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Math Help - Laminar flow down vertical plate

  1. #1
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    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}]
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  2. #2
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    What do you get for the derivative?
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  3. #3
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    Quote Originally Posted by Ackbeet View Post
    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 }
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  4. #4
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    So, setting that equal yields an x-value of what?
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  5. #5
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    Quote Originally Posted by Ackbeet View Post
    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.
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  6. #6
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    No need to apologize!

    So the max velocity is equal to ______?
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  7. #7
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    Quote Originally Posted by Ackbeet View Post
    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 }
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  8. #8
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    Looks good to me!
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