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Helmholtz's Theorems
In fluid mechanics, Helmholtz's theorems, named after Hermann von Helmholtz, describe the three-dimensional motion of fluid in the vicinity of vortex lines. These theorems apply to inviscid flows and flows where the influence of viscous forces are small and can be ignored. Helmholtz's three theorems are as follows: ;Helmholtz's first theorem: :The strength of a vortex line is constant along its length. ;Helmholtz's second theorem: :A vortex line cannot end in a fluid; it must extend to the boundaries of the fluid or form a closed path. ;Helmholtz's third theorem: :A fluid element that is initially irrotational remains irrotational. Helmholtz's theorems apply to inviscid flows. In observations of vortices in real fluids the strength of the vortices always decays gradually due to the dissipative effect of viscous forces. Alternative expressions of the three theorems are as follows: # The strength of a vortex tube does not vary with time. # Fluid elements lying on a vortex line at so ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fluid Mechanics
Fluid mechanics is the branch of physics concerned with the mechanics of fluids ( liquids, gases, and plasmas) and the forces on them. It has applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical and biomedical engineering, geophysics, oceanography, meteorology, astrophysics, and biology. It can be divided into fluid statics, the study of fluids at rest; and fluid dynamics, the study of the effect of forces on fluid motion. It is a branch of continuum mechanics, a subject which models matter without using the information that it is made out of atoms; that is, it models matter from a ''macroscopic'' viewpoint rather than from ''microscopic''. Fluid mechanics, especially fluid dynamics, is an active field of research, typically mathematically complex. Many problems are partly or wholly unsolved and are best addressed by numerical methods, typically using computers. A modern discipline, called computational fluid dynamics (CFD), is dev ... [...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 the result o ... [...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] |
Aerodynamics
Aerodynamics, from grc, ἀήρ ''aero'' (air) + grc, δυναμική (dynamics), is the study of the motion of air, particularly when affected by a solid object, such as an airplane wing. It involves topics covered in the field of fluid dynamics and its subfield of gas dynamics. The term ''aerodynamics'' is often used synonymously with gas dynamics, the difference being that "gas dynamics" applies to the study of the motion of all gases, and is not limited to air. The formal study of aerodynamics began in the modern sense in the eighteenth century, although observations of fundamental concepts such as aerodynamic drag were recorded much earlier. Most of the early efforts in aerodynamics were directed toward achieving Aircraft#Heavier than air – aerodynes, heavier-than-air flight, which was first demonstrated by Otto Lilienthal in 1891. Since then, the use of aerodynamics through mathematical analysis, empirical approximations, wind tunnel experimentation, and computer simu ... [...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 a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philip Saffman
Philip Geoffrey Saffman FRS (19 March 1931 – 17 August 2008) was a mathematician and the Theodore von Kármán Professor of Applied Mathematics and Aeronautics at the California Institute of Technology.. Education and early life Saffman was born to a Jewish family in Leeds, England, and educated at Roundhay Grammar School and Trinity College, Cambridge which he entered aged 15. He received his Bachelor of Arts degree in 1953, studied for Part III of the Cambridge Mathematical Tripos in 1954 and was awarded his PhD in 1956 for research supervised by George Batchelor. Career and research Saffman started his academic career as a lecturer at the University of Cambridge, then joined King's College London as a Reader. Saffman joined the Caltech faculty in 1964 and was named the Theodore von Kármán Professor in 1995. According to Dan Meiron, Saffman "really was one of the leading figures in fluid mechanics," and he influenced almost every subfield of that discipline. He is known ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kelvin's Circulation Theorem
In fluid mechanics, Kelvin's circulation theorem (named after William Thomson, 1st Baron Kelvin who published it in 1869) states:In a barotropic, ideal fluid with conservative body forces, the circulation around a closed curve (which encloses the same fluid elements) moving with the fluid remains constant with time. Stated mathematically: :\frac = 0 where \Gamma is the circulation around a material contour C(t). Stated more simply, this theorem says that if one observes a closed contour at one instant, and follows the contour over time (by following the motion of all of its fluid elements), the circulation over the two locations of this contour are equal. This theorem does not hold in cases with viscous stresses, nonconservative body forces (for example the Coriolis force) or non-barotropic pressure-density relations. Mathematical proof The circulation \Gamma around a closed material contour C(t) is defined by: :\Gamma(t) = \oint_C \boldsymbol \cdot \mathrm\boldsymbol where ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wingtip Vortices
