I have a question and an answer for couette flow question

[Goldberg]

Homework Statement

Fluid flows between 2 parallel plates, flow is fully developed and laminar, the distance between the plates is h
In the notes there is a general form of solution after integrating it 2 times. where a is h. but i saw in the book that we have to get +h/2 and -h/2 then add those equations find c1 and c2. but is there any easier way.
P.S. i wasn't able to find the final answer by using any of those things

Homework Equations

http://imgur.com/LwOFqy8

The Attempt at a Solution

http://imgur.com/0j2Ypr4

 

[Goldberg]

a step by step solution would be awesome, since this is the beginning and i want to understand the basic concept ruling these equations. i have watched videos online everywhere but can't get to the last (1-(2h/y)^2) part

 

[Chestermiller]

In one of your examples, y is measured up from the base, and the total channel height is a. In the other example, y is measured upward from the channel centerline, and the total channel height is h. The two examples are equivalent.

Chet

 

[Goldberg]

I tried solving it using y=o, when u=0
and y=h/2 when u=0.
still I am not able to find the same answer..
can someone tell me what's wrong
attempt jpeg:
http://postimg.org/image/u2srvitj7/

 

[Chestermiller]

I tried solving it using y=o, when u=0
and y=h/2 when u=0.
still I am not able to find the same answer..
can someone tell me what's wrong
attempt jpeg:
http://postimg.org/image/u2srvitj7/

For that case, you should be using u' = 0 at y = 0 and u = 0 at y = h/2.