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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. MY VECTOR CALCULUS PLAYLIST: ►VECTOR CALCULUS (Calc IV) • Calculus IV: Vector Calculus (Line In... OTHER COURSE PLAYLISTS: ►DISCRETE MATH: • Discrete Math (Full Course: Sets, Log... ►LINEAR ALGEBRA: • Linear Algebra (Full Course) ►CALCULUS I: • Calculus I (Limits, Derivative, Integ... ► CALCULUS II: • Calculus II (Integration Methods, Ser... ►MULTIVARIABLE CALCULUS (Calc III): • Calculus III: Multivariable Calculus ... ►DIFFERENTIAL EQUATIONS: • How to solve ODEs with infinite serie... OTHER PLAYLISTS: ► Learning Math Series • 5 Tips To Make Math Practice Problems... ►Cool Math Series: • Cool Math Series BECOME A MEMBER: ►Join: / @drtrefor MATH BOOKS & MERCH I LOVE: ► My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett SOCIALS: ►Twitter (math based): / treforbazett ►Instagram (photography based): / treforphotography