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Taylor Scraping Flow
In fluid dynamics, Taylor scraping flow is a type of two-dimensional corner flow occurring when one of the wall is sliding over the other with constant velocity, named after G. I. Taylor. Flow description Consider a plane wall located at \theta=0 in the cylindrical coordinates (r,\theta), moving with a constant velocity U towards the left. Consider another plane wall(scraper), at an inclined position, making an angle \alpha from the positive x direction and let the point of intersection be at r=0. This description is equivalent to moving the scraper towards right with velocity U. The problem is singular at r=0 because at the origin, the velocities are discontinuous, thus the velocity gradient is infinite there. Taylor noticed that the inertial terms are negligible as long as the region of interest is within r\ll\nu/U( or, equivalently Reynolds number Re = Ur/\nu \ll 1), thus within the region the flow is essentially a Stokes flow. For example, George Batchelor gives a typical val ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fluid Dynamics
In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases. It has several subdisciplines, including (the study of air and other gases in motion) and (the study of water and other liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moment (physics), moments on aircraft, determining the mass flow rate of petroleum through pipeline transport, pipelines, weather forecasting, predicting weather patterns, understanding nebulae in interstellar space, understanding large scale Geophysical fluid dynamics, geophysical flows involving oceans/atmosphere and Nuclear weapon design, 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 fl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Corner Flow
Corner may refer to: People * Corner (surname) * House of Cornaro, a noble Venetian family (''Corner'' in Venetian dialect) Places * Corner, Alabama, a community in the United States *Corner Inlet, Victoria, Australia * Corner River, a tributary of Harricana River, in Ontario, Canada * Corner Township, Custer County, Nebraska, a township in the United States Arts, entertainment, and media Music * ''The Corner'' (album), an album by the Hieroglyphics * "The Corner" (song), a 2005 song by Common * "Corner", a song by Allie Moss from her 2009 EP ''Passerby'' * "Corner", a song by Blue Stahli from their 2010 album '' Blue Stahli'' * "The Corner", a song by Dermot Kennedy from his 2019 album '' Without Fear'' * "The Corner", a song by Rodney Atkins from his 2011 album '' Take a Back Road'' * "The Corner", a song by Staind from their 2008 album '' The Illusion of Progress'' Other uses in arts, entertainment, and media * Corner painters, a Danish artists association * ''The Corner'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reynolds Number
In fluid dynamics, the Reynolds number () is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between Inertia, inertial and viscous forces. At low Reynolds numbers, flows tend to be dominated by laminar flow, laminar (sheet-like) flow, while at high Reynolds numbers, flows tend to be turbulence, 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 (fluid dynamics), 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–turbulent transition, laminar to turbulent flow and is used in the scaling of similar but different-sized fl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stokes Flow
Stokes flow (named after George Gabriel Stokes), also named creeping flow or creeping motion,Kim, S. & Karrila, S. J. (2005) ''Microhydrodynamics: Principles and Selected Applications'', Dover. . is a type of fluid flow where advection, advective inertial forces are small compared with Viscosity, viscous forces. The Reynolds number is low, i.e. \mathrm \ll 1. This is a typical situation in flows where the fluid velocities are very slow, the viscosities are very large, or the length-scales of the flow are very small. Creeping flow was first studied to understand lubrication. In nature, this type of flow occurs in the swimming of microorganisms and sperm. In technology, it occurs in paint, Microelectromechanical systems, MEMS devices, and in the flow of viscous polymers generally. The equations of motion for Stokes flow, called the Stokes equations, are a linearization of the Navier–Stokes equations, and thus can be solved by a number of well-known methods for linear different ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
George Batchelor
George Keith Batchelor FRS (8 March 1920 – 30 March 2000) was an Australian applied mathematician and fluid dynamicist. He was for many years a professor of applied mathematics in the University of Cambridge, and was founding head of the Department of Applied Mathematics and Theoretical Physics (DAMTP). In 1956 he founded the influential ''Journal of Fluid Mechanics'' which he edited for some forty years. Prior to Cambridge he studied at Melbourne High School and University of Melbourne. As an applied mathematician (and for some years at Cambridge a co-worker with Sir Geoffrey Taylor in the field of turbulent flow), he was a keen advocate of the need for physical understanding and sound experimental basis. His ''An Introduction to Fluid Dynamics'' (CUP, 1967) is still considered a classic of the subject, and has been re-issued in the ''Cambridge Mathematical Library'' series, following strong current demand. Unusual for an 'elementary' textbook of that era, it presented ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stream Function
