. . . . . . . . . . . . "Th\u00E9orie des \u00E9coulements \u00E0 potentiel de vitesse"@fr . . . "En dynamique des fluides, un \u00E9coulement est potentiel lorsque son champ des vitesses v est le gradient d'une fonction scalaire, le potentiel des vitesses \u03C6 : Puisque le rotationnel d'un gradient est toujours \u00E9gal \u00E0 z\u00E9ro, un \u00E9coulement potentiel est toujours irrotationnel : Si l'\u00E9coulement est incompressible, la divergence de v est \u00E9gale \u00E0 z\u00E9ro : Le potentiel des vitesses \u03C6 est alors une solution de l'\u00E9quation de Laplace : o\u00F9 est le Laplacien, ou l'op\u00E9rateur laplacien, parfois aussi not\u00E9 . \n* Portail de la physique"@fr . . . . . . . . . . "\u0633\u0631\u064A\u0627\u0646 \u0643\u0627\u0645\u0646"@ar . . . . "La teor\u00EDa de flujo potencial pretende describir el comportamiento cinem\u00E1tico de los fluidos bas\u00E1ndose en el concepto matem\u00E1tico de funci\u00F3n potencial, asegurando que el campo de velocidades (que es un campo vectorial) del flujo de un fluido es igual al gradiente de una funci\u00F3n potencial que determina el movimiento de dicho fluido: donde el campo de velocidades queda definido como El signo menos en la ecuaci\u00F3n de arriba es s\u00F3lo una convenci\u00F3n de signos sobre la definici\u00F3n de . Puede definirse sin el signo menos, y la formulaci\u00F3n que se obtendr\u00EDa ser\u00EDa la misma. A un fluido que se comporta seg\u00FAn esta teor\u00EDa se le denomina fluido potencial, que da lugar a un flujo potencial. Una de las primeras personas en aplicar esta formulaci\u00F3n para el flujo de un fluido fue D'Alembert. Estudi\u00F3 la fuerza de resistencia producida por un flujo de fluido sobre un cuerpo que se opon\u00EDa a este en dos dimensiones cuando la soluci\u00F3n a este problema era completamente desconocida y Newton, a pesar de haberlo estudiado, no hab\u00EDa llegado a conclusiones satisfactorias. D'Alembert defini\u00F3 la funci\u00F3n de corriente, , para describir la trayectoria que tuviera cada part\u00EDcula de un fluido a trav\u00E9s del tiempo. Esta funci\u00F3n corriente est\u00E1 determinada, en el plano, por dos variables espaciales y para cada valor de la igualdad determina un lugar geom\u00E9trico llamado l\u00EDnea de corriente."@es . "Conformal power one.svg"@en . . . . . . . . . "Conformal power two third.svg"@en . . . . . . . . . . . "Examples of conformal maps for the power law"@en . . . "\u00C9coulement potentiel"@fr . . . . . "In fluid dynamics, potential flow (or ideal flow) describes the velocity field as the gradient of a scalar function: the velocity potential. As a result, a potential flow is characterized by an irrotational velocity field, which is a valid approximation for several applications. The irrotationality of a potential flow is due to the curl of the gradient of a scalar always being equal to zero. In the case of an incompressible flow the velocity potential satisfies Laplace's equation, and potential theory is applicable. However, potential flows also have been used to describe compressible flows. The potential flow approach occurs in the modeling of both stationary as well as nonstationary flows.Applications of potential flow are for instance: the outer flow field for aerofoils, water waves, electroosmotic flow, and groundwater flow. For flows (or parts thereof) with strong vorticity effects, the potential flow approximation is not applicable."