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Jeffery–Hamel Flow
In fluid dynamics Jeffery–Hamel flow is a flow created by a converging or diverging channel with a source or sink of fluid volume at the point of intersection of the two plane walls. It is named after George Barker Jeffery(1915) and Georg Hamel(1917), but it has subsequently been studied by many major scientists such as von Kármán and Levi-Civita, Walter Tollmien, F. Noether, W.R. Dean, Rosenhead, Louis Rosenhead "The steady two-dimensional radial flow of viscous fluid between two inclined plane walls." Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. Vol. 175. No. 963. The Royal Society, 1940. Landau,Lev Landau, and E. M. Lifshitz. "Fluid Mechanics Pergamon." New York 61 (1959). G.K. Batchelor etc. A complete set of solutions was described by Edward Fraenkel in 1962. Flow description Consider two stationary plane walls with a constant volume flow rate Q is injected/sucked at the point of intersection of plane walls and let ... [...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 a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
No-slip Condition
In fluid dynamics, the no-slip condition for viscous fluids assumes that at a solid boundary, the fluid will have zero velocity relative to the boundary. The fluid velocity at all fluid–solid boundaries is equal to that of the solid boundary. Conceptually, one can think of the outermost molecules of fluid as stuck to the surfaces past which it flows. Because the solution is prescribed at given locations, this is an example of a Dirichlet boundary condition. Physical justification Particles close to a surface do not move along with a flow when adhesion is stronger than cohesion. At the fluid-solid interface, the force of attraction between the fluid particles and solid particles (Adhesive forces) is greater than that between the fluid particles (Cohesive forces). This force imbalance brings down the fluid velocity to zero. The no slip condition is only defined for viscous flows and where continuum concept is valid. Exceptions As with most of the engineering approximations, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Potential Theory
In mathematics and mathematical physics, potential theory is the study of harmonic functions. The term "potential theory" was coined in 19th-century physics when it was realized that two fundamental forces of nature known at the time, namely gravity and the electrostatic force, could be modeled using functions called the gravitational potential and electrostatic potential, both of which satisfy Poisson's equation—or in the vacuum, Laplace's equation. There is considerable overlap between potential theory and the theory of Poisson's equation to the extent that it is impossible to draw a distinction between these two fields. The difference is more one of emphasis than subject matter and rests on the following distinction: potential theory focuses on the properties of the functions as opposed to the properties of the equation. For example, a result about the singularities of harmonic functions would be said to belong to potential theory whilst a result on how the solution dep ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complete Elliptic Integral Of The Second Kind
In integral calculus, an elliptic integral is one of a number of related functions defined as the value of certain integrals, which were first studied by Giulio Fagnano and Leonhard Euler (). Their name originates from their originally arising in connection with the problem of finding the arc length of an ellipse. Modern mathematics defines an "elliptic integral" as any function which can be expressed in the form f(x) = \int_^ R \left(t, \sqrt \right) \, dt, where is a rational function of its two arguments, is a polynomial of degree 3 or 4 with no repeated roots, and is a constant. In general, integrals in this form cannot be expressed in terms of elementary functions. Exceptions to this general rule are when has repeated roots, or when contains no odd powers of or if the integral is pseudo-elliptic. However, with the appropriate reduction formula, every elliptic integral can be brought into a form that involves integrals over rational functions and the three ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complete Elliptic Integral Of The First Kind
In integral calculus, an elliptic integral is one of a number of related functions defined as the value of certain integrals, which were first studied by Giulio Fagnano and Leonhard Euler (). Their name originates from their originally arising in connection with the problem of finding the arc length of an ellipse. Modern mathematics defines an "elliptic integral" as any function which can be expressed in the form f(x) = \int_^ R \left(t, \sqrt \right) \, dt, where is a rational function of its two arguments, is a polynomial of degree 3 or 4 with no repeated roots, and is a constant. In general, integrals in this form cannot be expressed in terms of elementary functions. Exceptions to this general rule are when has repeated roots, or when contains no odd powers of or if the integral is pseudo-elliptic. However, with the appropriate reduction formula, every elliptic integral can be brought into a form that involves integrals over rational functions and the three Lege ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jacobi Elliptic Functions
In mathematics, the Jacobi elliptic functions are a set of basic elliptic functions. They are found in the description of the motion of a pendulum (see also pendulum (mathematics)), as well as in the design of electronic elliptic filters. While trigonometric functions are defined with reference to a circle, the Jacobi elliptic functions are a generalization which refer to other conic sections, the ellipse in particular. The relation to trigonometric functions is contained in the notation, for example, by the matching notation \operatorname for \sin. The Jacobi elliptic functions are used more often in practical problems than the Weierstrass elliptic functions as they do not require notions of complex analysis to be defined and/or understood. They were introduced by . Carl Friedrich Gauss had already studied special Jacobi elliptic functions in 1797, the lemniscate elliptic functions in particular, but his work was published much later. Overview There are twelve Jacobi elliptic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harold Jeffreys
