan to alter the course of the Bisenzio river in Florence.
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Galileo Galilei, A Discouse Presented to the Most Serene Don Cosimo II, Great Duke of Tuscany, Concerning the Natation of Bodies Upon, and Submersion in, the Water. Translated from the second Italian edition by Thomas Salusbury. Introduction and notes by Stillman Drake. University of Illinois Press, 1960. Dover Phoenix edition, 2005.
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Galileo Galilei, Discourses and Mathematical Demonstrations Relating to Two New Sciences. Translated by Henry Crew and Alfonso De Salvio. Introduction by Antonio Favaro. Macmillan, 1914. Dover, 1954.
Newton
Sir Isaac Newton’s (1642-1727) Principia Mathematica (1687) is divided into three books. Most of Book 2 is on fluid mechanics, and Clifford Truesdell famously described the material as “almost entirely original” though “much of it is false”. For example, Newton was the first ever to publish an estimate of the speed of sound in air, but he could not reconcile his prediction with later experimental measurements. (Laplace later showed that Newton neglected to account for heat variations, so his estimate was wrong.) However Book 2 does contain enduring contributions, and Newtonian fluids are named in its author’s honor, since he had proposed that the shear stress on an immersed surface is proportional to the velocity gradient normal to that surface. Newton also theoretically deduced that air resistance is directly proportional to three factors: air density (as Galileo proposed), a measure of surface area (as Leonardo Da Vinci thought), and the square of the velocity, the latter in agreement with Edme Marriotte’s experiments. (There also seems to be a discussion of fluid resistance in Newton’s Opticks, Book 3, Query 28.) For a flat plate moving at an angle of attack relative to the fluid, Newton included a sine-squared of the angle of attack as a factor in that relationship, anticipating future developments in hypersonic flow, according to John D. Anderson. (Newton’s ulterior motive in treating fluid mechanics in the Principia was to debunk Descartes’ ether-vortex theory of the universe.)
- Isaac Newton, Philosophiae Naturalis Principia Mathematica. Translated from the third Latin edition by I. Bernard Cohen and Anne Whitman, assisted by Julia Budenz. University of California Press, 1999.
At least two of Newton’s successors as Lucasian Chair of Mathematics, Cambridge University, were themselves titanic figures in the history of fluid mechanics: Sir Geoge Gabriel Stokes (1819-1903), and Sir M. James Lighthill (1924-1998).
The 18th Century
Modern hydrodynamic theory was founded in this era by the Swiss savants, Daniel Bernoulli, his jealous father Johann, and Leonhard Euler, with key roles played by the Frenchmen, Clairaut, D’Alembert, and Lagrange (see Notes on the History of Fluid Mechanics at the end of this page). As Lagrange wrote in the second edition of his Analytical Mechanics (1811), “Euler was the first to give the general formulas for the motion of fluids, based on the laws of their equilibrium and presented in the simple and clear notation of partial differences…With this discovery all of fluid mechanics was reduced to a single approach to analysis and if the equations which comprise it were integrable it would be possible in any case to completely determine the parameters of the motion and of the action of a fluid moved by arbitrary forces.”
It is notable that the Italian physicist, Laura Bassi (1711-1778), who was modern Europe’s second female recipient of a doctoral degree, first female science faculty member, and first female science department chair, all at the University of Bologna, was a hydrodynamicist. While she is better known for promoting Newtonian mechanics and Franklinian electricity in Italy, and for her experimental work on electricity, one of her few surviving publications is on fluid mechanics. Is she, then, the first published female hydrodynamicist?
- Laura Bassi, 1757: De problemate quodam hydrometrico. De Bononiensi Scientiarum et Artium Instituto atque Academia Commentarii, IV: 61-73.
At the end of the century (1800), Charles-Augustin de Coloumb (1736-1806), better known for his electrostatic force law, published a series of measurements of viscosity using–you guessed it–a torsion wire device.
- C.-A. Coulomb, 1800: Experiences destinees a determiner la coherence des fluides et les loins de leur resistance dans les mouvements tres lents. Memoires des Sciences Mathematiques et Physiques, de l’Institut National des Sciences et Arts, 3: 246-305.