@en . "Potentialstr\u00F6mung"@de . "vertical"@en . "\u041F\u043E\u0442\u0435\u043D\u0446\u0438\u0430\u0301\u043B\u044C\u043D\u043E\u0435 \u0442\u0435\u0447\u0435\u0301\u043D\u0438\u0435 \u2014 \u0431\u0435\u0437\u0432\u0438\u0445\u0440\u0435\u0432\u043E\u0435 \u0434\u0432\u0438\u0436\u0435\u043D\u0438\u0435 \u0436\u0438\u0434\u043A\u043E\u0441\u0442\u0438 \u0438\u043B\u0438 \u0433\u0430\u0437\u0430, \u043F\u0440\u0438 \u043A\u043E\u0442\u043E\u0440\u043E\u043C \u0434\u0435\u0444\u043E\u0440\u043C\u0430\u0446\u0438\u044F \u0438 \u043F\u0435\u0440\u0435\u043C\u0435\u0449\u0435\u043D\u0438\u0435 \u043C\u0430\u043B\u043E\u0433\u043E \u043E\u0431\u044A\u0451\u043C\u0430 \u0436\u0438\u0434\u043A\u043E\u0441\u0442\u0438 \u043F\u0440\u043E\u0438\u0441\u0445\u043E\u0434\u0438\u0442 \u0431\u0435\u0437 \u0432\u0440\u0430\u0449\u0435\u043D\u0438\u044F (\u0432\u0438\u0445\u0440\u044F). \u041F\u0440\u0438 \u043F\u043E\u0442\u0435\u043D\u0446\u0438\u0430\u043B\u044C\u043D\u043E\u043C \u0442\u0435\u0447\u0435\u043D\u0438\u0438 \u0441\u043A\u043E\u0440\u043E\u0441\u0442\u044C \u0436\u0438\u0434\u043A\u043E\u0441\u0442\u0438 \u043C\u043E\u0436\u0435\u0442 \u0431\u044B\u0442\u044C \u043F\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043B\u0435\u043D\u0430 \u0441\u043B\u0435\u0434\u0443\u044E\u0449\u0438\u043C \u043E\u0431\u0440\u0430\u0437\u043E\u043C: \u0433\u0434\u0435 \u2014 \u043D\u0435\u043A\u043E\u0442\u043E\u0440\u0430\u044F \u0441\u043A\u0430\u043B\u044F\u0440\u043D\u0430\u044F \u0444\u0443\u043D\u043A\u0446\u0438\u044F, \u043D\u0430\u0437\u044B\u0432\u0430\u0435\u043C\u0430\u044F \u043F\u043E\u0442\u0435\u043D\u0446\u0438\u0430\u043B\u043E\u043C \u0441\u043A\u043E\u0440\u043E\u0441\u0442\u0438 \u0442\u0435\u0447\u0435\u043D\u0438\u044F. \u0414\u0432\u0438\u0436\u0435\u043D\u0438\u0435 \u0440\u0435\u0430\u043B\u044C\u043D\u044B\u0445 \u0436\u0438\u0434\u043A\u043E\u0441\u0442\u0435\u0439 \u0431\u0443\u0434\u0435\u0442 \u043F\u043E\u0442\u0435\u043D\u0446\u0438\u0430\u043B\u044C\u043D\u044B\u043C \u0432 \u0442\u0435\u0445 \u043E\u0431\u043B\u0430\u0441\u0442\u044F\u0445, \u0433\u0434\u0435 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0435 \u0441\u0438\u043B \u0432\u044F\u0437\u043A\u043E\u0441\u0442\u0438 \u043D\u0438\u0447\u0442\u043E\u0436\u043D\u043E \u043C\u0430\u043B\u043E \u043F\u043E \u0441\u0440\u0430\u0432\u043D\u0435\u043D\u0438\u044E \u0441 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0435\u043C \u0441\u0438\u043B \u0434\u0430\u0432\u043B\u0435\u043D\u0438\u044F \u0438 \u0432 \u043A\u043E\u0442\u043E\u0440\u044B\u0445 \u043D\u0435\u0442 \u0437\u0430\u0432\u0438\u0445\u0440\u0435\u043D\u0438\u0439, \u043E\u0431\u0440\u0430\u0437\u043E\u0432\u0430\u0432\u0448\u0438\u0445\u0441\u044F \u0437\u0430 \u0441\u0447\u0451\u0442 \u0441\u0440\u044B\u0432\u0430 \u0441\u043E \u0441\u0442\u0435\u043D\u043E\u043A \u043F\u043E\u0433\u0440\u0430\u043D\u0438\u0447\u043D\u043E\u0433\u043E \u0441\u043B\u043E\u044F \u0438\u043B\u0438 \u0437\u0430 \u0441\u0447\u0451\u0442 \u043D\u0435\u0440\u0430\u0432\u043D\u043E\u043C\u0435\u0440\u043D\u043E\u0433\u043E \u043D\u0430\u0433\u0440\u0435\u0432\u0430\u043D\u0438\u044F. \u041D\u0435\u043E\u0431\u0445\u043E\u0434\u0438\u043C\u044B\u043C \u0438 \u0434\u043E\u0441\u0442\u0430\u0442\u043E\u0447\u043D\u044B\u043C \u0443\u0441\u043B\u043E\u0432\u0438\u0435\u043C \u043F\u043E\u0442\u0435\u043D\u0446\u0438\u0430\u043B\u044C\u043D\u043E\u0441\u0442\u0438 \u0442\u0435\u0447\u0435\u043D\u0438\u044F \u044F\u0432\u043B\u044F\u044E\u0442\u0441\u044F \u0440\u0430\u0432\u0435\u043D\u0441\u0442\u0432\u0430: \u0412 \u0434\u0432\u0443\u043C\u0435\u0440\u043D\u043E\u043C \u0441\u043B\u0443\u0447\u0430\u0435 \u043F\u043E\u0442\u0435\u043D\u0446\u0438\u0430\u043B\u044C\u043D\u043E\u0435 \u0442\u0435\u0447\u0435\u043D\u0438\u0435 \u043F\u043E\u043B\u043D\u043E\u0441\u0442\u044C\u044E \u043E\u043F\u0438\u0441\u044B\u0432\u0430\u0435\u0442\u0441\u044F \u043A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u044B\u043C \u043F\u043E\u0442\u0435\u043D\u0446\u0438\u0430\u043B\u043E\u043C."@ru . "\u041F\u043E\u0442\u0435\u043D\u0446\u0438\u0430\u043B\u044C\u043D\u043E\u0435 \u0442\u0435\u0447\u0435\u043D\u0438\u0435"@ru . . . . . . "En dynamique des fluides, un \u00E9coulement est potentiel lorsque son champ des vitesses v est le gradient d'une fonction scalaire, le potentiel des vitesses \u03C6 : Puisque le rotationnel d'un gradient est toujours \u00E9gal \u00E0 z\u00E9ro, un \u00E9coulement potentiel est toujours irrotationnel : Les \u00E9coulements potentiels servent le plus souvent \u00E0 d\u00E9crire des \u00E9coulements de fluides parfaits, c'est-\u00E0-dire des \u00E9coulements o\u00F9 la viscosit\u00E9 peut \u00EAtre n\u00E9glig\u00E9e, parce qu'un \u00E9coulement irrotationnel le reste tant que la viscosit\u00E9 est n\u00E9gligeable (\u00E9quation d'Euler avec l'hypoth\u00E8se que le champ de forces ext\u00E9rieures d\u00E9rive d'un potentiel). Si l'\u00E9coulement est incompressible, la divergence de v est \u00E9gale \u00E0 z\u00E9ro : Le potentiel des vitesses \u03C6 est alors une solution de l'\u00E9quation de Laplace : o\u00F9 est le Laplacien, ou l'op\u00E9rateur laplacien, parfois aussi not\u00E9 . A deux dimensions, les \u00E9quations des \u00E9coulements potentiels sont tr\u00E8s simples et peuvent \u00EAtre \u00E9tudi\u00E9es avec les outils de l'analyse complexe. \n* Portail de la physique"@fr . . . . "Conformal power minus one.svg"@en . "\u4F4D\u6D41"@zh . . . . . . . . . . . . . . . . "La teor\u00EDa de flujo potencial pretende describir el comportamiento cinem\u00E1tico de los fluidos bas\u00E1ndose en el concepto matem\u00E1tico de funci\u00F3n potencial, asegurando que el campo de velocidades (que es un campo vectorial) del flujo de un fluido es igual al gradiente de una funci\u00F3n potencial que determina el movimiento de dicho fluido: donde el campo de velocidades queda definido como"@es . . . "For a steady inviscid flow, the Euler equations \u2014 for the mass and momentum density \u2014 are, in subscript notation and in non-conservation form:\n:\n\nwhile using the summation convention: since occurs more than once in the term on the left hand side of the momentum equation, is summed over all its components . Further:\n* is the fluid density,\n* is the pressure,\n* are the coordinates and\n* are the corresponding components of the velocity vector .