Fluid Mechanics: Flow Between Parallel Plates-Force Balance Equation

[Romulus3]

Fluid Mechanics: Flow Between Parallel Plates--Force Balance Equation

Homework Statement

http://antishift.org/image.php?id=16807&size=full

Homework Equations

I know the equation for shear, tau=viscosity*velocity gradient. and pressure is obviously force/area.

The Attempt at a Solution

I solved this problem using navier-stokes equations, and using the assumptions given in the problem. however, the homework graders wrote to use force-balance equations instead, as stated in the problem. ><;;

The professor went over a similar example of a cylindrical fluid element, where the area factor was simply pi*r^2. however, I'm confused by the plates being infinite, so i can't seem to figure what the area is. how do i calculate the area of the fluid element? is it simply dy*dx? how is the pressure/pressure gradient affect being that the plates are infinite? I just need to know what the force balance equation looks like.

Here's a picture of my professor's lecture slide about the cylindrical fluid element and its force balance equation: http://antishift.org/image.php?id=16802&size=medium"

Thanks!

 

[haruspex]

The links to the question being broken, it is impossible to comment.