In fluid dynamics, two types of stream function (or streamfunction) are defined: * The two-dimensional (or Lagrange) stream function, introduced by Joseph Louis Lagrange in 1781, is defined for incompressible flow, incompressible (divergence-free), two-dimensional fluid flow, flows. * The Stokes stream function, named after George Gabriel Stokes, is defined for incompressible, three-dimensional flows with axisymmetry. The properties of stream functions make them useful for analyzing and graphically illustrating flows. The remainder of this article describes the two-dimensional stream function. Two-dimensional stream function Assumptions The two-dimensional stream function is based on the following assumptions: * The flow field can be described as two-dimensional plane flow, with velocity vector : \quad \mathbf = \begin u (x,y,t) \\ v (x,y,t) \\ 0 \end. * The velocity satisfies the continuity equation for incompressible flow: : \quad \nabla \cdot \mathbf = 0. * The domain h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Separation Of Variables
In mathematics, separation of variables (also known as the Fourier method) is any of several methods for solving ordinary differential equation, ordinary and partial differential equations, in which algebra allows one to rewrite an equation so that each of two variables occurs on a different side of the equation. Ordinary differential equations (ODE) A differential equation for the unknown f(x) is separable if it can be written in the form :\frac f(x) = g(x)h(f(x)) where g and h are given functions. This is perhaps more transparent when written using y = f(x) as: :\frac=g(x)h(y). So now as long as ''h''(''y'') ≠ 0, we can rearrange terms to obtain: : = g(x) \, dx, where the two variables ''x'' and ''y'' have been separated. Note ''dx'' (and ''dy'') can be viewed, at a simple level, as just a convenient notation, which provides a handy mnemonic aid for assisting with manipulations. A formal definition of ''dx'' as a differential (infinitesimal) is somewhat advanced. Al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Taylor
Taylor, Taylors or Taylor's may refer to: People * Taylor (surname) ** List of people with surname Taylor * Taylor (given name), including Tayla and Taylah * Taylor sept, a branch of Scottish clan Cameron * Justice Taylor (other) Places Australia * Electoral district of Taylor, South Australia * Taylor, Australian Capital Territory, planned suburb Canada * Taylor, British Columbia United States * Taylor, Alabama * Taylor, Arizona * Taylor, Arkansas * Taylor, Indiana * Taylor, Louisiana * Taylor, Maryland * Taylor, Michigan * Taylor, Mississippi * Taylor, Missouri * Taylor, Nebraska * Taylor, North Dakota * Taylor, New York * Taylor, Beckham County, Oklahoma * Taylor, Cotton County, Oklahoma * Taylor, Pennsylvania * Taylors, South Carolina * Taylor, Texas * Taylor, Utah * Taylor, Washington * Taylor, West Virginia * Taylor, Wisconsin * Taylor, Wyoming * Taylor County (other) * Taylor Township (other) Businesses and organisations ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wilhelm Schneider (engineer)
Wilhelm Schneider (born May 3, 1938) is an Austrian scientist and a specialist in fluid mechanics. He is an is Emeritus Professor of at TU Wien. Biography and research Wilhelm Schneider was born in Vienna, Austria in 1938. He graduated with a doctors' degree from TU Wien in 1963. He then worked at the DFVLR till 1968 and then at the Jet Propulsion Laboratory for a year and then joined the DFVLR in 1969. He moved to TU Wien in 1973 and became an emeritus professor in 2006. His research contributions are significant in many areas of fluid mechanics and related areas including supersonic and hypersonic flows, radiation gas dynamics, waves in fluids, jets, plumes & shear layers, convection flows, condensation, evaporation, fluidization, electric arcs and other topics. He became the corresponding member of the Austrian Academy of Sciences in 1989 and a full member in 1995. He also served as the chairman of the academy form 2002 to 2006. He is the recipient of many awards including ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Self-similar Solution
In mathematics, a self-similar object is exactly or approximately similar to a part of itself (i.e., the whole has the same shape as one or more of the parts). Many objects in the real world, such as coastlines, are statistically self-similar: parts of them show the same statistical properties at many scales. Self-similarity is a typical property of fractals. Scale invariance is an exact form of self-similarity where at any magnification there is a smaller piece of the object that is similar to the whole. For instance, a side of the Koch snowflake is both symmetrical and scale-invariant; it can be continually magnified 3x without changing shape. The non-trivial similarity evident in fractals is distinguished by their fine structure, or detail on arbitrarily small scales. As a counterexample, whereas any portion of a straight line may resemble the whole, further detail is not revealed. Peitgen ''et al.'' explain the concept as such: Since mathematically, a fractal may show s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Power-law Fluid
In continuum mechanics, a power-law fluid, or the Ostwald–de Waele relationship, is a type of generalized Newtonian fluid. This mathematical relationship is useful because of its simplicity, but only approximately describes the behaviour of a real non-Newtonian fluid. Power-law fluids can be subdivided into three different types of fluids based on the value of their flow behaviour index: pseudoplastic, Newtonian fluid, and dilatant. A first-order fluid is another name for a power-law fluid with exponential dependence of viscosity on temperature. As a Newtonian fluid in a circular pipe give a quadratic velocity profile, a power-law fluid will result in a power-law velocity profile. Description In continuum mechanics, a power-law fluid, or the Ostwald–de Waele relationship, is a type of generalized Newtonian fluid (time-independent non-Newtonian fluid) for which the shear stress, , is given by :\tau = K \left( \frac \right)^n where: * is the ''flow consistency index'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