\n\nThe speed of sound squared is equal to the derivative of the pressure with respect to the density , at constant entropy :\n\n:\n\nAs a result, the flow equations can be written as:\n\n:\n\nMultiplying the momentum equation with , and using the mass equation to eliminate the density gradient gives:\n\n:\n\nWhen divided by , and with all terms on one side of the equation, the compressible flow equation is:\n\n:\n\nNote that until this stage, no assumptions have been made regarding the flow .\n\nNow, for irrotational flow the velocity is the gradient of the velocity potential , and the local Mach number components are defined as:\n\n:\n\nWhen used in the flow equation, the full potential equation results:\n\n:\n\nWritten out in components, the form given at the beginning of this section is obtained. When a specific equation of state is provided, relating pressure and density , the speed of sound can be determined. Subsequently, together with adequate boundary conditions, the full potential equation can be solved ."@en . "\u0627\u0644\u0633\u0631\u064A\u0627\u0646 \u0627\u0644\u0643\u0627\u0645\u0646 \u0647\u0648 \u0627\u0644\u0633\u0631\u064A\u0627\u0646 \u0627\u0644\u0645\u0648\u0627\u0626\u0639 \u0627\u0644\u062E\u0627\u0644\u064A \u0645\u0646 \u0627\u0644\u062F\u0648\u0627\u0645\u064A\u0629 \u0648\u0627\u0644\u0644\u0632\u0648\u062C\u0629. \u0648\u064A\u062A\u0645 \u062D\u0644\u0647\u0627 \u0628\u0627\u0633\u062A\u062E\u062F\u0627\u0645 \u0645\u0639\u0627\u062F\u0644\u0627\u062A \u0644\u0627\u0628\u0644\u0627\u0633."@ar . . . "\u041F\u043E\u0442\u0435\u043D\u0446\u0438\u0430\u0301\u043B\u044C\u043D\u043E\u0435 \u0442\u0435\u0447\u0435\u0301\u043D\u0438\u0435 \u2014 \u0431\u0435\u0437\u0432\u0438\u0445\u0440\u0435\u0432\u043E\u0435 \u0434\u0432\u0438\u0436\u0435\u043D\u0438\u0435 \u0436\u0438\u0434\u043A\u043E\u0441\u0442\u0438 \u0438\u043B\u0438 \u0433\u0430\u0437\u0430, \u043F\u0440\u0438 \u043A\u043E\u0442\u043E\u0440\u043E\u043C \u0434\u0435\u0444\u043E\u0440\u043C\u0430\u0446\u0438\u044F \u0438 \u043F\u0435\u0440\u0435\u043C\u0435\u0449\u0435\u043D\u0438\u0435 \u043C\u0430\u043B\u043E\u0433\u043E \u043E\u0431\u044A\u0451\u043C\u0430 \u0436\u0438\u0434\u043A\u043E\u0441\u0442\u0438 \u043F\u0440\u043E\u0438\u0441\u0445\u043E\u0434\u0438\u0442 \u0431\u0435\u0437 \u0432\u0440\u0430\u0449\u0435\u043D\u0438\u044F (\u0432\u0438\u0445\u0440\u044F). \u041F\u0440\u0438 \u043F\u043E\u0442\u0435\u043D\u0446\u0438\u0430\u043B\u044C\u043D\u043E\u043C \u0442\u0435\u0447\u0435\u043D\u0438\u0438 \u0441\u043A\u043E\u0440\u043E\u0441\u0442\u044C \u0436\u0438\u0434\u043A\u043E\u0441\u0442\u0438 \u043C\u043E\u0436\u0435\u0442 \u0431\u044B\u0442\u044C \u043F\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043B\u0435\u043D\u0430 \u0441\u043B\u0435\u0434\u0443\u044E\u0449\u0438\u043C \u043E\u0431\u0440\u0430\u0437\u043E\u043C: \u0412 \u0434\u0432\u0443\u043C\u0435\u0440\u043D\u043E\u043C \u0441\u043B\u0443\u0447\u0430\u0435 \u043F\u043E\u0442\u0435\u043D\u0446\u0438\u0430\u043B\u044C\u043D\u043E\u0435 \u0442\u0435\u0447\u0435\u043D\u0438\u0435 \u043F\u043E\u043B\u043D\u043E\u0441\u0442\u044C\u044E \u043E\u043F\u0438\u0441\u044B\u0432\u0430\u0435\u0442\u0441\u044F \u043A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u044B\u043C \u043F\u043E\u0442\u0435\u043D\u0446\u0438\u0430\u043B\u043E\u043C."