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Magnus effect
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===Spinning cylinder=== [[file:streamline_of_magnus_effect.svg|thumb|200px|right|Streamlines for the potential flow around a spinning cylinder. The concentric circular streamlines of a [[Vortex#Irrotational vortices|free vortex]] have been superimposed on the parallel streamlines of a uniform flow.]] Streamlines are closer spaced immediately above the cylinder than below, so the air flows faster past the upper surface than past the lower surface. Bernoulli's principle shows that the pressure adjacent to the upper surface is lower than the pressure adjacent to the lower surface. The Magnus force acts vertically upwards on the cylinder.<ref>"When dynamic lift on an object occurs it is always associated with an unsymmetrical set of streamlines relatively close together on one side and relatively far apart on the other ... that correspond ... to circulation of fluid around the object." <br> β[the streamlines] are closer together above [the body] than they are below so that Bernoulli's principle predicts the observed dynamic lift." Resnick and Halliday (1966), ''PHYSICS'', Section 18-5</ref> Streamlines immediately above the cylinder are curved with radius little more than the radius of the cylinder. This means there is low pressure close to the upper surface of the cylinder. Streamlines immediately below the cylinder are curved with a larger radius than streamlines above the cylinder. This means there is higher pressure acting on the lower surface than on the upper.<ref>{{cite journal |last1=Babinsky |first1=Holger |title=How do wings work? |journal=Physics Education |date=November 2003 |volume=38 |issue=6 |pages=497β503 |doi=10.1088/0031-9120/38/6/001 |bibcode=2003PhyEd..38..497B |quote=...if a streamline is curved, there must be a pressure gradient across the streamline }}</ref> Air immediately above and below the cylinder is curving downwards, accelerated by the pressure gradient. A downwards force is acting on the air. [[Newton's third law]] predicts that the Magnus force and the downwards force acting on the air are equal in magnitude and opposite in direction.
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