Fluid Mechanics: Flow Between Parallel Plates-Force Balance Equation

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

Homework Statement



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

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" [Broken]

Thanks!
 
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