@ru . . . . "Friktionsfri str\u00F6mning inom str\u00F6mningsmekanik \u00E4r ett fl\u00F6de d\u00E4r fluidens viskositet \u00E4r lika med noll och d\u00E4rmed \u00E4r friktionen i fluiden f\u00F6rsumbar."@sv . . "En m\u00E9canique des fluides, la th\u00E9orie des \u00E9coulements \u00E0 potentiel de vitesse est une th\u00E9orie des \u00E9coulements de fluide o\u00F9 la viscosit\u00E9 est n\u00E9glig\u00E9e. Elle est tr\u00E8s employ\u00E9e en hydrodynamique. La th\u00E9orie se propose de r\u00E9soudre les \u00E9quations de Navier-Stokes dans les conditions suivantes : \n* l'\u00E9coulement est stationnaire \n* le fluide n'est pas visqueux \n* il n'y a pas d'action externe (flux de chaleur, \u00E9lectromagn\u00E9tisme, gravit\u00E9 ...)"@fr . . . "Die Str\u00F6mung eines Fluids (Fl\u00FCssigkeit oder Gas) ist eine Potentialstr\u00F6mung, wenn das Vektorfeld der Geschwindigkeiten mathematisch so geartet ist, dass es ein Potential besitzt. Das Potential kann man sich anschaulich als die H\u00F6he in einer Reliefkarte vorstellen, wo dann die Richtung der gr\u00F6\u00DFten Steigung in einem Punkt der dortigen Geschwindigkeit entspricht. Ein solches Potential ist in einem homogenen Fluid vorhanden, wenn die Str\u00F6mung rotationsfrei (wirbel- bzw. vortizit\u00E4tsfrei) ist und keine Z\u00E4higkeitskr\u00E4fte (Reibungskr\u00E4fte) auftreten oder diese vernachl\u00E4ssigbar klein sind. Jede aus der Ruhe heraus beginnende Str\u00F6mung eines homogenen, viskosit\u00E4tsfreien Fluids besitzt ein solches Potential."@de . "\u5728\u6D41\u9AD4\u52D5\u529B\u5B78\u4E2D\uFF0C\u4F4D\u6D41\uFF08Potential Flow\uFF09\u662F\u6307\u4E00\u9053\u662F\u4E00\u7D14\u91CF\u51FD\u6578\uFF08\u5373\u901F\u5EA6\u4F4D\uFF09\u7684\u68AF\u5EA6\u7684\u6D41\u3002\u56E0\u6B64\uFF0C\u4F4D\u6D41\u7684\u7279\u9EDE\u662F\u7121\u65CB\u6027\u901F\u5EA6\u5834\uFF0C\u9019\u662F\u5C0D\u65BC\u5E7E\u7A2E\u61C9\u7528\u7684\u6709\u6548\u8FD1\u4F3C\u3002\u4F4D\u6D41\u7684\u7121\u65CB\u6027\u662F\u56E0\u70BA\u68AF\u5EA6\u7684\u65CB\u5EA6\u59CB\u7D42\u70BA\u96F6\u7684\u95DC\u4FC2\u3002 \u5728\u4E0D\u53EF\u58D3\u7E2E\u6D41\u7684\u985E\u578B\u4E2D\uFF0C\u4F4D\u6D41\u6EFF\u8DB3\u62C9\u666E\u62C9\u65AF\u65B9\u7A0B\u8207\u3002\u7136\u800C\uFF0C\u4F4D\u6D41\u4E5F\u53EF\u7528\u4F86\u63CF\u8FF0\u53EF\u58D3\u7E2E\u6D41\u3002\u4F4D\u6D41\u8FD1\u4F3C\u767C\u751F\u65BC\u7A69\u6D41\u8207\u975E\u7A69\u6D41\u7684\u6A21\u578B\u4E0A\u3002 \u4F4D\u6D41\u61C9\u7528\u65BC\uFF1A\u7FFC\u578B\u3001\u6D77\u6D6A\u3001\u96FB\u6EF2\u6D41\u8207\u7684\u5916\u90E8\u6D41\u5834\u3002\u5C0D\u65BC\u6709\u5F37\u5927\u6E26\u6548\u61C9\u7684\u6D41\uFF0C\u4F4D\u6D41\u8FD1\u4F3C\u4E26\u4E0D\u9069\u7528\u3002"@zh . . "\u5728\u6D41\u9AD4\u52D5\u529B\u5B78\u4E2D\uFF0C\u4F4D\u6D41\uFF08Potential