hw_1 - Stokes equations Problem 5 Everybody knows from...

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Problem Set #1 ME 152B Winter, 2008 Due 5pm Friday, Jan 16 Reading: Munson, et al, Chapter 4, Sections 4.1(all), 4.2.1, 4.2.2, 4.2.3: Chapter 6, Sections 6.1.1, 6.1.2, 6.3(all) 6.4.1, 6.8: Chapter 7 (all) but especially 7.1, 7.2, 7.10 Problem 1 . Work Problem 4.21 and then answer this question: Why is there an acceleration when the flow is steady? Problem 2. Work Problem 4.28. Problem 3. Work Problem 4.34. Note that this problem teaches you that the time rate of change of a quantity depends both on the location and the velocity at which you measure/observe it. Problem 4. Work Problem 6.72. Hints: part (a) is an application of the continuity equation : for part (b), remember that acceleration is a vector, and for part (c), use the x-component of the Navier-
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Unformatted text preview: Stokes equations. Problem 5. Everybody knows from freshman physics that the period, T, of a simple pendulum depends on its length, L, and the Earth’s gravitational acceleration, but is independent of its mass. We can show this simply using dimensional analysis. The variable list is T, L, g and (possibly) m. (a) Using this list of variables, apply the Buckingham Pi theorem to prove this result, i.e. prove that the period is independent of the mass. (b) Form a dimensionless Pi group involving T, g and L, and use the result that there is only one Pi group to show that T = C (L/g) 1/2 , where C is a constant. Problem 6. Work Problem 7.10 Problem 7. Work Problem 7.11...
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