In physics, circulation is the line integral of a vector field around a closed curve. In fluid dynamics , the field is the fluid velocity field . In electrodynamics , it can be the electric or the magnetic field.
20-498: [REDACTED] Look up circulation in Wiktionary, the free dictionary. Circulation may refer to: Science and technology [ edit ] Atmospheric circulation , the large-scale movement of air Circulation (physics) , the path integral of the fluid velocity around a closed curve in a fluid flow field Circulatory system , a biological organ system whose primary function
40-578: A static magnetic field is, by Ampère's law , proportional to the total current enclosed by the loop ∮ ∂ S B ⋅ d l = μ 0 ∬ S J ⋅ d S = μ 0 I enc . {\displaystyle \oint _{\partial S}\mathbf {B} \cdot \mathrm {d} \mathbf {l} =\mu _{0}\iint _{S}\mathbf {J} \cdot \mathrm {d} \mathbf {S} =\mu _{0}I_{\text{enc}}.} For systems with electric fields that change over time,
60-661: A 2008 psychological thriller-fantasy film by Ryan Harper Circulation (journal) , a journal published by the American Heart Association Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with the title Circulation . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Circulation&oldid=1176051076 " Category : Disambiguation pages Hidden categories: Short description
80-530: A line integral between any two points in the field is independent of the path taken. It also implies that the vector field can be expressed as the gradient of a scalar function, which is called a potential . Circulation can be related to curl of a vector field V and, more specifically, to vorticity if the field is a fluid velocity field, ω = ∇ × V . {\displaystyle {\boldsymbol {\omega }}=\nabla \times \mathbf {V} .} By Stokes' theorem ,
100-412: A nitrogen oxide reduction technique used in most gasoline and diesel engines Library circulation , the activities around the lending of library books and other material to users of a lending library Ocean circulation , the large-scale movement of water Rhetorical circulation , the ways that texts and discourses move through time and space Other uses [ edit ] Print circulation ,
120-409: Is different from Wikidata All article disambiguation pages All disambiguation pages circulation [REDACTED] Look up circulation in Wiktionary, the free dictionary. Circulation may refer to: Science and technology [ edit ] Atmospheric circulation , the large-scale movement of air Circulation (physics) ,
140-555: Is known as the Kutta–Joukowski theorem. This equation applies around airfoils, where the circulation is generated by airfoil action ; and around spinning objects experiencing the Magnus effect where the circulation is induced mechanically. In airfoil action, the magnitude of the circulation is determined by the Kutta condition . The circulation on every closed curve around the airfoil has
160-450: Is the angle between the vectors V and d l . The circulation Γ of a vector field V around a closed curve C is the line integral : Γ = ∮ C V ⋅ d l . {\displaystyle \Gamma =\oint _{C}\mathbf {V} \cdot \mathrm {d} \mathbf {l} .} In a conservative vector field this integral evaluates to zero for every closed curve. That means that
180-440: Is to move substances to and from cells Circulation problem , a generalization of network flow problems Circulation (architecture) , the flow of people through a building Circulation (currency) , all currency held by consumers and businesses, but not by financial institutions and governments Exhaust gas recirculation , a nitrogen oxide reduction technique used in most gasoline and diesel engines Library circulation ,
200-632: The flux of curl or vorticity vectors through a surface S is equal to the circulation around its perimeter, Γ = ∮ ∂ S V ⋅ d l = ∬ S ∇ × V ⋅ d S = ∬ S ω ⋅ d S {\displaystyle \Gamma =\oint _{\partial S}\mathbf {V} \cdot \mathrm {d} \mathbf {l} =\iint _{S}\nabla \times \mathbf {V} \cdot \mathrm {d} \mathbf {S} =\iint _{S}{\boldsymbol {\omega }}\cdot \mathrm {d} \mathbf {S} } Here,
220-534: The activities around the lending of library books and other material to users of a lending library Ocean circulation , the large-scale movement of water Rhetorical circulation , the ways that texts and discourses move through time and space Other uses [ edit ] Print circulation , the average number of copies of a publication Circulation Festival , an annual circus and fire performance festival held in Dunedin, New Zealand Circulation (film) ,
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#1732859420587240-431: The average number of copies of a publication Circulation Festival , an annual circus and fire performance festival held in Dunedin, New Zealand Circulation (film) , a 2008 psychological thriller-fantasy film by Ryan Harper Circulation (journal) , a journal published by the American Heart Association Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with
260-404: The closed integration path ∂S is the boundary or perimeter of an open surface S , whose infinitesimal element normal d S = n dS is oriented according to the right-hand rule . Thus curl and vorticity are the circulation per unit area, taken around a local infinitesimal loop. In potential flow of a fluid with a region of vorticity , all closed curves that enclose the vorticity have
280-417: The curl of the electric field is equal to the negative rate of change of the magnetic field, ∇ × E = − ∂ B ∂ t {\displaystyle \nabla \times \mathbf {E} =-{\frac {\partial \mathbf {B} }{\partial t}}} or that the circulation of the electric field around a loop is equal to the negative rate of change of
300-658: The magnetic field flux through any surface spanned by the loop, by Stokes' theorem ∮ ∂ S E ⋅ d l = ∬ S ∇ × E ⋅ d S = − d d t ∫ S B ⋅ d S . {\displaystyle \oint _{\partial S}\mathbf {E} \cdot \mathrm {d} \mathbf {l} =\iint _{S}\nabla \times \mathbf {E} \cdot \mathrm {d} \mathbf {S} =-{\frac {\mathrm {d} }{\mathrm {d} t}}\int _{S}\mathbf {B} \cdot \mathrm {d} \mathbf {S} .} Circulation of
320-494: The path integral of the fluid velocity around a closed curve in a fluid flow field Circulatory system , a biological organ system whose primary function is to move substances to and from cells Circulation problem , a generalization of network flow problems Circulation (architecture) , the flow of people through a building Circulation (currency) , all currency held by consumers and businesses, but not by financial institutions and governments Exhaust gas recirculation ,
340-613: The same value for circulation. In fluid dynamics, the lift per unit span (L') acting on a body in a two-dimensional flow field is directly proportional to the circulation, i.e. it can be expressed as the product of the circulation Γ about the body, the fluid density ρ {\displaystyle \rho } , and the speed of the body relative to the free-stream v ∞ {\displaystyle v_{\infty }} : L ′ = ρ v ∞ Γ {\displaystyle L'=\rho v_{\infty }\Gamma } This
360-468: The same value, and is related to the lift generated by each unit length of span. Provided the closed curve encloses the airfoil, the choice of curve is arbitrary. Circulation is often used in computational fluid dynamics as an intermediate variable to calculate forces on an airfoil or other body. In electrodynamics, the Maxwell-Faraday law of induction can be stated in two equivalent forms: that
380-472: The title Circulation . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Circulation&oldid=1176051076 " Category : Disambiguation pages Hidden categories: Short description is different from Wikidata All article disambiguation pages All disambiguation pages Circulation (physics) Circulation
400-758: Was first used independently by Frederick Lanchester , Martin Kutta and Nikolay Zhukovsky . It is usually denoted Γ ( Greek uppercase gamma ). If V is a vector field and d l is a vector representing the differential length of a small element of a defined curve, the contribution of that differential length to circulation is dΓ : d Γ = V ⋅ d l = | V | | d l | cos θ . {\displaystyle \mathrm {d} \Gamma =\mathbf {V} \cdot \mathrm {d} \mathbf {l} =\left|\mathbf {V} \right|\left|\mathrm {d} \mathbf {l} \right|\cos \theta .} Here, θ
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