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Unformatted text preview: v x and v y , as well as the cylindrical components v r (radial component) and v (tangential coordinate). Assign numerical values to all components. 4. The flow of a fluid past a wedge is described by the potential ( r, ) = cr sin , where c and are constants, and ( r, ) are the cylindrical coordinates of a point in the fluid (the potential is independent of z ). Verify that this function satisfies Laplaces equation, 2 = 0 . 5. Expand the function y ( x ) = e x sin x in a Taylor series about x = 0 , keeping the first 2 nonzero terms. 6. Solve the ordinary differential equation (cylindrical coordinates) 1 r d d r r d v z d r = C, where C is a constant, subject to the boundary conditions v z = 0 at r = R (0 < < 1) , v z = 0 at r = R. Here, and R are also constants. 1...
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- Spring '10