Navier Stokes Equation to create a Velocity Profile

[Varidius]

Homework Statement

An incompressible, viscous fluid is placed between horizontal, infinite, parallel
plates. The two plates move in opposite directions with constant velocities U1 and U2. 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.

Homework Equations

Obviously the "standard" Navier-Stokes Equation

Can anyone help me, I've never been properly able to understand and utilise the Navier-Stokes Equation?

 

[hcelik]

Maybe this link can be helpful for you:

http://www.engineering.uiowa.edu/~fluids/Posting/Schedule/Quiz/Quiz8.pdf