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Calculus and Beyond Homework Help
Vector Calculus: Air flowing through loop of straight lines
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[QUOTE="LCKurtz, post: 5006669, member: 198114"] It isn't usually proven in most calculus courses, but if ##\nabla \cdot \vec V = 0## in a simply connected region, then there is a vector field ##\vec F## such that ##\vec V = \nabla \times \vec F##. That says ##\iint_{S} \vec V\cdot d\vec S =\iint_{S} \nabla \times F\cdot d\vec S = \int_C \vec F\cdot d\vec R## for any open surface ##S## bounded by the curve ##C##. Since the right side doesn't depend on ##S## but only on ##\vec F## and ##C##, you can use any surface bounded by the curve to calculate the left side. There are a couple of obvious surfaces you could use. [/QUOTE]
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Vector Calculus: Air flowing through loop of straight lines
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