Unidirectional flow
= Unidirectional flow
{title2=$\boldsymbol u=u(y)\boldsymbol e_x$}
A unidirectional flow has velocity parallel to a single fixed direction, for example $\boldsymbol u=u(y)\boldsymbol e_x$. If the speed is independent of the coordinate along that direction, the convective acceleration $(\boldsymbol u\cdot\nabla)\boldsymbol u$ vanishes. The steady <Navier-Stokes equation> then reduces to a linear balance of the pressure gradient and viscosity, as in <Couette flow> and <Poiseuille flow>.