= Magnus effect
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The <Magnus effect> is a transverse <force> on a spinning body in relative motion through a <fluid>. Rotation changes the surrounding <circulation>, <pressure> distribution and wake. In a two-dimensional cylinder model, the <Kutta–Joukowski theorem> gives <force> per unit span $\mathbf F'=\rho\mathbf U\times(\Gamma\hat{\mathbf z})$, with relative <fluid> <velocity> $\mathbf U$ and <circulation> $\Gamma$ positive anticlockwise viewed from $+z$. Real <viscosity> and boundary-layer behavior help determine the <circulation>; impermeability alone does not determine it from spin rate.
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