How to estimate the performance of a pump using Navier Stokes?

[owlwise2010]

Homework Statement

Fluid Mechanics Homework:
Flows between two horizontal parallel plates
apart. The upper plate is moving with a uniform speed U, while the lower one is kept stationary. A constant pressure gradient of dp/dx is applied

Relevant Equations

Navier Stokes and Volumetric flow

Hello everyone,
Attached is the homework problem (FluidHmk.PNG) as well as the attempt (Attempted 1 and 2).

Just wanted to know if this is method to approach the problem

Thanks in advance.

 

[cjl]

Your approach looks very reasonable to me based on a quick glance over everything. I don't have time right now to actually go through and check the numbers, but it seems that you've taken the correct view of the problem, and nothing jumps out at me as being obviously incorrect.

I'll try to check back later this evening when I have more time to actually look over it in more depth if nobody else has a chance. In the meantime, maybe @boneh3ad has time to take a look (he's one of the only other people I'm aware of on the forum with a fluids background)?

 

[cjl]

I finally got a chance to go through in more detail, and it all looks correct to me. I might have left the factor of l in a while longer rather than just calling it 1, but the problem statement didn't actually specify that it needed to be in terms of l (and it fundamentally doesn't change anything about the problem), so this seems fine to me.