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D'Alembert's Paradox
In fluid dynamics, d'Alembert's paradox (or the hydrodynamic paradox) is a contradiction reached in 1752 by French mathematician Jean le Rond d'Alembert. D'Alembert proved that – for incompressible and inviscid potential flow – the drag force is zero on a body moving with constant velocity relative to the fluid.Grimberg, Pauls & Frisch (2008). Zero drag is in direct contradiction to the observation of substantial drag on bodies moving relative to fluids, such as air and water; especially at high velocities corresponding with high Reynolds numbers. It is a particular example of the reversibility paradox. D’Alembert, working on a 1749 Prize Problem of the Berlin Academy on flow drag, concluded: ''"It seems to me that the theory (potential flow), developed in all possible rigor, gives, at least in several cases, a strictly vanishing resistance, a singular paradox which I leave to future Geometers .e. mathematicians - the two terms were used interchangeably at that timeto e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alembert
Alembert and its variants may refer to: People: *Jean le Rond d'Alembert (1717–1783), French mathematician, mechanician, physicist, philosopher, and music theorist *Sandy D'Alemberte (1933–2019), American lawyer and politician Places: *D'Alembert (crater), a lunar impact crater Mathematics and Physics: *d'Alembert's formula, a mathematical formula *d'Alembert's paradox, a statement concerning inviscid flow *d'Alembert's principle, a statement of the fundamental classical laws of motion *d'Alembert–Euler condition, a mathematical and physical condition *D'Alembert operator, an operator of the Einstein equation *Ratio test, also known as d'Alembert's test, a test for the convergence of a series {{disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scientific Consensus
Scientific consensus is the generally held judgment, position, and opinion of the majority or the supermajority of scientists in a particular field of study at any particular time. Consensus is achieved through scholarly communication at conferences, the publication process, replication of reproducible results by others, scholarly debate, and peer review. A conference meant to create a consensus is termed as a consensus conference. Such measures lead to a situation in which those within the discipline can often recognize such a consensus where it exists; however, communicating to outsiders that consensus has been reached can be difficult, because the "normal" debates through which science progresses may appear to outsiders as contestation. On occasion, scientific institutes issue position statements intended to communicate a summary of the science from the "inside" to the "outside" of the scientific community, or consensus review articles or surveys may be published. In cases ... [...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 advective inertial forces are small compared with 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, sperm and the flow of lava. In technology, it occurs in paint, 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 differential equations. The primary Green's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
George Gabriel Stokes
Sir George Gabriel Stokes, 1st Baronet, (; 13 August 1819 – 1 February 1903) was an Irish English physicist and mathematician. Born in County Sligo, Ireland, Stokes spent all of his career at the University of Cambridge, where he was the Lucasian Professor of Mathematics from 1849 until his death in 1903. As a physicist, Stokes made seminal contributions to fluid mechanics, including the Navier–Stokes equations; and to physical optics, with notable works on polarization and fluorescence. As a mathematician, he popularised "Stokes' theorem" in vector calculus and contributed to the theory of asymptotic expansions. Stokes, along with Felix Hoppe-Seyler, first demonstrated the oxygen transport function of hemoglobin and showed color changes produced by aeration of hemoglobin solutions. Stokes was made a baronet by the British monarch in 1889. In 1893 he received the Royal Society's Copley Medal, then the most prestigious scientific prize in the world, "for his researches and d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adhémar Jean Claude Barré De Saint-Venant
Adhémar Jean Claude Barré de Saint-Venant (23 August 1797 – 6 January 1886) was a mechanician and mathematician who contributed to early stress analysis and also developed the unsteady open channel flow shallow water equations, also known as the Saint-Venant equations that are a fundamental set of equations used in modern hydraulic engineering. The one-dimensional Saint-Venant equation is a commonly used simplification of the shallow water equations. Although his full surname was Barré de Saint-Venant in mathematical literature other than French he is known as Saint-Venant. His name is also associated with Saint-Venant's principle of statically equivalent systems of load, Saint-Venant's theorem and for Saint-Venant's compatibility condition, the integrability conditions for a symmetric tensor field to be a strain. In 1843 he published the correct derivation of the Navier–Stokes equations for a viscous flow and was the first to "properly identify the coefficient of viscosity ... [...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] |
