= Blasius force theorem
{c}
{title2=$X-iY=(i\rho/2)\oint_C(W')^2\,dz$}
For a steady two-dimensional <incompressible flow> and <irrotational flow> around an impermeable body, the displayed contour formula gives the <force> on the body per unit span. Here $W'=u-iv$ is the <complex velocity>, $\rho$ is the constant <mass density>, and $C$ runs counterclockwise around the body, excluding other fluid singularities. To verify the sign, <Bernoulli's principle> gives $p=p_0-\rho|q|^2/2$. On a counterclockwise boundary, the complex pressure force is $d(X-iY)=-ip\,d\bar z$. Tangency gives $q\,dz=\bar q\,d\bar z$, and therefore $|q|^2d\bar z=q^2dz$. Integrating removes the constant $p_0$ term and gives the formula. The theorem is named after <Heinrich Blasius>.
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