Couette-Poiseuille flow
= Couette-Poiseuille flow
{c}
{title2=$u(y)=Uy/a+(G/2)y(a-y)$}
<Couette-Poiseuille flow> superposes wall-driven shear and pressure-driven parabolic flow between no-slip parallel plates. With one plate moving at $U$, separation $a$, and $dp/dx=-\rho\nu G$, the displayed profile has volume flux $Ua/2+Ga^3/12$ per unit width. Requiring zero flux gives $G=-6U/a^2$ and $u=U[3(y/a)^2-2y/a]$, with a pressure gradient induced by return-flow constraints.