= Power-law Couette-Poiseuille flow
{title2=$\sigma_{xy}=G(\alpha h-y)$}
For plates at y=+-h moving at velocities +-U and pressure gradient -G, <force balance> fixes the displayed stress. The <power-law fluid> law gives $u_y=(Gh/k)^{1/n}\operatorname{sgn}(\alpha-y/h)|\alpha-y/h|^{1/n}$. Integrating from the lower no-slip wall yields $u=-U+hn(Gh/k)^{1/n}[|\alpha+1|^{1+1/n}-|\alpha-y/h|^{1+1/n}]/(n+1)$. The upper wall fixes alpha uniquely for k,n,G,U>0. Absolute values are essential when the shear reverses inside the gap.
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