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"Quick" Green-Gauss theorem Question
HELLO! I am a grad student in Mech & Aero Engineering and have come across a bit of trouble with one of my problems. I'd appreciate your assistance.
"Given a general closed surface S for which the position vector and normal are known at every point, derive a formula for the volume enclosed by S. Verify your relation for the special case of a sphere."
I know to begin with the Green-Gauss theorem, which relates surface integrals to volume integrals (sorry I don't know how to display mathematics in here), but I'm not sure how to manipulate the bounded volume and isolate!
thank you - Ciao
HELLO! I am a grad student in Mech & Aero Engineering and have come across a bit of trouble with one of my problems. I'd appreciate your assistance.
"Given a general closed surface S for which the position vector and normal are known at every point, derive a formula for the volume enclosed by S. Verify your relation for the special case of a sphere."
I know to begin with the Green-Gauss theorem, which relates surface integrals to volume integrals (sorry I don't know how to display mathematics in here), but I'm not sure how to manipulate the bounded volume and isolate!
thank you - Ciao