Q:If a fluid with density 400 flows with a velocity field v = –5yi + 5xj + 2zk, find the fluid flow rate outward through the sphere x^2 + y^2 + z^2 = 49.
All I have so far is the following:
F(x, y, z) = 400*(–5yi + 5xj + 2zk)
r(phi, theta) = 7sin(phi)cos(theta)i + 7sin(phi)sin(theta)j + 7cos(phi)k
where crossing rphixrtheta = 49sin^2(phi)cos(theta)i+49sin^2(phi)sin(theta)j + 49sin(phi)cos(phi)k
Can I now just do F(r(phi, theta) dotted with the above, over the integral, from 0 to pi of (phi) and 0 to 2pi of(theta)?
I am so lost.
EDIT: Never mind: I got it. It was just a calculation error.
All I have so far is the following:
F(x, y, z) = 400*(–5yi + 5xj + 2zk)
r(phi, theta) = 7sin(phi)cos(theta)i + 7sin(phi)sin(theta)j + 7cos(phi)k
where crossing rphixrtheta = 49sin^2(phi)cos(theta)i+49sin^2(phi)sin(theta)j + 49sin(phi)cos(phi)k
Can I now just do F(r(phi, theta) dotted with the above, over the integral, from 0 to pi of (phi) and 0 to 2pi of(theta)?
I am so lost.
EDIT: Never mind: I got it. It was just a calculation error.