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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 equat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Claude-Louis Navier
Claude-Louis Navier (born Claude Louis Marie Henri Navier; ; 10 February 1785 – 21 August 1836) was a French mechanical engineer, affiliated with the French government, and a physicist who specialized in continuum mechanics. The Navier–Stokes equations refer eponymously to him, with George Gabriel Stokes. Biography After the death of his father in 1793, Navier's mother left his education in the hands of his uncle Émiland Gauthey, an engineer with the Corps of Bridges and Roads ''(Corps des Ponts et Chaussées)''. In 1802, Navier enrolled at the École polytechnique, and in 1804 continued his studies at the École Nationale des Ponts et Chaussées, from which he graduated in 1806. He eventually succeeded his uncle as ''Inspecteur general'' at the Corps des Ponts et Chaussées. He directed the construction of bridges at Choisy, Asnières and Argenteuil in the Department of the Seine, and built a footbridge to the Île de la Cité in Paris. His 1824 design for th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gradient
In vector calculus, the gradient of a scalar-valued differentiable function of several variables is the vector field (or vector-valued function) \nabla f whose value at a point p is the "direction and rate of fastest increase". If the gradient of a function is non-zero at a point , the direction of the gradient is the direction in which the function increases most quickly from , and the magnitude of the gradient is the rate of increase in that direction, the greatest absolute directional derivative. Further, a point where the gradient is the zero vector is known as a stationary point. The gradient thus plays a fundamental role in optimization theory, where it is used to maximize a function by gradient ascent. In coordinate-free terms, the gradient of a function f(\bf) may be defined by: :df=\nabla f \cdot d\bf where ''df'' is the total infinitesimal change in ''f'' for an infinitesimal displacement d\bf, and is seen to be maximal when d\bf is in the direction of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Existence Theorem
In mathematics, an existence theorem is a theorem which asserts the existence of a certain object. It might be a statement which begins with the phrase " there exist(s)", or it might be a universal statement whose last quantifier is existential (e.g., "for all , , ... there exist(s) ..."). In the formal terms of symbolic logic, an existence theorem is a theorem with a prenex normal form involving the existential quantifier, even though in practice, such theorems are usually stated in standard mathematical language. For example, the statement that the sine function is continuous everywhere, or any theorem written in big O notation, can be considered as theorems which are existential by nature—since the quantification can be found in the definitions of the concepts used. A controversy that goes back to the early twentieth century concerns the issue of purely theoretic existence theorems, that is, theorems which depend on non-constructive foundational material such as the axi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magnetohydrodynamics
Magnetohydrodynamics (MHD; also called magneto-fluid dynamics or hydromagnetics) is the study of the magnetic properties and behaviour of electrically conducting fluids. Examples of such magnetofluids include plasmas, liquid metals, salt water, and electrolytes. The word ''magnetohydrodynamics'' is derived from ' meaning magnetic field, ' meaning water, and ' meaning movement. The field of MHD was initiated by Hannes Alfvén, for which he received the Nobel Prize in Physics in 1970. The fundamental concept behind MHD is that magnetic fields can induce currents in a moving conductive fluid, which in turn polarizes the fluid and reciprocally changes the magnetic field itself. The set of equations that describe MHD are a combination of the Navier–Stokes equations of fluid dynamics and Maxwell’s equations of electromagnetism. These differential equations must be solved simultaneously, either analytically or numerically. History The first r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maxwell's Equations
Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. The equations provide a mathematical model for electric, optical, and radio technologies, such as power generation, electric motors, wireless communication, lenses, radar etc. They describe how electric field, electric and magnetic fields are generated by electric charge, charges, electric current, currents, and changes of the fields.''Electric'' and ''magnetic'' fields, according to the theory of relativity, are the components of a single electromagnetic field. The equations are named after the physicist and mathematician James Clerk Maxwell, who, in 1861 and 1862, published an early form of the equations that included the Lorentz force law. Maxwell first used the equations to propose that light is an electromagnetic phenomenon. The modern f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Airfoil
An airfoil (American English) or aerofoil (British English) is the cross-sectional shape of an object whose motion through a gas is capable of generating significant lift, such as a wing, a sail, or the blades of propeller, rotor, or turbine. A solid body moving through a fluid produces an aerodynamic force. The component of this force perpendicular to the relative freestream velocity is called lift. The component parallel to the relative freestream velocity is called drag. An airfoil is a streamlined shape that is capable of generating significantly more lift than drag. Airfoils can be designed for use at different speeds by modifying their geometry: those for subsonic flight generally have a rounded leading edge, while those designed for supersonic flight tend to be slimmer with a sharp leading edge. All have a sharp trailing edge. Foils of similar function designed with water as the working fluid are called hydrofoils. The lift on an airfoil is primarily th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flow Conditioning