Thomas Young
Thomas Young, M.D. (1773-1829), best known for his demonstration of the interference of light, as well as for Young’s modulus in elasticity theory, also contributed to the theory of capillary flow and wetting (1805). Befitting his medical background, Young also wrote a theoretical study of cardiovascular fluid mechanics (1808).
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T. Young, 1805: An essay on the cohesion of fluids. Philosophical Transactions of the Royal Society of London, 95: 67-87.
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T. Young, 1808: Hydraulic investigations, subservient to an intended Croonian lecture on the motion of the blood. Philosophical Transactions of the Royal Society of London, 98: 164-186.
Faraday
According to Peter A. Davidson, Michael Faraday (1791-1867) “tried to measure the voltage induced by the Thames flowing through the Earth’s magnetic field”, allegedly the “first experiment” in magnetohydrodynamics. After 3 days of effort at the Waterloo bridge, Faraday wrote “I could not…obtain any satisfactory results.” (An illustration of this experiment may be found here.) Of course, Faraday waves are a phenomenon (observed in both granular media or liquids on a vibrating platform) named in his honor, though Faraday’s own paper acknowledges prior work by Oersted, Wheatstone, Weber, “and probably others”. On the practical side, in 1841 Faraday developed and patented a chimney to vent oil lamp combustion products out of the lanthorn of St. Catherine’s lighthouse.
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Michael Faraday, 1831: On a peculiar class of acoustical figures; and on certain forms assumed by groups of particles upon vibrating elastic surfaces. Philosophical Transactions of the Royal Society of London, 121: 299-340.
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Michael Faraday, 1832: The Bakerian Lecture–Experimental Researches in Electricity–Second Series. Philosophical Transactions of the Royal Society of London, 122: 163-194.
Maxwell (and Boltzmann)
Keith Moffatt writes of James Clerk Maxwell’s (1831-1879) research in hydrodynamics: “his publications were few but nevertheless ground-breaking in their originality”. Of course, as mentioned, the conceptual and mathematical appartus of hydrodynamic theory was employed by Maxwell in the early stages of developing his electromagnetic field theory. Meanwhile, after Maxwell’s first paper on the kinetic theory of gases, he and his wife Katherine carried out a series of experiments to measure the viscosity of air at various conditions, confirming that it is independent of pressure. Elizabeth Garber says that these experiments, published in 1866, “became one of the most significant pieces of evidence in favour of his kinetic theory”. Maxwell’s second paper on kinetic theory (1867) shows how the Navier-Stokes equations may be obtained within the theory. Ludwig Boltzmann (1844-1906), of course, completed Maxwell’s kinetic theory, also making the connection with the macroscopic Navier-Stokes equations (Lectures on Gas Theory, Part I, Secs. 20 & 22). A cryptic passage in Serrin (1958) claims that Boltzmann was the first to propose that the symmetry of the Cauchy stress tensor be an axiom, rather than a theorem (as Cauchy had presented it). As Hershel Markovitz (1977) reminds us, Boltzmann (along with Maxwell and Kelvin) contributed to early theories of viscoelasticity, one of the simplest examples of a non-Newtonian fluid.
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J. Clerk Maxwell, 1866: The Bakerian Lecture–On the viscosity or internal friction of air and other gases. Philosophical Transactions of the Royal Society of London, 156: 249-268.
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J. Clerk Maxwell, 1867: On the dynamical theory of gases. Philosophical Transactions of the Royal Society of London, 157: 49-88.
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L. Boltzmann, 1896 & 1898: Vorlesungen uber Gastheorie, Parts I and II. J. A. Barth.