Flow\uFF09\u662F\u6307\u4E00\u9053\u662F\u4E00\u7D14\u91CF\u51FD\u6578\uFF08\u5373\u901F\u5EA6\u4F4D\uFF09\u7684\u68AF\u5EA6\u7684\u6D41\u3002\u56E0\u6B64\uFF0C\u4F4D\u6D41\u7684\u7279\u9EDE\u662F\u7121\u65CB\u6027\u901F\u5EA6\u5834\uFF0C\u9019\u662F\u5C0D\u65BC\u5E7E\u7A2E\u61C9\u7528\u7684\u6709\u6548\u8FD1\u4F3C\u3002\u4F4D\u6D41\u7684\u7121\u65CB\u6027\u662F\u56E0\u70BA\u68AF\u5EA6\u7684\u65CB\u5EA6\u59CB\u7D42\u70BA\u96F6\u7684\u95DC\u4FC2\u3002 \u5728\u4E0D\u53EF\u58D3\u7E2E\u6D41\u7684\u985E\u578B\u4E2D\uFF0C\u4F4D\u6D41\u6EFF\u8DB3\u62C9\u666E\u62C9\u65AF\u65B9\u7A0B\u8207\u3002\u7136\u800C\uFF0C\u4F4D\u6D41\u4E5F\u53EF\u7528\u4F86\u63CF\u8FF0\u53EF\u58D3\u7E2E\u6D41\u3002\u4F4D\u6D41\u8FD1\u4F3C\u767C\u751F\u65BC\u7A69\u6D41\u8207\u975E\u7A69\u6D41\u7684\u6A21\u578B\u4E0A\u3002 \u4F4D\u6D41\u61C9\u7528\u65BC\uFF1A\u7FFC\u578B\u3001\u6D77\u6D6A\u3001\u96FB\u6EF2\u6D41\u8207\u7684\u5916\u90E8\u6D41\u5834\u3002\u5C0D\u65BC\u6709\u5F37\u5927\u6E26\u6548\u61C9\u7684\u6D41\uFF0C\u4F4D\u6D41\u8FD1\u4F3C\u4E26\u4E0D\u9069\u7528\u3002"@zh . "\uD3EC\uD150\uC15C \uC720\uB3D9"@ko . . . . . . . . . . . . . . . "En m\u00E9canique des fluides, la th\u00E9orie des \u00E9coulements \u00E0 potentiel de vitesse est une th\u00E9orie des \u00E9coulements de fluide o\u00F9 la viscosit\u00E9 est n\u00E9glig\u00E9e. Elle est tr\u00E8s employ\u00E9e en hydrodynamique. La th\u00E9orie se propose de r\u00E9soudre les \u00E9quations de Navier-Stokes dans les conditions suivantes : \n* l'\u00E9coulement est stationnaire \n* le fluide n'est pas visqueux \n* il n'y a pas d'action externe (flux de chaleur, \u00E9lectromagn\u00E9tisme, gravit\u00E9 ...)"@fr . . . . . . "Conformal power two.svg"@en . . . . . "Examples of conformal maps for the power law , for different values of the power . Shown is the -plane, showing lines of constant potential and streamfunction , while ."@en . . . "Die Str\u00F6mung eines Fluids (Fl\u00FCssigkeit oder Gas) ist eine Potentialstr\u00F6mung, wenn das Vektorfeld der Geschwindigkeiten mathematisch so geartet ist, dass es ein Potential besitzt. Das Potential kann man sich anschaulich als die H\u00F6he in einer Reliefkarte vorstellen, wo dann die Richtung der gr\u00F6\u00DFten Steigung in einem Punkt der dortigen Geschwindigkeit entspricht. Ein solches Potential ist in einem homogenen Fluid vorhanden, wenn die Str\u00F6mung rotationsfrei (wirbel- bzw. vortizit\u00E4tsfrei) ist und keine Z\u00E4higkeitskr\u00E4fte (Reibungskr\u00E4fte) auftreten oder diese vernachl\u00E4ssigbar klein sind. Jede aus der Ruhe heraus beginnende Str\u00F6mung eines homogenen, viskosit\u00E4tsfreien Fluids besitzt ein solches Potential. Eine Potentialstr\u00F6mung ist der rotationsfreie Spezialfall der Str\u00F6mung eines homogenen, viskosit\u00E4tsfreien Fluids, das durch die Euler\u2019schen Gleichungen beschrieben wird; diese gelten auch f\u00FCr Str\u00F6mungen mit Rotation (Wirbelstr\u00F6mung). Wenn jedoch bei Scherbewegungen die Z\u00E4higkeit ber\u00FCcksichtigt werden muss, wie z. B. in Grenzschichten oder im Zentrum eines Wirbels, so ist mit den Navier-Stokes-Gleichungen zu rechnen. Potentialstr\u00F6mungen k\u00F6nnen als sehr gute N\u00E4herung von laminaren Str\u00F6mungen bei niedrigen Reynolds-Zahlen verwendet werden, wenn die fluiddynamische Grenzschicht an den R\u00E4ndern der Str\u00F6mung keine wesentliche Rolle spielt. In der station\u00E4ren Potentialstr\u00F6mung inkompressibler Fluide gilt die bernoullische Druckgleichung global, die technische Rohrstr\u00F6mungen gut beschreibt. Wegen ihrer einfachen Berechenbarkeit werden Potentialstr\u00F6mungen auch als Anfangsn\u00E4herung bei der iterativen Berechnung der Navier-Stokes-Gleichungen in der numerischen Str\u00F6mungsmechanik verwendet."