= Blasius force from a Laurent coefficient at infinity
{c}
{title2=$F_x-iF_y=-\pi\rho\,[z^{-1}]q(z)^2$}
For a two-dimensional steady ideal flow outside a body, let $q=w'$ be the <complex velocity>. Suppose $q$ is holomorphic in the exterior and $q^2$ has a <Laurent series> near infinity, with coefficient $a_{-1}$ of $z^{-1}$. Orient the body contour counterclockwise and assume the usual impermeability and Bernoulli hypotheses of the <Blasius force theorem>. Deforming the contour to a large circle gives $\oint q^2dz=2\pi i a_{-1}$. Substitution in Blasius' formula proves $F_x-iF_y=-\pi\rho a_{-1}$.
In particular, $q(z)=q_\infty+O(z^{-2})$ makes the force zero: its square has no reciprocal term. This criterion handles branch-cut obstacles by applying the contour in their analytic exterior, rather than separately assigning forces to endpoint singularities.
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