# Thread: Laminar flow down vertical plate

1. ## Laminar flow down vertical plate

I am trying to find the maximum velocity of the flow using the equation below. However, I cannot come across the correct derivation (which I must set equal to 0 to find my maximum velocity). I keep getting an x in my final answer....

$v_{z}(x)= \frac{\rho g\delta^{2} }{2\mu }[1-(\frac{x}{\delta })^{2}]$

2. What do you get for the derivative?

3. Originally Posted by Ackbeet
What do you get for the derivative?
After distributing the $\frac{\rho g\delta ^{2}}{2\mu }$, simplifying, and finding the derivative I get v'(x)= $\frac{-xg\rho }{\mu }$

4. So, setting that equal yields an x-value of what?

5. Originally Posted by Ackbeet
So, setting that equal yields an x-value of what?
Wow. The maximum velocity occurs at x=0, evaluating the original function at x=0.... My apologizes for the thread.

6. No need to apologize!

So the max velocity is equal to ______?

7. Originally Posted by Ackbeet
No need to apologize!

So the max velocity is equal to ______?
The maximum velocity is, $\nu _{z max}=\frac{\rho g\delta ^{2}}{2\mu }$

8. Looks good to me!