2.20 Problem Set 2A Name: ____________________ 1. The velocity vector field ),,(),,,(wvutzyxV=±is given by ktixyVˆˆ22+=±. At the point (-1,2,0) evaluate the following: (a)VV±±±××∇)((b)VV±±±)(∇⋅2. Stokes’ Theorem states that for a 2-sided surface Sin three dimensions having a closed curveCas its boundary, ±±⋅=×∇⋅SCldVdSVn²±±±)(ˆ.whereV±is a continuously differentiable vector function, nˆ is the unit normal to the chosen positve side of S, and ld±is in the corresponding positive direction along C.Verify the theorem using direct integration for the case where jxiyVˆˆ22+=±and Sis a circular disk of radius Rin the x-yplane having knˆˆ=.3. Suppose a fluid is rotating about an axis fixed in space at a constant angular velocity
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