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

1. Dec 29, 2017

### Snoldermus

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?

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2. Dec 29, 2017

### scottdave

Please clarify the surface S(,) and missing arguments for cosine, sine and the z coordinate.

3. Dec 29, 2017

### Snoldermus

Sry, i copied it and it messed it up a bit, thought i fixed it though here is a picture should be clear

4. Dec 30, 2017

### Delta²

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.

5. Dec 30, 2017

### Snoldermus

Thanks :) what i thought aswell