ps_2a - 2.20 Problem Set 2A Name 1 The velocity vector...

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2 . 2 0 Problem Set 2A Name: ____________________ 1. The velocity vector field ) , , ( ) , , , ( w v u t z y x V = ± is given by k t i xy V ˆ ˆ 2 2 + = ± . At the point (-1,2,0) evaluate the following: (a) V V ± ± ± × × ) ( (b) V V ± ± ± ) ( 2. Stokes’ Theorem states that for a 2-sided surface S in three dimensions having a closed curve C as its boundary, ±± = × SC l d V dS V n ² ± ± ± ) ( ˆ . where V ± is a continuously differentiable vector function, n ˆ is the unit normal to the chosen positve side of S , and l d ± is in the corresponding positive direction along C . Verify the theorem using direct integration for the case where j x i y V ˆ ˆ 2 2 + = ± and S is a circular disk of radius R in the x-y plane having k n ˆ ˆ = . 3. Suppose a fluid is rotating about an axis fixed in space at a constant angular velocity
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