Helmholtz and Kelvin
Of course, two of the 19th century’s greatest thermodynamicists were also among its greatest hydrodynamicists: Hermann von Helmholtz, M.D. (1821-1894) and William Thomson (Lord Kelvin, 1824-1907). They contributed fundamental work to both fields (and Kelvin, in addition, to electromagnetism). To mention just a few examples in hydrodynamics: Helmholtz’s vortex theorems and Kelvin’s circulation theorem are fundamental for inviscid flows; the Kelvin-Helmholtz instability is named after them both. Helmholtz was the first to define vorticity, and also made contributions to acoustics. Helmholtz’s 1868 work on using conformal mapping to study discontinuous two-dimensional flow was picked up and used by others including Gustav Robert Kirchoff (1824-1887) and Lord Rayleigh (see below). (While Kirchoff made important contributions to hydrodynamics, he was even more influential in solid mechanics.) Helmholtz and Kelvin made major contributions to the theory of hydrodynamic waves of various types, but Kelvin famously refused to believe that powered flight was possible.
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H. von Helmholtz, 1858: Uber integrale der hydrodynamischen gleichungen, welche den wirbelbewegungen entsprechen. Journal fur die Reine und Angewandte Mathematik, 55: 25-55.
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H. von Helmholtz, 1868: Uber discontinuirlicht flussigkeitsbewegungen. Monatsberichte der Koniglichen Preussische Akademie der Wissenschaften zu Berlin, 23: 215–228.
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W. Thomson, 1869: On vortex motion. Transactions of the Royal Society of Edinburgh, 25: 217-260.
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W. Thomson, 1871: Hydokinetic solutions and observations. Philosophical Magazine, 42: 362–377.
Rayleigh
John William Strutt, Lord Rayleigh (1842-1919, Nobel in Physics 1904), made major contributions to acoustics and other areas of theoretical hydrodynamics (wave motion, cavitation, aerodynamic heating at hypersonic speeds), as well as dimensional analysis. In the field of hydrodynamic instabilities alone, the Plateau-Rayleigh, Rayleigh-Benard, and Rayleigh-Taylor instabilities bear his name.
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Lord Rayleigh, 1878: On the instability of jets. Proceedings of the London Mathematical Society, s1-10: 4-13.
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Lord Rayleigh, 1916: On convection currents in a horizontal layer of fluid when the higher temperature is on the under side. Philosophical Magazine, series 6, 32: 529-546.
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Lord Rayleigh, 1916: On the dynamics of revolving fluids. Proceedings of the Royal Society of London, series A, 93: 148-154.
Einstein’s folly
Using a fallacious argument based on the Venturi effect, Albert Einstein (1879-1955) proposed a “cat’s back” airfoil design in 1916 that failed miserably when tested by a Berlin aircraft company. The test pilot, Paul Ehrhardt, survived, but years later, a few months before Einstein died, he told Ehrhardt “I have often been ashamed of my folly of those days.” (A second test pilot, Otto Reichert, crashed but also survived.) “Einstein’s folly” is discussed by Bloor (2011, pp. 296-302), Illy (2012), and Calaprice et al. (2015, p. 297). Bloor writes that “Einstein had little knowledge of current developments in the field of aerodynamics. This episode is a salutory reminder of the difference between fundamental physics and technical mechanics. Eminence in the former does not guarantee competence in the latter.”
- A. Einstein, 1916: Elementare theorie der wasserwellen und des fluges. Die Naturwissenschaften, 4: 509-510.
In Einstein’s defense, his discussion of the “teacup effect” (where loose tea leaves tend to gather at the center of the cup after stirring) is generally thought to be sound. It appears in a paper discussing the meadering of rivers and Baer’s Law. (Kip Thorne and Roger Blandford, in their Modern Classical Physics, treat the teacup effect using Ekman boundary layer theory; see their Exercise 14.22.)
- A. Einstein, 1926: Die ursache der maanderbildung der flusslaufe und des sogenannten Baerschen Gesetzes. Naturwissenschaften, 14, 223–224.
Einstein’s doctoral dissertation included a theoretical prediction for the viscosity of a dilute suspension of spheres, a result still taught (e.g., Gary Leal’s Advanced Transport Phenomena, 2007). His very first scientific paper in 1901 was on a molecular model for capillarity. In 1920, Einstein wrote a paper on the molecular relaxation technique, related to the dispersion of sound velocity in a chemically reacting gas mixture. Einstein’s greatest contribution to hydrodynamics may be that he encouraged his post-doc, Robert H. Kraichnan (1928-2008) to work in fluid mechanics; Kraichnan later made influential contributions to the theory of turbulence. Einstein’s son Hans Albert (1904-1973) was a distinguished hydraulic engineer who worked at the U.S. Dept. of Agriculture, CalTech, and UC Berkeley.
