Couette flow is a hypothetical fully$-$developed flow between two parallel plates sepa$-$

rated by some distance which are infinitely long in $x$ and infinitely wide into the page,

where one of the plates is moving in the $x$ direction relative to the other, and where

pressure between the plates is uniform. The flow profile has a well$-$known solution of

$u=V\frac{y}{h},v=0,$ where $V$ is the velocity of the top plate relative to the bottom and $h$

is the distance between the plates. Find an expression for $(x,y),$ the streamfunction

in the $(x,y)$ plane, for this flow. You may take the $=0$ streamline wherever is most

convenient.