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] |
Form Drag
Parasitic drag, also known as profile drag, is a type of aerodynamic drag that acts on any object when the object is moving through a fluid. Parasitic drag is a combination of form drag and skin friction drag. It affects all objects regardless of whether they are capable of generating lift. Total drag on an aircraft is made up of parasitic drag and lift-induced drag. Parasitic drag comprises all types of drag except lift-induced drag. Form drag Form drag arises because of the shape of the object. The general size and shape of the body are the most important factors in form drag; bodies with a larger presented cross-section will have a higher drag than thinner bodies; sleek ("streamlined") objects have lower form drag. Form drag follows the drag equation, meaning that it increases with the square of the velocity, and thus becomes more important for high-speed aircraft. Form drag depends on the longitudinal section of the body. A prudent choice of body profile is essential for a l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wake (physics)
In fluid dynamics, a wake may either be: * the region of recirculating flow immediately behind a moving or stationary blunt body, caused by viscosity, which may be accompanied by flow separation and turbulence, or * the wave pattern on the water surface downstream of an object in a flow, or produced by a moving object (e.g. a ship), caused by density differences of the fluids above and below the free surface and gravity (or surface tension). Viscosity The wake is the region of disturbed flow (often turbulent) downstream of a solid body moving through a fluid, caused by the flow of the fluid around the body. For a blunt body in subsonic external flow, for example the Apollo or Orion capsules during descent and landing, the wake is massively separated and behind the body is a reverse flow region where the flow is moving toward the body. This phenomenon is often observed in wind tunnel testing of aircraft, and is especially important when parachute systems are involved, becau ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flow Separation
In fluid dynamics, flow separation or boundary layer separation is the detachment of a boundary layer from a surface into a wake. A boundary layer exists whenever there is relative movement between a fluid and a solid surface with viscous forces present in the layer of fluid close to the surface. The flow can be externally, around a body, or internally, in an enclosed passage. Boundary layers can be either laminar or turbulent. A reasonable assessment of whether the boundary layer will be laminar or turbulent can be made by calculating the Reynolds number of the local flow conditions. Separation occurs in flow that is slowing down, with pressure increasing, after passing the thickest part of a streamline body or passing through a widening passage, for example. Flowing against an increasing pressure is known as flowing in an adverse pressure gradient. The boundary layer separates when it has travelled far enough in an adverse pressure gradient that the speed of the bound ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bluff Body
In fluid dynamics, the drag coefficient (commonly denoted as: c_\mathrm, c_x or c_) is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment, such as air or water. It is used in the drag equation in which a lower drag coefficient indicates the object will have less aerodynamic or hydrodynamic drag. The drag coefficient is always associated with a particular surface area. The drag coefficient of any object comprises the effects of the two basic contributors to fluid dynamic drag: skin friction and form drag. The drag coefficient of a lifting airfoil or hydrofoil also includes the effects of lift-induced drag. The drag coefficient of a complete structure such as an aircraft also includes the effects of interference drag. Definition The drag coefficient c_\mathrm d is defined as c_\mathrm d = \dfrac where: * F_\mathrm d is the drag force, which is by definition the force component in the direction of the flow velocity; * \ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Skin Friction
Skin friction drag is a type of aerodynamic or hydrodynamic drag, which is resistant force exerted on an object moving in a fluid. Skin friction drag is caused by the viscosity of fluids and is developed from laminar drag to turbulent drag as a fluid moves on the surface of an object. Skin friction drag is generally expressed in terms of the Reynolds number, which is the ratio between inertial force and viscous force. Total drag can be decomposed into a skin friction drag component and a pressure drag component, where pressure drag includes all other sources of drag including lift-induced drag. In this conceptualisation, lift-induced drag is an artificial abstraction, part of the horizontal component of the aerodynamic reaction force. Alternatively, total drag can be decomposed into a parasitic drag component and a lift-induced drag component, where parasitic drag is all components of drag except lift-induced drag. In this conceptualisation, skin friction drag is a component of pa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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