Sir Harold Jeffreys, FRS (22 April 1891 – 18 March 1989) was a British mathematician, statistician, geophysicist, and astronomer. His book, ''Theory of Probability'', which was first published in 1939, played an important role in the revival of the objective Bayesian view of probability. Education Jeffreys was born in Fatfield, County Durham, England, the son of Robert Hal Jeffreys, headmaster of Fatfield Church School, and his wife, Elizabeth Mary Sharpe, a school teacher. He was educated at his father's school then studied at Armstrong College in Newcastle upon Tyne Newcastle upon Tyne ( RP: , ), or simply Newcastle, is a city and metropolitan borough in Tyne and Wear, England. The city is located on the River Tyne's northern bank and forms the largest part of the Tyneside built-up area. Newcastle is a ..., then part of the Durham University, University of Durham, and with the University of London External Programme. Career Jeffreys became a fellow of St John ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Norman Riley (professor)
Norman Riley is an Emeritus Professor of Applied Mathematics at the University of East Anglia in Norwich (UK). Biography Following High School education at Calder High School, Mytholmroyd he read Mathematics at Manchester University graduating with first class honours in 1956, followed by a PhD in 1959. Norman Riley served for one year as an Assistant Lecturer at Manchester University and then spent four years as a lecturer at Durham University before he joined the then new University of East Anglia in 1964, the year that saw the first significant intake of students to the university. Promotion to Reader in 1966 was followed by promotion to a Personal Chair in 1971. He retired in 1999. Married in 1959 he has one son and one daughter. Research contributions His research contributions in the field of fluid mechanics, over five decades, have included: unsteady flows with application to acoustic levitation and the loading on the submerged horizontal pontoons of tethered leg platf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philip Drazin
Philip Gerald Drazin (25 May 1934 – 10 January 2002) was a British mathematician and a leading international expert in fluid dynamics. He completed his PhD at the University of Cambridge under G. I. Taylor in 1958. He was awarded the Smith's Prize in 1957. After leaving Cambridge, he spent two years at MIT before moving to the University of Bristol, where he stayed and became a Professor until retiring in 1999. After retiring, he lectured at the University of Oxford and the University of Bath until his death in 2002. Drazin worked on hydrodynamic stability and the transition to turbulence. His 1974 paper ''On a model of instability of a slowly-varying flow'' introduced the concept of a global mode solution to a system of partial differential equations such as the Navier-Stokes equations. He also worked on solitons. In 1998 he was awarded the Symons Gold Medal of the Royal Meteorological Society. References External links Philip Gerald Drazinat the Mathematics Genealogy Pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elliptic Functions
In the mathematical field of complex analysis, elliptic functions are a special kind of meromorphic functions, that satisfy two periodicity conditions. They are named elliptic functions because they come from elliptic integrals. Originally those integrals occurred at the calculation of the arc length of an ellipse. Important elliptic functions are Jacobi elliptic functions and the Weierstrass \wp-function. Further development of this theory led to hyperelliptic functions and modular forms. Definition A meromorphic function is called an elliptic function, if there are two \mathbb- linear independent complex numbers \omega_1,\omega_2\in\mathbb such that : f(z + \omega_1) = f(z) and f(z + \omega_2) = f(z), \quad \forall z\in\mathbb. So elliptic functions have two periods and are therefore also called ''doubly periodic''. Period lattice and fundamental domain Iff is an elliptic function with periods \omega_1,\omega_2 it also holds that : f(z+\gamma)=f(z) for every li ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reynolds Number
In fluid mechanics, the Reynolds number () is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between inertial and viscous forces. At low Reynolds numbers, flows tend to be dominated by laminar (sheet-like) flow, while at high Reynolds numbers flows tend to be turbulent. The turbulence results from differences in the fluid's speed and direction, which may sometimes intersect or even move counter to the overall direction of the flow (eddy currents). These eddy currents begin to churn the flow, using up energy in the process, which for liquids increases the chances of cavitation. The Reynolds number has wide applications, ranging from liquid flow in a pipe to the passage of air over an aircraft wing. It is used to predict the transition from laminar to turbulent flow and is used in the scaling of similar but different-sized flow situations, such as between an aircraft model in a wind tunnel and the full-size ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gerald B
Gerald is a male Germanic given name meaning "rule of the spear" from the prefix ''ger-'' ("spear") and suffix ''-wald'' ("rule"). Variants include the English given name Jerrold, the feminine nickname Jeri and the Welsh language Gerallt and Irish language Gearalt. Gerald is less common as a surname. The name is also found in French as Gérald. Geraldine is the feminine equivalent. Given name People with the name Gerald include: Politicians * Gerald Boland, Ireland's longest-serving Minister for Justice * Gerald Ford, 38th President of the United States * Gerald Gardiner, Baron Gardiner, Lord Chancellor from 1964 to 1970 * Gerald Häfner, German MEP * Gerald Klug, Austrian politician * Gerald Lascelles (other), several people * Gerald Nabarro, British Conservative politician * Gerald S. McGowan, US Ambassador to Portugal * Gerald Wellesley, 7th Duke of Wellington, British diplomat, soldier, and architect Sports * Gerald Asamoah, Ghanaian-born German footba ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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