= Equilateral triangular pipe flow
{title2=$w=\dfrac{p_z}{4a\mu}(x^2-3y^2)(x-a)$}
For a straight pipe with cross-section $0<x<a$, $|y|<x/\sqrt3$, steady unidirectional <incompressible flow> reduces the <Navier-Stokes equations> to $\mu\nabla_\perp^2w=p_z$, with constant axial <pressure gradient>. The displayed cubic <polynomial> vanishes on every wall, and its transverse <Laplacian> is $p_z/\mu$. The axial drag per unit length on each of the three equal walls is $-p_za^2/(3\sqrt3)$. This follows by integrating the viscous <traction> on one wall; summing the three <forces> equals the <pressure gradient> times the triangular <area>.
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