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Landau–Squire Jet
In fluid dynamics, Landau–Squire jet or Submerged Landau jet describes a round submerged jet issued from a point source of momentum into an infinite fluid medium of the same kind. This is an exact solution to the incompressible form of the Navier-Stokes equations, which was first discovered by Lev Landau in 1944 and later by Herbert Squire in 1951. The self-similar equation was in fact first derived by N. A. Slezkin in 1934, but never applied to the jet. Following Landau's work, V. I. Yatseyev obtained the general solution of the equation in 1950. Mathematical description The problem is described in spherical coordinates (r,\theta,\phi) with velocity components (u,v,0). The flow is axisymmetric, i.e., independent of \phi. Then the continuity equation and the incompressible Navier–Stokes equations reduce to : \begin & \frac \frac(r^2u) + \frac\frac(v\sin\theta) = 0 \\ pt& u\frac + \frac \frac - \frac= - \frac \frac + \nu \left(\nabla^2 u - \frac - \frac \frac - \frac \right) \ ... [...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] |
Lev Landau
Lev Davidovich Landau (russian: Лев Дави́дович Ланда́у; 22 January 1908 – 1 April 1968) was a Soviet- Azerbaijani physicist of Jewish descent who made fundamental contributions to many areas of theoretical physics. His accomplishments include the independent co-discovery of the density matrix method in quantum mechanics (alongside John von Neumann), the quantum mechanical theory of diamagnetism, the theory of superfluidity, the theory of second-order phase transitions, the Ginzburg–Landau theory of superconductivity, the theory of Fermi liquids, the explanation of Landau damping in plasma physics, the Landau pole in quantum electrodynamics, the two-component theory of neutrinos, and Landau's equations for ''S'' matrix singularities. He received the 1962 Nobel Prize in Physics for his development of a mathematical theory of superfluidity that accounts for the properties of liquid helium II at a temperature below (). Life Early years Landau was born ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Herbert Squire
Herbert Brian Squire FRS (13 July 1909 – 22 November 1961), was a British aerospace engineer and Zaharoff Professor of Aviation at Imperial College London. Biography Born on 13 July 1909, Squire was educated at Bedford School and at Balliol College, Oxford, where he read mathematics. After research at the University of Oxford, and at the University of Göttingen between 1932 and 1933, he became a scientific officer at the Royal Aircraft Establishment. In 1946 he was appointed as chairman of the Helicopter Committee of the Aeronautics Research Council and, in 1947, he was appointed as principal scientific officer at the Royal Aircraft Establishment, working on jet propulsion. Between 1952 and 1961 he was Zaharoff Professor of Aviation at Imperial College London. He was elected as a Fellow of the Royal Society The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of scien ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Quarterly Journal Of Mechanics And Applied Mathematics
''The Quarterly Journal of Mechanics and Applied Mathematics'' is a quarterly, peer-reviewed scientific journal covering research on classical mechanics and applied mathematics. The editors-in-chief are P. W. Duck, P. A. Martin and N. V. Movchan. The journal was established in 1948 to meet a need for a separate English journal that publishes articles focusing on classical mechanics only, in particular, including fluid mechanics and solid mechanics, that were usually published in journals like ''Proceedings of the Royal Society'' and ''Philosophical Transactions of the Royal Society ''Philosophical Transactions of the Royal Society'' is a scientific journal published by the Royal Society. In its earliest days, it was a private venture of the Royal Society's secretary. It was established in 1665, making it the first journa ...''. Abstracting and indexing The journal is abstracted and indexed in, References External links * {{DEFAULTSORT:Quarterly Journal of Mechanics and A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Landau001
Landau ( pfl, Landach), officially Landau in der Pfalz, is an autonomous (''kreisfrei'') town surrounded by the Südliche Weinstraße ("Southern Wine Route") district of southern Rhineland-Palatinate, Germany. It is a university town (since 1990), a long-standing cultural centre, and a market and shopping town, surrounded by vineyards and wine-growing villages of the Palatinate wine region. Landau lies east of the Palatinate forest, on the German Wine Route. It contains the districts (''Ortsteile'') of Arzheim, Dammheim, Godramstein, Mörlheim, Mörzheim, Nussdorf, Queichheim, and Wollmesheim. History Landau was first mentioned as a settlement in 1106. It was in the possession of the counts of Leiningen-Dagsburg-Landeck, whose arms, differenced by an escutcheon of the Imperial eagle, served as the arms of Landau until 1955. The town was granted a charter in 1274 by King Rudolf I of Germany, who declared the town a Free Imperial Town in 1291; nevertheless Prince-Bishop Emich of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Landau010
