Editing Potential flow (section)

{{Short description|Velocity field as the gradient of a scalar function}}
{{About||potential flow around a cylinder|Potential flow around a circular cylinder}}
[[Image:Streamlines around a NACA 0012.svg|thumb|300px|right|Potential-flow [[Streamlines, streaklines, and pathlines|streamlines]] around a [[NACA airfoil|NACA 0012 airfoil]] at 11° [[angle of attack]], with upper and lower [[streamtube]]s identified. The flow is two-dimensional and the airfoil has infinite span.]]
In [[fluid dynamics]], '''potential flow''' or '''irrotational flow''' refers to a description of a fluid flow with no [[vorticity]] in it. Such a description typically arises in the limit of vanishing [[viscosity]], i.e., for an [[inviscid fluid]] and with no vorticity present in the flow.

Potential 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 [[Conservative vector field#Irrotational vector fields|irrotational velocity field]], which is a valid approximation for several applications. The irrotationality of a potential flow is due to the [[Curl (mathematics)|curl]] of the gradient of a [[Scalar (physics)|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 flow]]s and [[Hele-Shaw flow]]s. The potential flow approach occurs in the modeling of both stationary as well as nonstationary flows.  

Applications of potential flow include: the outer flow field for [[airfoil|aerofoil]]s, [[ocean surface wave|water waves]], [[electroosmotic flow]], and [[groundwater flow equation|groundwater flow]]. For flows (or parts thereof) with strong [[vorticity]] effects, the potential flow approximation is not applicable. In flow regions where vorticity is known to be important, such as [[Wake (physics)|wake]]s and [[boundary layer]]s, potential flow theory is not able to provide reasonable predictions of the flow.<ref name=B_378_380>Batchelor (1973) pp. 378–380.</ref> However, there are often large regions of a flow in which the assumption of irrotationality is valid, allowing the use of potential flow for various applications; these include flow around [[aircraft]], [[groundwater flow]], [[acoustics]], [[water wave]]s, and [[electroosmotic flow]].<ref name=Kirby>{{Citation| last = Kirby | first = B.J. | title=Micro- and Nanoscale Fluid Mechanics: Transport in Microfluidic Devices.| url=http://www.kirbyresearch.com/textbook| year=2010| publisher=Cambridge University Press | isbn=978-0-521-11903-0}}</ref>