An incompressible, viscous fluid is placed between horizontal, infinite, parallel plates as is shown in the figure below. The two plates move in opposite directions with constant velocities, $U_1$ and $U_2,$ as shown. The pressure gradient in the $x$ direction is zero, and the only body force is due to the fluid weight. Use the Navier$-$Stokes equations to derive an expression for the velocity distribution between the plates. Assume laminar flow. Express your answer in terms of $y,b,U_1$ and $U_2.$

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