Flux/ Divergence Theorem interpretation

1. Aug 2, 2013

leehufford

Hello,

I am approaching the end of my multivariable/ vector analysis "Calc III" class and have a question about flux.

My book states that flux, ∫∫ F $\bullet$ N dS measures the fluid flow "across" a surface S per unit time.

Now, the divergence theorem ∫∫∫ divF dV measures the "same thing" but fluid flow THROUGH a solid. How can fluid flow over a surface and through a solid be equated for the same regoin? Is it actually fluid flow THROUGH a surface and not OVER it? That would make more sense.

Hopefully some people who are further along in their math journey can explain this for me. Thanks in advance,

Lee

2. Aug 2, 2013

WannabeNewton

Hi Lee! Thankfully this just seems to be a problem with the usage of English phrases. "Across" here means "through" and not "over".

3. Aug 2, 2013

HallsofIvy

Its like "running across the finish line".