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Compute the circulation of velocity about the circle

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Reference no: EM131614681

Question: A vortex that rotates at constant angular velocity ω about the z-axis has velocity vector field v→ = ω(-yi→ + xj→).

(a) Sketch the vector field with ω = 1 and the vector field with ω = -1.

(b) Determine the speed v→ of the vortex as a function of the distance from its center.

(c) Compute div v→ and curl v→.

(d) Compute the circulation of v→ counterclockwise about the circle of radius R in the xy-plane, centered at the origin.

Reference no: EM131614681

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