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Due: In class, Friday September 28, 2007 Name For instructor or TA use only: Problem Score Points 1 15 2 10 3 10 4 15 5 10 6 40 ME 521 Fall Semester, 2007 Homework Set # 4 Professor J. M. Cimbala Total: 100 1 . (15 pts) Text problem 2.1 . 2 . (10 pts) In class, Cauchy’s equation was derived for deformation of any medium, fluid or solid. We then applied Stokes’ assumptions to generate the famous Navier-Stokes equation. Based on this derivation, it would seem that the final equation might be more properly called the Cauchy-Stokes equation . Look up some references on the history of this equation, and explain the role of Navier. Provide a brief discussion of the history of the Navier-Stokes equation, along with a list of reference(s) used. 3 . (10 pts) Text problem 4.1 . 4 . (15 pts) Consider a small fluid element in the x 1 - x 2 plane, as sketched to the right. ( a ) Use Stokes theorem (see Chapter 2) to find the x 3 component of vorticity. ( b ) Read Section 3.8 in Kundu’s text. As the fluid element above shrinks to zero size, does the second-to-last sentence of Section 3.8 hold?
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This note was uploaded on 07/23/2008 for the course ME 521 taught by Professor Cimbala during the Fall '07 term at Pennsylvania State University, University Park.
- Fall '07