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.

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. The earliest human civilizations began near the shores of rivers, and consequently coincided with the dawn of hydrology, hydraulics, and hydraulic engineering.

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.

The fundamental principles of hydrostatics and dynamics were given by Archimedes in his work On Floating Bodies (Περὶ τῶν ὀχουμένων), around 250 BC. In it, Archimedes develops the law of buoyancy, also known as Archimedes' principle. This principle states that a body immersed in a fluid experiences a buoyant force equal to the weight of the fluid it displaces. Archimedes maintained that each particle of a fluid mass, when in equilibrium, is equally pressed in every direction; and he inquired into the conditions according to which a solid body floating in a fluid should assume and preserve a position of equilibrium.

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. The siphon is a simple instrument; but the forcing pump is a complicated invention, which could scarcely have been expected in the infancy of hydraulics. It was probably suggested to Ctesibius by the Egyptian wheel or Noria, which was common at that time, and which was a kind of chain pump, consisting of a number of earthen pots carried round by a wheel. In some of these machines the pots have a valve in the bottom which enables them to descend without much resistance, and diminishes greatly the load upon the wheel; and, if we suppose that this valve was introduced so early as the time of Ctesibius, it is not difficult to perceive how such a machine might have led to the invention of the forcing pump. Biruni introduced the method of checking tests during experiments and measured the weights of various liquids. He also recorded the differences in weight between freshwater and saline water, and between hot water and cold water. During his experiments on fluid mechanics, Biruni invented the conical measure, in order to find the ratio between the weight of a substance in air and the weight of water displaced. Al Khazini, in The Book of the Balance of Wisdom (1121), invented a hydrostatic balance.

In the 9th century, Banū Mūsā brothers' Book of Ingenious Devices described a number of early automatic controls in fluid mechanics. Two step level controls for fluids, an early form of discontinuous variable structure controls, was developed by the Banu Musa brothers. They also described an early feedback controller for fluids. According to Donald Routledge Hill, the Banu Musa brothers were "masters in the exploitation of small variations" in hydrostatic pressures and in using conical valves as "in line" components in flow systems, "the first known use of conical valves as automatic controllers." float valve The Banu Musa also developed an early fail safe system where "one can withdraw small quantities of liquid repeatedly, but if one withdraws a large quantity, no further extractions are possible." In 1206, Al Jazari's Book of Knowledge of Ingenious Mechanical Devices described many hydraulic machines. Of particular importance were his water raising pumps. The first known use of a crankshaft in a chain pump was in one of al Jazari's saqiya machines. The concept of minimizing intermittent working is also first implied in one of al Jazari's saqiya chain pumps, which was for the purpose of maximising the efficiency of the saqiya chain pump. Al Jazari also invented a twin cylinder reciprocating piston suction pump, which included the first suction pipes, suction pumping, double action pumping, and made early uses of valves and a crankshaft connecting rod mechanism. This pump is remarkable for three reasons: the first known use of a true suction pipe (which sucks fluids into a partial vacuum) in a pump, the first application of the double acting principle, and the conversion of rotary to reciprocating motion, via the crankshaft connecting rod mechanism.

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.

Benedetto Castelli, and Evangelista Torricelli, two of the disciples of Galileo, applied the discoveries of their master to the science of hydrodynamics. 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. Torricelli, observing that in a jet where the water rushed through a small ajutage it rose to nearly the same height with the reservoir from which it was supplied, imagined that it ought to move with the same velocity as if it had fallen through that height by the force of gravity, and hence he deduced the proposition that the velocities of liquids are as the square root of the head, apart from the resistance of the air and the friction of the orifice. This theorem was published in 1643, at the end of his treatise De motu gravium projectorum, and it was confirmed by the experiments of Raffaello Magiotti on the quantities of water discharged from different ajutages under different pressures (1648). The friction of water, investigated for slow speeds by Coulomb, was measured for higher speeds by William Froude (1810–1879), whose work is of great value in the theory of ship resistance (Brit. Assoc. Report., 1869), and stream line motion was studied by Professor Osborne Reynolds and by Professor Henry S. Hele Shaw.

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.

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 Vortex theory of the atom of William Thomson, later Lord Kelvin. His basic idea was that atoms were to be represented as vortex motions in the ether. This theory predated the quantum theory by several decades and because of the scientific standing of its originator received considerable attention. Many profound insights into vortex dynamics were generated during the pursuit of this theory. Other interesting corollaries were the first counting of simple knots by P. G. Tait, today considered a pioneering effort in graph theory, topology and knot theory. Ultimately, Kelvin's vortex atom was seen to be wrong headed but the many results in vortex dynamics that it precipitated have stood the test of time. Kelvin himself originated the notion of circulation and proved that in an inviscid fluid circulation around a material contour would be conserved. This result singled out by Einstein in "Zum hundertjährigen Gedenktag von Lord Kelvins Geburt, Naturwissenschaften, 12 (1924), 601–602," (title translation: "On the 100th Anniversary of Lord Kelvin's Birth"), as one of the most significant results of Kelvin's work provided an early link between fluid dynamics and topology. 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 Walter Gröbli. In spite of having been written in Göttingen in the general circle of scientists surrounding Helmholtz and Kirchhoff, and in spite of having been mentioned in Kirchhoff's well known lectures on theoretical physics and in other major texts such as Lamb's Hydrodynamics, this solution was largely forgotten. A 1949 paper by the noted applied mathematician J. L. Synge created a brief revival, but Synge's paper was in turn forgotten. A quarter century later a 1975 paper by E. A. Novikov and a 1979 paper by H. Aref on chaotic advection finally brought this important earlier work to light. 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". 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.