The founders of quantum theory
Einstein of course had a hand in the creation of quantum theory, but what about the others? Max Planck (1858-1947) included a volume on The Mechanics of Deformable Bodies in his 5-volume published lectures on theoretical physics, and similarly Arnold Sommerfeld (1868-1951) included one with the same title in his own 6-volume published lectures. Both books cover solid and fluid mechanics. Sommerfeld’s most famous result in fluid mechanics is the Orr-Sommerfeld equation for stability; he also made major contribution to lubrication theory. Sommerfeld advised his doctoral student Werner Heisenberg (1901-1976) to write a thesis on hydrodynamics, which he did, and Heisenberg later worked in turbulence theory. Among the principle founders of quantum theory, Heisenberg seems to be the most committed hydrodynamicist; he continued to ponder fluid dynamics late in his career, as illustrated by his Physics Today piece of 1967. (The “sad story” of Heisenberg’s thesis defense is recounted by David Cassidy here.) Niels Bohr (1885-1962) worked on a problem of hydrodynamic instability (1909), extending a theory of Rayleigh’s. It was Bohr’s first scientific publication. Finally I mention Cark Eckart (1902-1973), of the Wigner-Eckart theorem, on the main page of this site. He proved the equivalence of the wave and matrix mechanics formulations of Schrodinger and Heisenberg, respectively, but was scooped by Schrodinger, who beat Eckart to publication. As I mention on the main page, Eckart later had a consequential career in geophysical hydrodynamics. He also wrote a fundamental paper on bulk fluid streaming generated by a sound wave, a phenomenon now known as Eckart streaming.
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N. Bohr, 1909: Determination of the surface tension of water by the method of jet vibration. Philosophical Transactions of the Royal Society, A209: 441-458.
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A. Sommerfeld, 1909: Ein beitrag zur hydrodynamischen erklarung der turbulenten flussigkeitsbewegung. Atti del Congresso Internazionale dei Matematici, Rome, 1908, ed. by G. Castelnuovo (Accademia dei Lincei, Rome), vol. 3: 116-124.
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W. Heisenberg, 1924: Uber stabilitat und turbulenz von flussigkeitsstrommen. Annalen der Physik, 15: 577-627.
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W. Heisenberg, 1967: Nonlinear problems in physics. Physics Today, 20 (5): 27-33.
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C. Eckart, 1948: Vortices and streams caused by sound waves. Physical Review, 73: 68-76.
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C. Eckert, 1960: Hydrodynamics of Oceans and Atmopsheres. Pergamon Press.
According to George Uhlenbeck (1900-1988), who was a student of Paul Ehrenfest (1880-1933), the latter “never mentioned the hydrodynamical equations” because the frontier of physics was quantum theory and nuclear structure, with the rest dismissed as “desperation physics” by Wolfgang Pauli (1900-1958)! However, Uhlenbeck succeeded Hendrik Kramers (1894-1952) as professor of physics and mechanics at Utrecht, and discovered that Kramers had always included a semester on classical hydrodynamics in his three year cycle of courses. Uhlenbeck decided to offer a course on the subject, having taught it to himself: “It made a great impression on me, and I think that every physicist should have some familiarity with the field. It will do even the high energy physicists some good.”