@de . . . . "In fluid dynamics, potential flow (or ideal flow) describes the velocity field as the gradient of a scalar function: the velocity potential. As a result, a potential flow is characterized by an irrotational velocity field, which is a valid approximation for several applications. The irrotationality of a potential flow is due to the curl of the gradient of a scalar always being equal to zero."@en . . . "58320"^^ . . "In fluidodinamica, la teoria del flusso potenziale descrive il campo della velocit\u00E0 come gradiente di una funzione scalare detta potenziale. Di conseguenza, un flusso potenziale \u00E8 caratterizzato da un campo di velocit\u00E0 irrotazionale, il quale \u00E8 una valida approssimazione per diverse applicazioni, sia in condizioni stazionarie che non stazionarie. L'irrotazionalit\u00E0 di un flusso potenziale \u00E8 dovuta al fatto che il rotore di un gradiente \u00E8 sempre nullo. Nel caso di un flusso incomprimibile (in molti testi tecnici \u00E8 riportata anche la dizione incompressibile), il potenziale soddisfa l'equazione di Laplace. D'altra parte la teoria potenziale \u00E8 stata anche impiegata per descrivere flussi compressibili. L'approccio pu\u00F2 inoltre modellare sia flussi stazionari che instazionari. Applicazioni della schematizzazione di flusso potenziale sono ad esempio: flussi esterni su superfici aerodinamiche, onde marine e flussi di falde acquifere. Per flussi (o zone di flusso) con marcati effetti vorticosi, l'approssimazione di flusso potenziale non \u00E8 applicabile."@it . "Teor\u00EDa de flujo potencial"@es . . . . . . . . . . "In de stromingsleer is een stroming in een snelheidsveld een potentiaalstroming, als dat veld een potentiaal heeft. De stroming is dande gradi\u00EBnt van de snelheidspotentiaal, een scalaire functie. Omdat de rotatie van een gradi\u00EBnt altijd nul is, zijn potentiaalstromingen rotatievrij, hetgeen voor verschillende toepassingen een geoorloofde benadering is."@nl . . "\uD3EC\uD150\uC15C \uC720\uB3D9(potential\u6D41\u52D5,potential flow)\uC740 \uC804\uAE30 \uB610\uB294 \uC804\uC790\uACF5\uD559 \uBC0F \uC720\uCCB4 \uB3D9\uC5ED\uD559\uC5D0\uC11C \uC810\uC131\uC774 \uC5C6\uB294 \uC644\uC804 \uC720\uCCB4(\uC774\uC0C1\uC720\uCCB4)\uC758 \uD750\uB984\uC744 \uAC00\uB9AC\uD0A8\uB2E4. \uB9F4\uB3CC\uC774\uAC00 \uC5C6\uB294 \uD750\uB984\uC73C\uB85C, \uACC4\uC0B0\uACFC \uC774\uD574\uAC00 \uC27D\uB2E4\uACE0 \uC54C\uB824\uC838\uC788\uB2E4."@ko . . . "Conformal power one and a half.svg"@en . "250"^^ . . . . "\u0627\u0644\u0633\u0631\u064A\u0627\u0646 \u0627\u0644\u0643\u0627\u0645\u0646 \u0647\u0648 \u0627\u0644\u0633\u0631\u064A\u0627\u0646 \u0627\u0644\u0645\u0648\u0627\u0626\u0639 \u0627\u0644\u062E\u0627\u0644\u064A \u0645\u0646 \u0627\u0644\u062F\u0648\u0627\u0645\u064A\u0629 \u0648\u0627\u0644\u0644\u0632\u0648\u062C\u0629. \u0648\u064A\u062A\u0645 \u062D\u0644\u0647\u0627 \u0628\u0627\u0633\u062A\u062E\u062F\u0627\u0645 \u0645\u0639\u0627\u062F\u0644\u0627\u062A \u0644\u0627\u0628\u0644\u0627\u0633."