Editing Circulation (physics) (section)

{{short description|Line integral of the fluid velocity around a closed curve}}
[[File:General circulation-vorticity diagram.svg|300px|thumb|Field lines of a vector field {{math|'''v'''}}, around the boundary of an open curved surface with infinitesimal line element {{math|''d'''''l'''}} along boundary, and through its interior with {{math|''dS''}} the infinitesimal surface element and {{math|'''n'''}} the [[unit vector|unit]] normal to the surface. '''Top:''' Circulation is the line integral of {{math|'''v'''}} around a closed loop {{math|''C''}}. Project {{math|'''v'''}} along {{math|''d'''''l'''}}, then sum. Here {{math|'''v'''}} is split into components perpendicular (⊥) parallel ( ‖ ) to {{math|''d'''''l'''}}, the parallel components are [[tangent]]ial to the closed loop and contribute to circulation, the perpendicular components do not. '''Bottom:''' Circulation is also the [[flux]] of vorticity {{math|1='''ω''' = '''∇''' × '''v'''}} through the surface, and the [[curl (mathematics)|curl]] of {{math|'''v'''}} is ''heuristically'' depicted as a helical arrow (not a literal representation). Note the projection of {{math|'''v'''}} along {{math|''d'''''l'''}} and curl of {{math|'''v'''}} may be in the negative sense, reducing the circulation.]]

In physics, '''circulation''' is the [[line integral]] of a [[vector field]] around a closed curve embedded in the field. In [[fluid dynamics]], the field is the fluid [[velocity field]]. In [[Electromagnetism|electrodynamics]], it can be the electric or the magnetic field.

In [[aerodynamics]], it finds applications in the calculation of [[Lift (force)|lift]], for which circulation was first used independently by [[Frederick Lanchester]],<ref>{{cite book |last1=Lanchester |first1=Frederick. W |title=AERODYNAMICS |date=1907 |publisher=ARCHIBALD CONSTABLE & CO. |location=London}}</ref> [[Ludwig Prandtl]],<ref>{{cite book |last1=Prandtl |first1=Ludwig |title=APPLICATIONS OF MODERN HYDRODYNAMICS TO AERONAUTICS |date=1922 |publisher=National Advisory Committee for Aeronautics |location=United States |url=https://ntrs.nasa.gov/api/citations/19930091180/downloads/19930091180.pdf}}</ref> [[Martin Kutta]] and [[Nikolay Zhukovsky (scientist)|Nikolay Zhukovsky]].<ref>Anderson, John D. (1984), ''Fundamentals of Aerodynamics'', Section 2.13, McGraw Hill</ref> It is usually denoted {{math|Γ}} (uppercase [[gamma]]).