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Howarth–Dorodnitsyn Transformation
In fluid dynamics, Howarth–Dorodnitsyn transformation (or Dorodnitsyn-Howarth transformation) is a density-weighted coordinate transformation, which reduces compressible flow conservation equations to simpler form (in most cases, to incompressible form). The transformation was first used by Anatoly Dorodnitsyn in 1942 and later by Leslie Howarth in 1948. The transformation of y coordinate (usually taken as the coordinate normal to the predominant flow direction) to \eta is given by :\eta = \int_0^y \frac \ dy, where \rho is the density and \rho_\infty is the density at infinity. The transformation is extensively used in boundary layer theory and other gas dynamics problems. Stewartson–Illingworth transformation Keith Stewartson and C. R. Illingworth, independently introduced in 1949, a transformation that extends the Howarth–Dorodnitsyn transformation. The transformation reads asN. Curle and HJ Davies: Modern Fluid Dynamics, Vol. 2, Compressible Flow :\xi = \int_0^x \frac\f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fluid Dynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modelling fission weapon detonation. Fluid dynamics offers a systematic structure—which underlies these practical disciplines—that embraces empirical and semi-empirical laws derived from flow measurement and used to solve practical problems. The solution to a fluid dynamics problem typically involves the calculation of various properties of the fluid, such as flow velocity, pressure, density, and temperature, as functions of space and time. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Density
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematically, density is defined as mass divided by volume: : \rho = \frac where ''ρ'' is the density, ''m'' is the mass, and ''V'' is the volume. In some cases (for instance, in the United States oil and gas industry), density is loosely defined as its weight per unit volume, although this is scientifically inaccurate – this quantity is more specifically called specific weight. For a pure substance the density has the same numerical value as its mass concentration. Different materials usually have different densities, and density may be relevant to buoyancy, purity and packaging. Osmium and iridium are the densest known elements at standard conditions for temperature and pressure. To simplify comparisons of density across different s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anatoly Dorodnitsyn
Anatoly Alekseyevich Dorodnitsyn (Russian: Анатолий Алексеевич Дородницын) 19 November (per Julian Calendar), 2 December (per Gregorian Calendar), 1910 – 7 June 1994, Moscow) was a Russian mathematician who worked as an engineer in the Soviet space program. Dorodnitsyn was a Full member of the Russian Academy of Sciences (1953),and a professor at the Department of physical and mathematical sciences (1949), majoring in geophysics. In same cases (for example, in English version some official blanks in Russia) the following translations were also used: Anatolii instead Anatoly and (or) Dorodnicyn instead Dorodnitsyn. Biography Dorodnitsyn was born in the village of Bashino, Kashira County (Tula Governorate), Russian Empire, the son of a village medical doctor, Alexei Petrovich Dorodnitsyn, a graduate of the University of Tartu (now Estonia), and Nina Ivanovna Dorodnitsyna, née Vyshemirskaya, the only daughter of an Orthodox priest. He was the third ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leslie Howarth
Leslie Howarth FRS (23 May 1911 – 22 September 2001) was a British mathematician who dealt with hydrodynamics and aerodynamics. Biography Howarth was educated at Accrington Grammar School, from where he moved to University of Manchester with Sydney Goldstein and then at the University of Cambridge (Caius and Gonville College) with a bachelor's degree in 1933 and a doctorate at Goldstein in 1936. Leslie married Eva Priestley when he was still a research student. Afterwards, he was a lecturer at King's College, Cambridge. In 1937–38 he was with Theodore von Kármán at Caltech. During World War II he worked first in ballistics and from 1942 on the Armament Research Department. After the war, he was a lecturer at St John's College, Cambridge, where Abdus Salam was one of his students, and from 1949 Professor of Applied Mathematics at the University of Bristol. In 1964 he became Henry Overton Wills Professor and Head of the Mathematics Faculty. From 1957 to 1960 he was dean of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boundary Layer
In physics and fluid mechanics, a boundary layer is the thin layer of fluid in the immediate vicinity of a bounding surface formed by the fluid flowing along the surface. The fluid's interaction with the wall induces a no-slip boundary condition (zero velocity at the wall). The flow velocity then monotonically increases above the surface until it returns to the bulk flow velocity. The thin layer consisting of fluid whose velocity has not yet returned to the bulk flow velocity is called the velocity boundary layer. The air next to a human is heated resulting in gravity-induced convective airflow, airflow which results in both a velocity and thermal boundary layer. A breeze disrupts the boundary layer, and hair and clothing protect it, making the human feel cooler or warmer. On an aircraft wing, the velocity boundary layer is the part of the flow close to the wing, where viscous forces distort the surrounding non-viscous flow. In the Earth's atmosphere, the atmospheric boun ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Keith Stewartson
Keith Stewartson (20 September 1925 – 7 May 1983) was an English mathematician and fellow of the Royal Society. Early life The youngest of three children, Stewartson was born to an English baker in 1925. He was raised in Billingham, County Durham, where he attended Stockton Secondary School, and went to St Catharine's College, Cambridge in 1942. He won the Drury Prize in 1943 for his work in Mathematical Tripos. Career After graduation, with the Second World War still on-going, Stewartson began employment with the Ministry of Aircraft Production. During his time there he studied compressible fluid flow problems. After the war he returned to Cambridge and received the Mayhew Prize in 1946. He resumed research under the guidance of Leslie Howarth on boundary layer theory. His research led to his first publication, "Correlated incompressible and compressible boundary layers", which was published by the Royal Society in 1949. He received his doctorate the same year and became a l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sound Speed
The speed of sound is the distance travelled per unit of time by a sound wave as it propagates through an elastic medium. At , the speed of sound in air is about , or one kilometre in or one mile in . It depends strongly on temperature as well as the medium through which a sound wave is propagating. At , the speed of sound in air is about . The speed of sound in an ideal gas depends only on its temperature and composition. The speed has a weak dependence on frequency and pressure in ordinary air, deviating slightly from ideal behavior. In colloquial speech, ''speed of sound'' refers to the speed of sound waves in air. However, the speed of sound varies from substance to substance: typically, sound travels most slowly in gases, faster in liquids, and fastest in solids. For example, while sound travels at in air, it travels at in water (almost 4.3 times as fast) and at in iron (almost 15 times as fast). In an exceptionally stiff material such as diamond, sound travels at , ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Specific Heat Ratio
In thermal physics and thermodynamics, the heat capacity ratio, also known as the adiabatic index, the ratio of specific heats, or Laplace's coefficient, is the ratio of the heat capacity at constant pressure () to heat capacity at constant volume (). It is sometimes also known as the ''isentropic expansion factor'' and is denoted by ( gamma) for an ideal gasγ first appeared in an article by the French mathematician, engineer, and physicist Siméon Denis Poisson: * On p. 332, Poisson defines γ merely as a small deviation from equilibrium which causes small variations of the equilibrium value of the density ρ. In Poisson's article of 1823 – * γ was expressed as a function of density D (p. 8) or of pressure P (p. 9). Meanwhile, in 1816 the French mathematician and physicist Pierre-Simon Laplace had found that the speed of sound depends on the ratio of the specific heats. * However, he didn't denote the ratio as γ. In 1825, Laplace stated that the speed of sound is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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