Notes on the history of fluid mechanics
Archimdedes (287-212 BC) formulated the principles of buoyancy and hydrostatics (On Floating Bodies), an enduring contribution from the classical world. (However, it is a mistake to dismiss hydrostatics, as A. M. Binnie did, as “a limited subject invented and virtually finished by Archimedes.”) Hero of Alexandria (first century AD) formulated the hydraulic continuity equation. During the Renaissance, Leonardo Da Vinci (1452-1519) rediscovered the hydraulic continuity equation (but did not publish it) and made extensive studies of fluid flow (e.g., Del Moto e Misura Dell’Acqua, posthumously compiled from DaVinci’s writings). The hydraulic continuity equation was rediscovered yet again in 1628 by Galileo’s student, Benedetto Castelli (c1577-c1644). Simon Stevin (1548-1620), Evangelista Torricelli (1608-1647), Blaise Pascal (1623-1662), and Robert Boyle (1627-1691) are known for introducing and elaborating the concept of fluid pressure, including its measurement (Torricelli’s barometer), Pascal’s Principle, Boyle’s gas law, and the hydrostatic paradox (first explained by Stevin). Torricelli also studied his famous efflux problem. Edme Marriotte (1620-1684) was the first to experimentally establish that the force of air resistance is proportional to the square of the fluid velocity, using a beam dynamometer (1673). Christiaan Huygens (1629-1695) actually established the same result four years earlier, but did not publish until 1690, accusing the then-deceased Marriotte of plagiarism. (As mentioned above, Newton supplied the first theory supporting this experimental result in 1687.)
The modern theory of hydrodynamics, and the kinetic theory of gases, were both founded by Daniel Bernoulli (1700-1783) with his publication of Hydrodynamica (1738). This event provoked his jealous father Johann to publish Hydraulica (1743), backdating it to appear to have preceded his son’s work. Also in 1743 came Alexis Clairaut’s (1713-1765) study of the equilbirium of rotating fluids (he was studying the shape of the Earth). In 1744, Jean le Rond D’Alembert (1717-1783) formulated the modern mass balance law for incompressible flow, using a field theoretic formulation, as well as his famous paradox on fluid resistance (reinforced in another paper of 1752). Bernoulli’s Swiss compatriot Leonhard Euler (1707-1783) introduced the momentum balance equation that bears his name in 1755; he also established the modern understanding of fluid pressure. These efforts represent the formulation of hydrodynamics as a local field theory, governed by coupled, nonlinear partial differential equations, and analyzed using vector (and tensor) calculus. This formulation serves as a model for later field theories in physics (beginning explicitly with Maxwell’s electromagnetic theory). Joseph-Louis Lagrange (1736-1813) extended this work in 1788, introducting both the velocity potential and the streamfunction, and used D’Alembert’s 1749 complex variable formulation of two-dimensional flow to introduce conformal mapping methods, later exploited by Helmholtz and others. In 1768, Antoine Chezey (1718-1798) formulated the basic equation for one-dimensional open channel flow. The century also saw major experimental advances, such as the Borda-Carnot equation, empirically describing the losses in total head at a sudden expansion of a pipe, a regime in which Bernoulli’s equation breaks down. The law is named after French engineers, Jean-Charles de Borda (1733-1799) and Lazare Carnot (1753-1823), the latter being the father of the great thermodynamicist, Sadi Carnot.
The 19th century saw the introduction of Augustin-Louis Cauchy’s (1789-1857) stress principle (1827) and general equation of motion for continua (1828). The Navier-Stokes equations were developed by multiple individuals (see Darrigol, 2002): the first was in 1822 by Claude Louis Marie Henri Navier (1785-1836), and the last and most definitive was in 1845 by Sir George Gabriel Stokes (1819-1903). (In between, Darrigol tells us, were Cauchy, Simeon-Denis Poisson, and A. J. C. Barre de Saint-Venant.) Stokes made numerous other major contributions to theoretical hydrodynamics such as the problem of creeping flow. Major experimental results on viscous flow in a pipe were made by French physiologist Jean Poiseuille (1797–1869) and German hydraulicist Gotthilf Hagen ((1797–1884). Hagen was also the first to distinguish betweeen laminar and turbulent flows. Henry Darcy (1803–1858) did pioneering work on flow in porous media.