Wingtip vortices are circular patterns of rotating air left behind a wing as it generates lift.Clancy, L.J., ''Aerodynamics'', section 5.14 One wingtip vortex trails from the tip of each wing. Wingtip vortices are sometimes named ''trailing'' or ''lift-induced vortices'' because they also occur at points other than at the wing tips. Indeed, vorticity is trailed at any point on the wing where the lift varies span-wise (a fact described and quantified by the lifting-line theory); it eventually rolls up into large vortices near the wingtip, at the edge of flap devices, or at other abrupt changes in wing planform. Wingtip vortices are associated with induced drag, the imparting of downwash, and are a fundamental consequence of three-dimensional lift generation. Careful selection of wing geometry (in particular, wingspan), as well as of cruise conditions, are design and operational methods to minimize induced drag. Wingtip vortices form the primary component of wake turbulence. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Horseshoe Vortex
The horseshoe vortex model is a simplified representation of the vortex system present in the flow of air around a wing. This vortex system is modelled by the ''bound vortex'' (bound to the wing) and two '' trailing vortices'', therefore having a shape vaguely reminiscent of a horseshoe. A starting vortex is shed as the wing begins to move through the fluid, which dissipates under the action of viscosity, as do the trailing vortices far behind the aircraft. The downwash is associated with induced drag and is a component of the system of trailing vortices. The horseshoe vortex model is unrealistic in that it implies uniform circulation (and hence, according to the Kutta–Joukowski theorem, uniform lift) at all sections on the wingspan. In a more realistic model, the lifting-line theory, the vortex strength varies along the wingspan, and the loss in vortex strength is shed as a vortex ''sheet'' all along the trailing edge, rather than as a single trail at the wing-tips. Neverthe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Starting Vortex
In fluid dynamics, the starting vortex is a vortex which forms in the air adjacent to the trailing edge of an airfoil as it is accelerated from rest. It leaves the airfoil (which now has an equal but opposite "bound vortex" around it), and remains (nearly) stationary in the flow. It rapidly decays through the action of viscosity. The initial (and quite brief) presence of a starting vortex as an airfoil begins to move was predicted by early aerodynamicists, and eventually photographed. Whenever the speed or angle of attack of an airfoil changes there is a corresponding amount of vorticity deposited in the wake behind the airfoil, joining the two trailing vortices. This vorticity is a continuum of mini-starting-vortexes. The wake behind an aircraft is a continuous sheet of weak vorticity, between the two trailing vortices, and this accounts for the changes in strength of the trailing vortices as the airspeed of the aircraft and angle of attack on the wing change during fli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lift (force)
A fluid flowing around an object exerts a force on it. Lift is the component of this force that is perpendicular to the oncoming flow direction. It contrasts with the drag force, which is the component of the force parallel to the flow direction. Lift conventionally acts in an upward direction in order to counter the force of gravity, but it can act in any direction at right angles to the flow. If the surrounding fluid is air, the force is called an aerodynamic force. In water or any other liquid, it is called a hydrodynamic force. Dynamic lift is distinguished from other kinds of lift in fluids. Aerostatic lift or buoyancy, in which an internal fluid is lighter than the surrounding fluid, does not require movement and is used by balloons, blimps, dirigibles, boats, and submarines. Planing lift, in which only the lower portion of the body is immersed in a liquid flow, is used by motorboats, surfboards, windsurfers, sailboats, and water-skis. Overview A fluid flowing arou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hermann Von Helmholtz
Hermann Ludwig Ferdinand von Helmholtz (31 August 1821 – 8 September 1894) was a German physicist and physician who made significant contributions in several scientific fields, particularly hydrodynamic stability. The Helmholtz Association, the largest German association of research institutions, is named in his honor. In the fields of physiology and psychology, Helmholtz is known for his mathematics concerning the eye, theories of vision, ideas on the visual perception of space, color vision research, the sensation of tone, perceptions of sound, and empiricism in the physiology of perception. In physics, he is known for his theories on the conservation of energy, work in electrodynamics, chemical thermodynamics, and on a mechanical foundation of thermodynamics. As a philosopher, he is known for his philosophy of science, ideas on the relation between the laws of perception and the laws of nature, the science of aesthetics, and ideas on the civilizing power of science. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
