= Advective and pressure contributions to circulatory lift
{title2=$\oint(\mathbf u\cdot\mathbf n)\mathbf u\,dl=\tfrac12\boldsymbol\Gamma\times\mathbf U$}
For <uniform flow> $\mathbf U$ plus a <line vortex> of counterclockwise <circulation> $\Gamma$, the outward advective <momentum flux> around a large circle is $\rho\boldsymbol\Gamma\times\mathbf U/2$. The <Bernoulli equation> supplies an equal <pressure> contribution. Their sum is the force on the fluid; the force on an obstacle per unit span is its negative, $\rho\mathbf U\times\boldsymbol\Gamma$. Retaining only the advective term loses half the lift and obscures its sign.
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