@ar . . . . "Conformal power three.svg"@en . . "Friktionsfri str\u00F6mning"@sv . "We shall begin with mass conservation equation\n: \n\nConsider the first term. Using Bernoulli's principle we way write\n: \n\nIn similar fashion, the second term may be written\n: \n\nCollecting terms, and rearranging, the mass conservation equation becomes\n:"@en . "In de stromingsleer is een stroming in een snelheidsveld een potentiaalstroming, als dat veld een potentiaal heeft. De stroming is dande gradi\u00EBnt van de snelheidspotentiaal, een scalaire functie. Omdat de rotatie van een gradi\u00EBnt altijd nul is, zijn potentiaalstromingen rotatievrij, hetgeen voor verschillende toepassingen een geoorloofde benadering is. In het geval van een onsamendrukbare stroming moet de snelheidspotentiaal aan de Laplace-vergelijking voldoen. Dan is potentiaaltheorie \u2013 gedefinieerd als de studie van harmonische functies \u2013 van toepassing, met een snelheidspotentiaal die specifiek geschikt is voor het bestudeerde stromingsprobleem. Maar ook voor samendrukbare stromingen, bijvoorbeeld bij geluid en voor vliegtuigen bij hogere machgetallen, wordt de potentiaalstromingsbenadering gebruikt. Verder vindt potentiaalstroming toepassing bij zowel stationaire als instationaire stromingen. Potentiaalstroming wordt onder andere toegepast voor: het snelheidsveld rond vliegtuigvleugels (buiten grenslaag en zog), oppervlaktegolven, en grondwaterstroming. Voor stromingen \u2013 of deelgebieden in stromingsvelden \u2013 met sterke vorticiteitseffecten geeft potentiaaltheorie geen bruikbare benadering van de stroming."@nl . "Potential flow"@en . . . "1112667940"^^ . . . . . . "Conformal power half.svg"@en . "Flusso potenziale"@it . . . . "Derivation of the full potential equation"@en . "Potentiaalstroming"@nl . . . . . "In fluidodinamica, la teoria del flusso potenziale descrive il campo della velocit\u00E0 come gradiente di una funzione scalare detta potenziale. Di conseguenza, un flusso potenziale \u00E8 caratterizzato da un campo di velocit\u00E0 irrotazionale, il quale \u00E8 una valida approssimazione per diverse applicazioni, sia in condizioni stazionarie che non stazionarie. L'irrotazionalit\u00E0 di un flusso potenziale \u00E8 dovuta al fatto che il rotore di un gradiente \u00E8 sempre nullo."@it . "33965"^^ . . . . "\uD3EC\uD150\uC15C \uC720\uB3D9(potential\u6D41\u52D5,potential flow)\uC740 \uC804\uAE30 \uB610\uB294 \uC804\uC790\uACF5\uD559 \uBC0F \uC720\uCCB4 \uB3D9\uC5ED\uD559\uC5D0\uC11C \uC810\uC131\uC774 \uC5C6\uB294 \uC644\uC804 \uC720\uCCB4(\uC774\uC0C1\uC720\uCCB4)\uC758 \uD750\uB984\uC744 \uAC00\uB9AC\uD0A8\uB2E4. \uB9F4\uB3CC\uC774\uAC00 \uC5C6\uB294 \uD750\uB984\uC73C\uB85C, \uACC4\uC0B0\uACFC \uC774\uD574\uAC00 \uC27D\uB2E4\uACE0 \uC54C\uB824\uC838\uC788\uB2E4."@ko . . . . . . . . . "Friktionsfri str\u00F6mning inom str\u00F6mningsmekanik \u00E4r ett fl\u00F6de d\u00E4r fluidens viskositet \u00E4r lika med noll och d\u00E4rmed \u00E4r friktionen i fluiden f\u00F6rsumbar."@sv .