Hydrodynamics

Information about Hydrodynamics

Hydrodynamics simulation of the Rayleigh-Taylor instability ^[1]

Hydrodynamics, also known as liquid-dynamics in limited academic circles, (literally, "water motion") is fluid dynamics applied to liquids, such as water, alcohol, oil, and blood. However, this distinction from fluid dynamics as a whole is not always fully observed.

Blaise Pascal in the 1600s contributed some of the initial theory to this field. The term originates from the work of Daniel Bernoulli, based on the title of his work called Hydrodynamica (1738). He and Leonhard Euler established the general equations of hydrodynamics.

The practice was continued by Joseph Louis Lagrange (1736-1813) with the Euler-Lagrange system, Jean le Rond d'Alembert (1717-1783) discovered the Cauchy-Riemann equations, Pierre-Simon Laplace (1749-1827) with the governing equation in the potential flow named after him, Hermann Ludwig Ferdinand von Helmholtz (1821-1894) and William Thomson, Lord Kelvin (1824-1907) with Kelvin-Helmholtz instability (see also the Rayleigh-Taylor, Plateau-Rayleigh and Richtmyer-Meshkov instabilities) and Helmholtz's work on vortices.

An analogous field of study, the dynamics of electrically conducting fluids in magnetic fields is called magnetohydrodynamics.

Footnotes

1. ^ Shengtai Li, Hui Li "Parallel AMR Code for Compressible MHD or HD Equations" (Los Alamos National Laboratory) [1]

Characteristics

A liquid's shape is determined by, not confined to, the container it fills.
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Water is a common chemical substance that is essential to all known forms of life.^[1] In typical usage, water refers only to its liquid form or state, but the substance also has a solid state, ice, and a gaseous state, water vapor.
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alcohol is any organic compound in which a hydroxyl group (-OH) is bound to a carbon atom of an alkyl or substituted alkyl group. The general formula for a simple acyclic alcohol is C_nH_2n+1OH.
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Petroleum (Latin Petroleum derived from Greek πέτρα (Latin petra) - rock + έλαιον (Latin oleum) - oil) or crude oil
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Blood is a specialized biological fluid consisting of red blood cells (also called RBCs or erythrocytes), white blood cells (also called leukocytes) and platelets (also called thrombocytes) suspended in a complex fluid medium known as blood plasma.
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Blaise Pascal (pronounced [blɛːz paskal]), (June 19 1623 – August 19 1662) was a French mathematician, physicist, and religious philosopher. He was a child prodigy who was educated by his father.
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Daniel Bernoulli (February 8, 1700 – March 17, 1782) was a Dutch-born mathematician who spent much of his life in Basel, Switzerland where he died. A member of a talented family of mathematicians, physicists and philosophers, he is particularly remembered for his
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Leonhard Euler

Portrait by Johann Georg Brucker
Born March 15 1707
Basel, Switzerland
Died September 18 [O.S.
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Joseph Louis, comte de Lagrange

Joseph Louis Lagrange
Born January 25 1736
Turin, Italy
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Jean le Rond d'Alembert (November 16, 1717 – October 29, 1783) was a French mathematician, mechanician, physicist and philosopher. He was also co-editor with Denis Diderot of the Encyclopédie. D'Alembert's method for the wave equation is named after him.
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In mathematics, the Cauchy-Riemann differential equations in complex analysis, named after Augustin Cauchy and Bernhard Riemann, are two partial differential equations which provide a necessary but not sufficient condition for a function to be holomorphic.
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Pierre-Simon, marquis de Laplace

Posthumous portrait by Madame Feytaud, 1842
Born 1749-03-23
Beaumont-en-Auge, Normandy, France
Died March 5 1827 (aged 79)
Paris, France
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potential flow obeys the following equations

(zero rotation)

(zero divergence = volume conservation)

Equivalently,

where:

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Hermann von Helmholtz

Hermann Ludwig Ferdinand von Helmholtz
Born July 31 1821
Potsdam, Germany
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William Thomson, 1st Baron Kelvin, OM, GCVO, PC, PRS, FRSE, (26 June 1824 – 17 December 1907) was a British mathematical physicist, engineer, and outstanding leader in the physical sciences of the 19th century.
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Rayleigh-Taylor instability, or RT instability (after Lord Rayleigh and G. I. Taylor), occurs any time a dense, heavy fluid is being accelerated by light fluid. This is the case with a cloud and shock system, or when a fluid of a certain density floats above a fluid of
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The Plateau-Rayleigh instability, often called the Rayleigh instability, explains why and how a falling stream of fluid breaks up into smaller packets with the same volume but less surface area. It is related to the Rayleigh-Taylor instability.
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