- #1
glid02
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Here's the question:
A fluid has density 2 and velocity field http://ada.math.uga.edu/webwork2_files/tmp/equations/92/09afbe0bd85ee163f9c2c6664132361.png .[/URL]
Find the rate of flow outward through the sphere http://ada.math.uga.edu/webwork2_files/tmp/equations/49/de1fad897871c3c2ac5109463da2a11.png .[/URL]
So far I've found n, which is
1/2x+1/2y+1/2z
and F dot n gives z^2.
I converted to spherical coordinates and z^2 is equal to 4cos^2[phi].
My integral is set up as:
4*(int[0-2pi] int[0-pi] (cos^2[phi]*sin[phi]dphi dtheta.
The first integral is -1/3cos^3[phi] from 0-pi which is 1/3 - - 1/3 = 2/3
The second integral gives 2/3*2*pi, so the entire thing is 4*2/3*2*pi.
I thought I was just supposed to multiply that by 2 (the density) but that's not the right answer. Can someone tell me what I did wrong or what I'm supposed to do with the density?
Thanks a lot.
A fluid has density 2 and velocity field http://ada.math.uga.edu/webwork2_files/tmp/equations/92/09afbe0bd85ee163f9c2c6664132361.png .[/URL]
Find the rate of flow outward through the sphere http://ada.math.uga.edu/webwork2_files/tmp/equations/49/de1fad897871c3c2ac5109463da2a11.png .[/URL]
So far I've found n, which is
1/2x+1/2y+1/2z
and F dot n gives z^2.
I converted to spherical coordinates and z^2 is equal to 4cos^2[phi].
My integral is set up as:
4*(int[0-2pi] int[0-pi] (cos^2[phi]*sin[phi]dphi dtheta.
The first integral is -1/3cos^3[phi] from 0-pi which is 1/3 - - 1/3 = 2/3
The second integral gives 2/3*2*pi, so the entire thing is 4*2/3*2*pi.
I thought I was just supposed to multiply that by 2 (the density) but that's not the right answer. Can someone tell me what I did wrong or what I'm supposed to do with the density?
Thanks a lot.
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