History of fluid mechanics
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.
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.
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.
In 3rd century CE, Cao Chong describes the story of weighing the elephant by observing displacement of the boats loaded with different weights.
[2] The fundamental principles of hydrostatics and dynamics were given by Archimedes in his work On Floating Bodies (Ancient Greek: Περὶ τῶν ὀχουμένων), around 250 BC.
[4] In the Greek school at Alexandria, which flourished under the auspices of the Ptolemies, attempts were made at the construction of hydraulic machinery, and about 120 BC the fountain of compression, the siphon, and the forcing-pump were invented by Ctesibius and Hero.
[4] 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 Sextus Julius Frontinus, inspector of the public fountains at Rome in the reigns of Nerva and Trajan.
[7] In the 9th century, Banū Mūsā brothers' Book of Ingenious Devices described a number of early automatic controls in fluid mechanics.
"[11] The double-concentric siphon and the funnel with bent end for pouring in different liquids, neither of which appear in any earlier Greek works, were also original inventions by the Banu Musa brothers.
In 1628 Castelli published a small work, Della misura dell' acque correnti, in which he satisfactorily explained several phenomena in the motion of fluids in rivers and canals; but he committed a great paralogism in supposing the velocity of the water proportional to the depth of the orifice below the surface of the vessel.
[4] The theorem of Torricelli was employed by many succeeding writers, but particularly by Edme Mariotte (1620–1684), whose Traité du mouvement des eaux, published after his death in the year 1686, is founded on a great variety of well-conducted experiments on the motion of fluids, performed at Versailles and Chantilly.
[4] The effects of friction and viscosity in diminishing the velocity of running water were noticed in the Principia of Sir Isaac Newton, who threw much light upon several branches of hydromechanics.
Taking advantage of these results, French engineer Henri Pitot afterwards showed that the retardations arising from friction are inversely as the diameters of the pipes in which the fluid moves.
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.
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 St Petersburg as early as 1726, was founded on two suppositions, which appeared to him conformable to experience.
But in the absence of a general demonstration of that principle, his results did not command the confidence which they would otherwise have deserved, and it became desirable to have a theory more certain, and depending solely on the fundamental laws of mechanics.
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.
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.
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.
[4] In 1858 Hermann von Helmholtz published his seminal paper "Über Integrale der hydrodynamischen Gleichungen, welche den Wirbelbewegungen entsprechen," in Journal für die reine und angewandte Mathematik, vol.
So important was the paper that a few years later P. G. Tait published an English translation, "On integrals of the hydrodynamical equations which express vortex motion", in Philosophical Magazine, vol.
The range of applicability of Helmholtz's work grew to encompass atmospheric and oceanographic flows, to all branches of engineering and applied science and, ultimately, to superfluids (today including Bose–Einstein condensates).
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.
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).
B. Francis (Lowell Hydraulic Experiments, Boston, Mass., 1855) led him to propose variations in the accepted formulae for the discharge over weirs, and a generation later a very complete investigation of this subject was carried out by Henri-Émile Bazin.
An elaborate inquiry on the flow of water in pipes and channels was conducted by Henry G. P. Darcy (1803–1858) and continued by Bazin, at the expense of the French government (Recherches hydrauliques, Paris, 1866).
[4] 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 Andreas Rudolf Harlacher contained valuable measurements of this kind, together with a comparison of the experimental results with the formulae of flow that had been proposed up to the date of its publication, and important data were yielded by the gaugings of the Mississippi made for the United States government by Andrew Atkinson Humphreys and Henry Larcom Abbot, by Robert Gordon's gaugings of the Irrawaddy River, and by Allen J. C. Cunningham's experiments on the Ganges canal.
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 Walter Gröbli.
The subsequent elucidation of chaos in the four-vortex problem, and in the advection of a passive particle by three vortices, made Gröbli's work part of "modern science".
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.
