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November 9th, 2013, 11:24 PM   #1
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Vector field, curl and divergence question

Hi, I'm having a little trouble interpreting the first part of the problem, consequently I don't really know how to find v(x, y, z).

What I interpret is that the fluid is rotating around the z-axis (since it says that the rotation is in the xy-plane), so the vector v would be v=(Vx, Vy, 0) and since it's counter clock-wise then it would become V=(-wx, -wy, 0). Is this correct or am I missing something?
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November 10th, 2013, 04:06 AM   #2
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Re: Vector field, curl and divergence question

Yes, v_z = 0. But you don't need to introduce a new variable like w. You have to determine v_x and v_y with correct sign. Think in polar coordinate system if necessary. If you pick up a point, its orbit will be a circle. The velocity is always perpendicular to the radii, that is the tangential. You can find the length of the velocity considering that the omega is consant: |v|=omega*|r|. So make a sketch and try to find the component of v.
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November 10th, 2013, 09:06 AM   #3
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Re: Vector field, curl and divergence question

Well yeah, what I meant by "w" was omega. Since I don't have the Greek letters here I used the one that looks like it.
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