Abstract
A formula for the Magnus force on a rotating and translating solid cylinder in a fluid is constructed for two different fluid models. In both cases the flow is steady and frictionless with no formation or shedding of eddies behind the cylinder. However, model one is founded on the assumption of irrotationality whereas model two is not but rather makes explicit use of the centrifugal force acting on the curving streamlines above the cylinder. Model two’s Magnus force comes out to be 15% larger in magnitude which is probably more than that can be accounted for by approximations made within the models. Observations will be needed to help decide which model comes closer to the truth. In the force formula the following factors are multiplied together: constant, fluid density, translation speed, and rotation frequency. For model one constant = 2; for model two constant = 2.3.
Highlights
The sideways force on a translating and rotating sphere or cylinder, is discussed in several fluid dynamics textbooks [1]-[3], but confusion can occur when it is combined with other effects, such as friction and eddy forming or shedding
If the OED (Oxford English Dictionary) is consulted [6], under Magnus effect is found: “The effect of rapid spinning on a cylinder moving through a fluid...”
Some of the confusion in the literature concerning the properties of the Magnus effect on rotating solid cylinders translating through a fluid may stem from the apparent lack of a published formula for the force
Summary
The sideways force on a translating and rotating sphere or cylinder, is discussed in several fluid dynamics textbooks [1]-[3], but confusion can occur when it is combined with other effects, such as friction and eddy forming or shedding. It is within a mixture of different effects that the concept of an “inverse” Magnus effect was introduced [4], which may or may not help with understanding what is going on with some of these fluid flows. Basic assumptions are: steady inviscid flow with no eddies forming on the back side of the cylinder, and the acceleration of gravity has no bearing on the problem
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