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==Magnus effect in potential flow== |
==Magnus effect in potential flow== |
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===Non-spinning cylinder=== |
===Non-spinning cylinder=== |
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[[Image:Potential cylinder.svg|thumb|200px|right|[[Streamlines, streaklines, and pathlines|Streamlines]] for the |
[[Image:Potential cylinder.svg|thumb|200px|right|[[Streamlines, streaklines, and pathlines|Streamlines]] for the [[potential flow around a circular cylinder]] in a uniform onflow.]] |
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The flow pattern is symmetric about a horizontal axis through the centre of the cylinder. At each point above the axis and its matching point below the axis, the spacing of streamlines is the same so velocities are the same at each point above the axis and its matching point below the axis. Bernoulli’s principle shows that, outside the [[boundary layers]], pressures are also the same at matching points. There is no lift acting on the cylinder. |
The flow pattern is symmetric about a horizontal axis through the centre of the cylinder. At each point above the axis and its matching point below the axis, the spacing of streamlines is the same so velocities are the same at each point above the axis and its matching point below the axis. Bernoulli’s principle shows that, outside the [[boundary layers]], pressures are also the same at matching points. There is no lift acting on the cylinder. |
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===Spinning cylinder=== |
===Spinning cylinder=== |
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[[file:streamline_of_magnus_effect.svg|thumb|200px|right]] |
[[file:streamline_of_magnus_effect.svg|thumb|200px|right]] |
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Streamlines are closer spaced 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. |
Streamlines are closer spaced 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. |
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Revision as of 11:29, 19 September 2024
Magnus effect in potential flow
Non-spinning cylinder
The flow pattern is symmetric about a horizontal axis through the centre of the cylinder. At each point above the axis and its matching point below the axis, the spacing of streamlines is the same so velocities are the same at each point above the axis and its matching point below the axis. Bernoulli’s principle shows that, outside the boundary layers, pressures are also the same at matching points. There is no lift acting on the cylinder.
Spinning cylinder
Streamlines are closer spaced 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.
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.[1]
Air immediately above and below the cylinder is curving downwards, accelerated by the pressure gradient. A downwards force is acting on the air.
Citations
- ^ "...if a streamline is curved, there must be a pressure gradient across the streamline..."Babinsky, Holger (November 2003), "How do wings work?", Physics Education, 38 (6): 497, Bibcode:2003PhyEd..38..497B, doi:10.1088/0031-9120/38/6/001, S2CID 1657792