An incompressible, viscous fluid is placed between horizontal, infinite, parallel plates as is shown in Fig. P6.79. 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.

Figure P6.79