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Unformatted text preview: Fluid Dynamics 3 2011/12 Sheet 6 Homework to be handed in 25th November: questions 2,3,4 1. (i) Show that in spherical polars, the potential of a uniform stream and of a dipole are (a) = Ur cos , and (b) =- cos r 2 , respectively. (ii) By using the expression for the Laplacian in spherical coordinates, confirm that each of these potentials satisfy Laplaces equation. (iii) Calculate u in spherical coordinates for each of the potentials. (iv) Verify that = Ur cos + A cos r 2 satisfies the boundary condition n = 0 on the surface of a sphere r = R for a suitably chosen A . 2. A sphere is moving with velocity U through an ideal, incompressible fluid, which is at rest at infinity. (i) Compute = ( A ) 1 r , where A is a constant vector, and show that 4 = 0. (ii) Placing x = 0 at the instantaneous centre of the sphere, compute the normal velocity u n u n on the surface. Determine A ....
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This note was uploaded on 01/20/2012 for the course MATH 33200 taught by Professor Eggers during the Fall '11 term at University of Bristol.
- Fall '11