Pressure-driven channel flow
= Pressure-driven channel flow
{title2=$\mu\Delta_\perp w=-G$}
A steady unidirectional incompressible viscous flow in a rigid channel, driven by $G=-dp/dz$, reduces the axial <momentum> equation to the displayed <Poisson equation>, with $w=0$ on the cross-sectional boundary. Circular-pipe flow is the <Hagen-Poiseuille flow> special case; an arbitrary cross section need not have that parabolic radial profile.