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Homework Help: Finding the velocity of flow described by a vector field

  1. Dec 29, 2017 #1
    1. The problem statement, all variables and given/known data
    Consider the surface, S, in the xyz-space with the parametric representation: S: (, ) = [cos() , sin() , ] −1/2 ≤ ≤ 1/2 0 ≤ ≤ os().
    The surface is placed in a fluid with the velocity potential f of a flow: = y*^2 + z*^2
    a) Find the velocity of the flow described by a vector field (, , ).

    b) What is the velocity at the point = (−1,5,0)

    2. Relevant equations


    3. The attempt at a solution

    so this is the solution given for a and b, however i don't understand the answer at b. How can the different equations just be summed into one number, i would understand it if was squared--> then taken the sum of the numbers --> then taken the squareroot. Can anyone confirmed that this solution is wrong?

    upload_2017-12-30_0-59-2.png
     

    Attached Files:

  2. jcsd
  3. Dec 29, 2017 #2

    scottdave

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    Please clarify the surface S(,) and missing arguments for cosine, sine and the z coordinate.
     
  4. Dec 29, 2017 #3
    Sry, i copied it and it messed it up a bit, thought i fixed it though here is a picture should be clear
    upload_2017-12-30_1-57-38.png
     
  5. Dec 30, 2017 #4

    Delta²

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    Velocity is a vector, so just saying that velocity is 16 seems to be wrong.

    Also the magnitude of the velocity vector at that point is not 16.
     
  6. Dec 30, 2017 #5
    Thanks :) what i thought aswell
     
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