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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[itex]\bullet[/itex]NdS measures the fluid flow "across" a surface S per unit time.

Now, the divergence theorem ∫∫∫ divFdV 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

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# Flux/ Divergence Theorem interpretation

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