Joseph Fourier (1768-1830) introduced his law of heat conductivity in 1822, and Adolf Fick (1829-1901) introduced his diffusion law in 1855. Giorgio Bidone (1781-1839) initiated the study of hydraulic jumps in papers of 1820 and 1826, a problem that engaged several later theorists including Gaspard Gustave de Coriolis (1792-1843) in 1836. John Scott Russell (1808-1882) discovered solitary waves during studies for a canal company in the 1830s and 40s. Osborne Reynolds (1832-1912) began the modern investigation of turbulent flow in 1883, and was also the first to demonstrate cavitation, and formulated the statistical theory of turbulence. Andrei N. Kolmogorov (1903-1987) and Alexander M. Obukhov (1918-1989) independently proposed turbulence scaling laws in 1941 that have had an enduring influence on the subject; as noted below, Heisenberg and von Weiszacker, and Lars Onsager, developed similar theories after the war. Apparently the Russian cosmologist Alexander A. Friedmann (1888-1925) also worked in turbulence theory.
Ludwig Prandtl (1875-1953) introduced the boundary layer concept in 1904. The two-dimensional theory of aerodynamic lift was formulated by Wilhelm Kutta (1867-1944) and Nikolai Egorovich Zhukovskii (1847-1921), while the three-dimensional theory is due to Prandtl and Frederick W. Lanchester (1868-1946), along with the work of Prandtl’s student Heinrich Blasius (1883-1970). G. I. Taylor (1886-1975), who made enduring contributions across fluid and solid mechanics (such as investigating the Taylor-Couette instability) and aerodynamicist Theodore von Karman (1881-1963), together with Prandtl, are the three most consequential hydrodynamicists of the 20th century.
For more on the history of fluid mechanics, Rouse and Ince (1957), Anderson (1997), Darrigol (2005), Eckert (2006), and Calero (2008) are particularly useful. The last three are complementary: Calero covers the period from Huyghens, Marriotte, and Newton, to Euler and Lagrange; Darrigol takes the story from the Bernoullis to Prandtl; and Eckert begins with Prandtl and ends on the eve of WWII. I have drawn liberally from these sources in the above. For a perspective on hydraulics in ancient civilizations, see Garbrecht (1987).
APPENDIX: Nobel Laureates and the Physics of Fluids
Here I list some selected Nobel Laureates in Physics (or Chemistry or Biology, noted as such), the year of their award, and a mention of a few of their involvements in fluid mechanics or the physics of fluids. In most cases such involvement was not the reason for their Nobel Prize.
Year | Laureate | Involvement with the physics of fluids or related activity |
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1901 | Wiliam C. Rontgen | Research on problems such as the effect of pressure on refractive index in various fluids, variations in the relationship between temperature and compressibility in water and other fluids; the spreading of oil drops on water. |
1902 | Hendrik A. Lorentz | Research in hydrodynamics included a well-known paper on slow, viscous flow, introducing the Lorentz reciprocal theorem, Stokeslets, the boundary integral method, and Lorentz’s reflection formula. |
1904 | John William Strutt, Lord Rayleigh | Hydrodynamic instabilities (e.g., Rayleigh-Benard, Rayleigh-Taylor, Plateau-Rayleigh); acoustics; many other contributions (see above). |
1906 | J. J. Thomson | His 1882 Adams Prize essay was on vortex rings, including applications to Kelvin’s vortex atom theory. Also contributed to viscoelastic theory. |
1911 | Wilhelm Wien | Wrote authoritative text, Lehrbuch der Hydrodynamik (S. Hirzel, Leipzig, 1900). |
1913 | Heike Kamerlingh Onnes | Experiments on liquid helium |
1918 | Max Planck | Wrote Mechanics of Deformable Bodies (second volume of his Introduction to Theoretical Physics). |
1921 | Albert Einstein | Doctoral dissertation in part on viscosity of solutions with added sugar; teacup effect; “Cat’s back” aerofoil (Einstein’s folly - see above). |
