A fluid with density 1230 flows with the velocity $\displaystyle V = y$i$\displaystyle +$j$\displaystyle + z$k. Find the rate of flow (of mass) upward through the paraboloid $\displaystyle z = 9 - \frac{1}{4}(x^2 + y^2), x^2 + y^2 \leq 36$.

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- May 24th 2009, 05:43 PMwik_chick88rate of flow
A fluid with density 1230 flows with the velocity $\displaystyle V = y$

**i**$\displaystyle +$**j**$\displaystyle + z$**k**. Find the rate of flow (of mass) upward through the paraboloid $\displaystyle z = 9 - \frac{1}{4}(x^2 + y^2), x^2 + y^2 \leq 36$. - May 25th 2009, 01:49 AMCalculus26
the density is mass/volume

Flux is Volume/time

You want then mass/time = density*flux

N = x/2i + y/2 j + k

V*N = xy/2 + y/2 + z = xy/2 +y/2 + 9-1/4(x^2 +y^2)

convert to Polar coordinates

and integrate over the disk of radius 6

If you have trouble see the attachment in the following post - May 25th 2009, 02:04 AMCalculus26
See attachment