= Fully developed flow
{title2=$\mathbf u=u(z)\hat{\mathbf x}$}
A fully developed parallel flow has a velocity profile independent of the streamwise coordinate. In a planar channel a representative profile is $\mathbf u=u(z)\hat{\mathbf x}$; wall conditions and translational symmetry remove cross-stream motion. The streamwise <pressure gradient> may remain nonzero, while the convective acceleration vanishes. Fully developed flow is a modeling branch, not a uniqueness assertion for all flows in that geometry.
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