# Math Help - rate of flow

1. ## rate of flow

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

2. 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

3. See attachment