Question

Find the flow rate

Answer 1

im lost.

Answer 2

the flow rate is v.ds isnt it?

Answer 3

isnt it?

Answer 4

Aren't you essentially finding the flux through the surface?

Answer 5

i believe so

Answer 6

oh wait, no not quite.

Answer 7

OHH THE LEGOMAN, PLEASE HELP ME WHEN YOU'RE DONE WITH CALC III (p.s. I hated calc 3.. got a C- so won't try helpin sorry..=( )

Answer 8

the book has a simliar exmaple with flux arrors point up towards the z axis

Answer 9

refreshing myself on the topic, one moment..

Answer 10

at least they look like flux vectors, haha

Answer 11

okay, thanks for the help

Answer 12

From what I can tell, the integration of a flux over an area gives the volumetric flow rate.

Answer 13

But I don't recall the easy way to calculate the flux (maybe there isn't one).

Answer 14

i think you compute the flow rate through tao so the flow rate through tao would give you \[\int\limits_{}^{}\int\limits_{s}^{} v dS \] ?

Answer 15

for the flux

Answer 16

\[v * e_n = <0,-1,0>dotted <?>\]

Answer 17

I think you really can just take the integral of F over the surface.

\[\int\int_S \vec{F}\cdot dS = \int \int _S\vec{F}\cdot \vec{n}\ dS \]

So we just need to compute the normal, dot it with the vector field, then integrate that over the surface.

Answer 18

so first lets calculate the area