Landau ( pfl, Landach), officially Landau in der Pfalz, is an autonomous (''kreisfrei'') town surrounded by the Südliche Weinstraße ("Southern Wine Route") district of southern Rhineland-Palatinate, Germany. It is a university town (since 1990), a long-standing cultural centre, and a market and shopping town, surrounded by vineyards and wine-growing villages of the Palatinate wine region. Landau lies east of the Palatinate forest, on the German Wine Route. It contains the districts (''Ortsteile'') of Arzheim, Dammheim, Godramstein, Mörlheim, Mörzheim, Nussdorf, Queichheim, and Wollmesheim. History Landau was first mentioned as a settlement in 1106. It was in the possession of the counts of Leiningen-Dagsburg-Landeck, whose arms, differenced by an escutcheon of the Imperial eagle, served as the arms of Landau until 1955. The town was granted a charter in 1274 by King Rudolf I of Germany, who declared the town a Free Imperial Town in 1291; nevertheless Prince-Bishop Emich of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spherical Coordinates
In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the ''radial distance'' of that point from a fixed origin, its ''polar angle'' measured from a fixed zenith direction, and the ''azimuthal angle'' of its orthogonal projection on a reference plane that passes through the origin and is orthogonal to the zenith, measured from a fixed reference direction on that plane. It can be seen as the three-dimensional version of the polar coordinate system. The radial distance is also called the ''radius'' or ''radial coordinate''. The polar angle may be called '' colatitude'', ''zenith angle'', '' normal angle'', or ''inclination angle''. When radius is fixed, the two angular coordinates make a coordinate system on the sphere sometimes called spherical polar coordinates. The use of symbols and the order of the coordinates differs among sources and disciplines. This article will us ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Navier–Stokes Equations
In physics, the Navier–Stokes equations ( ) are partial differential equations which describe the motion of viscous fluid substances, named after French engineer and physicist Claude-Louis Navier and Anglo-Irish physicist and mathematician George Gabriel Stokes. They were developed over several decades of progressively building the theories, from 1822 (Navier) to 1842–1850 (Stokes). The Navier–Stokes equations mathematically express conservation of momentum and conservation of mass for Newtonian fluids. They are sometimes accompanied by an equation of state relating pressure, temperature and density. They arise from applying Isaac Newton's second law to fluid motion, together with the assumption that the stress in the fluid is the sum of a diffusing viscous term (proportional to the gradient of velocity) and a pressure term—hence describing ''viscous flow''. The difference between them and the closely related Euler equations is that Navier–Stokes equations take ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Riccati Equation
In mathematics, a Riccati equation in the narrowest sense is any first-order ordinary differential equation that is quadratic in the unknown function. In other words, it is an equation of the form : y'(x) = q_0(x) + q_1(x) \, y(x) + q_2(x) \, y^2(x) where q_0(x) \neq 0 and q_2(x) \neq 0. If q_0(x) = 0 the equation reduces to a Bernoulli equation, while if q_2(x) = 0 the equation becomes a first order linear ordinary differential equation. The equation is named after Jacopo Riccati (1676–1754). More generally, the term Riccati equation is used to refer to matrix equations with an analogous quadratic term, which occur in both continuous-time and discrete-time linear-quadratic-Gaussian control. The steady-state (non-dynamic) version of these is referred to as the algebraic Riccati equation. Conversion to a second order linear equation The non-linear Riccati equation can always be converted to a second order linear ordinary differential equation (ODE): If :y'=q_0(x) + q_ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stream Function
The stream function is defined for incompressible flow, incompressible (divergence-free) fluid flow, flows in two dimensions – as well as in three dimensions with axisymmetry. The flow velocity components can be expressed as the derivatives of the scalar field, scalar stream function. The stream function can be used to plot Streamlines, streaklines, and pathlines, streamlines, which represent the trajectories of particles in a steady flow. The two-dimensional Lagrange stream function was introduced by Joseph Louis Lagrange in 1781. The Stokes stream function is for axisymmetrical three-dimensional flow, and is named after George Gabriel Stokes. Considering the particular case of fluid dynamics, the difference between the stream function values at any two points gives the volumetric flow rate (or volumetric flux) through a line connecting the two points. Since streamlines are tangent to the flow velocity vector of the flow, the value of the stream function must be constant along ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schlichting Jet
Schlichting jet is a steady, laminar, round jet, emerging into a stationary fluid of the same kind with very high Reynolds number. The problem was formulated and solved by Hermann Schlichting in 1933, who also formulated the corresponding planar Bickley jet problem in the same paper. The Landau-Squire jet from a point source is an exact solution of Navier-Stokes equations, which is valid for all Reynolds number, reduces to Schlichting jet solution at high Reynolds number, for distances far away from the jet origin. Flow description Consider an axisymmetric jet emerging from an orifice, located at the origin of a cylindrical polar coordinates (r,x), with x being the jet axis and r being the radial distance from the axis of symmetry. Since the jet is in constant pressure, the momentum flux in the x direction is constant and equal to the momentum flux at the origin, :J=2\pi\rho \int_0^\infty ru^2 d r = \text, where \rho is the constant density, (v,u) are the velocity components in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
