Flow Integrals and Circulation // Big Idea, Formula & Examples // Vector Calculus

When a vector field is a velocity field, a natural phenomenon we can measure is the Flow. This accumulates the tendency of the vector field to be tangential to the curve. If we imagine our field is a velocity field, the flow is measuring the degree to which a curve just naturally flows along with that velocity field. As a line integral, this is identical to our formula for work, it is just interpreted differently physically. When the path is a closed curve - i.e. starts and ends at the same point - then the flow integral is called the circulation of the vector field along a path. We see as examples a source field which has no flow and a spin field which has lots of flow.

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