Flow conditioning ensures that the “real world” environment closely resembles the “ laboratory” environment for proper performance of inferential flowmeters like orifice, turbine, coriolis, ultrasonic etc. Types of flow Basically, Flow in pipes can be classified as follows – * Fully developed flow (found in world-class flow laboratories) * Pseudo-fully developed flow * Non-swirling, non-symmetrical flow * Moderate swirling, non-symmetrical flow * High swirling, symmetrical flow Types of flow conditioners Flow conditioners shown in fig.(a) can be grouped into following three types – * Those that eliminate swirl only (tube bundles) * Those that eliminate swirl and non-symmetry, but do not produce pseudo fully developed flow * Those that eliminate swirl and non-symmetry and produce pseudo fully developed flow (high-performance flow conditioners) Straightening devices such as honeycombs and vanes inserted upstream of the flow meter can reduce the length of strai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ocean Current
An ocean current is a continuous, directed movement of sea water generated by a number of forces acting upon the water, including wind, the Coriolis effect, breaking waves, cabbeling, and temperature and salinity differences. Depth contours, shoreline configurations, and interactions with other currents influence a current's direction and strength. Ocean currents are primarily horizontal water movements. An ocean current flows for great distances and together they create the global conveyor belt, which plays a dominant role in determining the climate of many of Earth’s regions. More specifically, ocean currents influence the temperature of the regions through which they travel. For example, warm currents traveling along more temperate coasts increase the temperature of the area by warming the sea breezes that blow over them. Perhaps the most striking example is the Gulf Stream, which makes northwest Europe much more temperate for its high latitude compared to other ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Model (abstract)
A conceptual model is a representation of a system. It consists of concepts used to help people know, understand, or simulate a subject the model represents. In contrast, physical models are physical object such as a toy model that may be assembled and made to work like the object it represents. The term may refer to models that are formed after a conceptualization or generalization process. Conceptual models are often abstractions of things in the real world, whether physical or social. Semantic studies are relevant to various stages of concept formation. Semantics is basically about concepts, the meaning that thinking beings give to various elements of their experience. Overview Models of concepts and models that are conceptual The term ''conceptual model'' is normal. It could mean "a model of concept" or it could mean "a model that is conceptual." A distinction can be made between ''what models are'' and ''what models are made of''. With the exception of iconic m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Engineering
Engineering is the use of scientific method, scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad range of more specialized List of engineering branches, fields of engineering, each with a more specific emphasis on particular areas of applied mathematics, applied science, and types of application. See glossary of engineering. The term ''engineering'' is derived from the Latin ''ingenium'', meaning "cleverness" and ''ingeniare'', meaning "to contrive, devise". Definition The American Engineers' Council for Professional Development (ECPD, the predecessor of Accreditation Board for Engineering and Technology, ABET) has defined "engineering" as: The creative application of scientific principles to design or develop structures, machines, apparatus, or manufacturing processes, or works utilizing them singly or in combination; or to construct o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scientific
Science is a systematic endeavor that builds and organizes knowledge in the form of testable explanations and predictions about the universe. Science may be as old as the human species, and some of the earliest archeological evidence for scientific reasoning is tens of thousands of years old. The earliest written records in the history of science come from Ancient Egypt and Mesopotamia in around 3000 to 1200 BCE. Their contributions to mathematics, astronomy, and medicine entered and shaped Greek natural philosophy of classical antiquity, whereby formal attempts were made to provide explanations of events in the physical world based on natural causes. After the fall of the Western Roman Empire, knowledge of Greek conceptions of the world deteriorated in Western Europe during the early centuries (400 to 1000 CE) of the Middle Ages, but was preserved in the Muslim world during the Islamic Golden Age and later by the efforts of Byzantine Greek scholars who br ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Completely Integrable
In mathematics, integrability is a property of certain dynamical systems. While there are several distinct formal definitions, informally speaking, an integrable system is a dynamical system with sufficiently many conserved quantities, or first integrals, such that its behaviour has far fewer degrees of freedom than the dimensionality of its phase space; that is, its evolution is restricted to a submanifold within its phase space. Three features are often referred to as characterizing integrable systems: * the existence of a ''maximal'' set of conserved quantities (the usual defining property of complete integrability) * the existence of algebraic invariants, having a basis in algebraic geometry (a property known sometimes as algebraic integrability) * the explicit determination of solutions in an explicit functional form (not an intrinsic property, but something often referred to as solvability) Integrable systems may be seen as very different in qualitative character from more ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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