hw3_001

hw3_001 - t = 0). Problem 4. The free surface of a liquid...

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ME220A 1 Homework 3 (due at 12:30 pm on November 14, 2011) Problem 1. Using the method of matched asymptotic expansion, solve ± ¨ y - ˙ y + y = 0 , with y (0) = 0 , y (1) = 1 , ± ± 1 . Compare with the exact solution. Problem 2. Develop a 2D version of the Kolmogorov-Obukhov theory of fully developed turbulence. Problem 3. Formulate and solve the problem of viscous diffusion of a vortex line (i.e. a line where vorticity is concentrated at the time
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Unformatted text preview: t = 0). Problem 4. The free surface of a liquid is one of constant pressure. If an incompressible uid is placed in a cylindrical vessel and the whole is rotated with constant angular velocity , show that the free surface becomes a paraboloid of revolution. Problem 5. Determine a scaling for the period of oscillations of a gas bubble produced by a deep explosion under water....
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