1922 | Niels Bohr | Chain oscillations in liquid jets (Bohr, 1909); developed Gamow’s liquid drop model of the nucleus. |
1923 | Robert A. Millikan | Oil drop experiment requires use of Stokes formula for drag force on a slowly falling sphere |
1930 | C. V. Raman | Theory of Debye-Sears diffraction (see below) |
1932 | Werner Heisenberg | Doctoral dissertation under Sommerfeld on transition to turbulence in Poiseuille flow. Worked with with C. F. von Weizsacker on liquid drop model of the nucelus, and turbulence scaling law (similar to Kolmogorov-Obukhov’s). |
1932 (Chemistry) | Irving Langmuir | Discovered Langmuir circulation in the Sargasso Sea. |
1933 | Erwin Schrodinger | Research in atmospheric acoustics |
1936 (Chemistry) | Peter Debye | Debye-Sears diffraction |
1938 | Enrico Fermi | Relativistic hydrodynamics of collision products of high energy cosmic rays. Worked with John von Neumann on Rayleigh-Taylor instability. |
1952 | Edward M. Purcell | Life at low Reynolds number (Purcell, 1977). |
1956/1972 | John Bardeen | Two-fluid model of superconductivity (Bardeen, 1958). |
1957 | T. D. Lee | Two brief notes on turbulence (1950, 1951); statistical properties of hydrodynamic and magnetohydroynamic fields (1952). |
1962 | Lev D. Landau | Theory of superfluids; theory of turbulence; relativistic hydrodynamics (see Fermi above); classic text with Lifshitz, Fluid Mechanics. |
1965 | Richard P. Feynman | Circulation quantization in superfluids. Fluid mechanics chapters in classic Feynman Lectures on Physics. |
1965 | Julian Schwinger | Research on somnoluminescence. |
1967 | Hans A. Bethe | Worked on liquid drop model of nucleus. During WWII, on von Karman’s recommendation, Bethe and Teller worked on the theory of shock waves, before they were recruited to Los Alamos. Bethe also worked with J.G. Kirkwood on the pressure wave from an underwater explosion. |
1967 (Chemistry) | Manfred Eigen | Ultrasonic methods of producing chemical reactions/processes. |
1968 (Chemistry) | Lars Onsager | Turbulence scaling law (similar to Kolmogorov-Obukhov’s), 1945; 1949 papers on statistical hydrodynamics; Bose-Einstein condensation in liquid helium (Penrose & Onsager, 1956). |
1969 (Biology) | Max Delbruck | Saffman-Delbruck (1975) model for diffusion in lipid bilayers |
1970 | Hannes O. G. Alfven | Magnetohydrodynamic waves. |
1977 | Philip W. Anderson | Anderson’s equations for superfluid flow. |
1977 (Chemistry) | Ilya Prigogine | Theory of dissipative structures such as Benard cells in thermal convection. |
1978 | Pyotr L. Kapitsa | Superfluid liquid helium-4 |
1979 | Steven Weinberg | Relativistic hydrodynamics, e.g., Weinberg, 1971. |
1983 | Subramanyan Chandrasekhar | Hydrodynamic and magnetohydrodynamic instabilities; chaired APS-DFD in 1955. |
1991 | Pierre-Gilles DeGennes | Liquid crystals; capillarity and wetting. |
1996 | David Lee, Douglas Osheroff, and Robert Richardson | Superfluid liquid helium-3 |
1998 | Robert B. Laughlin, Horst L. Stormer, and Daniel C. Tsui | Fractional quantum hall effect in a quantum fluid. |
1999 (Chemistry) | Ahmed H. Zewail | Nanofluidics of molten lead in a single zinc oxide nanotube (Lorenz & Zewail, 2014). |
2001 | Eric A. Cornell, Wolfgang Ketterle, and Carl Wiemann | Bose-Einstein condensation in dilute alkali atom gases, which is a superfluid. |
2003 | Anthony J. Leggett | Contributions to theory of superfluids. |
2004 | Frank Wilczek | Physics of swimming (Schapere and Wilczek, 1987, 1989a,b). |
2016 | David J. Thouless and J. Michael Kosterlitz | Proposed new type of phase transition observable in superfluids. |
2017 | Kip S. Thorne | Astrophysical hydrodynamics; fluid mechanics chapters in Modern Classical Physics (with R. Blandford). |
2019 | P. J. E. Peebles | Hydrodynamic models in cosmology |
2021 | Syukuro Manabe and Klaus Hasselmann | Fundamental contributions to climate modeling |
2021 | Giorgio Parisi | Multifractal description of turbulence (with coauthors). |
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