# hw_09 - Due In class Friday November 9 2007 Name ME 521...

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Due: In class, Friday November 9, 2007 Name For instructor or TA use only: Problem Score Points 1 15 2 15 3 20 4 20 5 15 6 15 ME 521 Fall Semester, 2007 Homework Set # 9 Professor J. M. Cimbala Total: 100 1 . (15 pts) Text problem 3.8 . Note : Draw a sketch of a 3-D fluid element of dimensions ( dr , rd θ , dz ), then analyze the three components individually, one face at a time. Check your answers with those given in Appendix B1. 2 . (15 pts) Consider the incompressible Navier-Stokes equation in planar (2-D) polar coordinates, as given in Appendix B2. Notice that the viscous term, , contains some “extra” terms, involving 2 u ν G 2 r u r and 2 2 r u r . Have you ever wondered where these extra terms come from? Now you will find out. ( a ) Show that unit vectors and e r e JJG are functions of , and that in fact / r ee ∂ ∂= JJ GJ G J and / r ∂∂ = G J . ( b ) Expand the viscous term carefully, using rr uu e u e =+ G J G , and show that the equations in Appendix B2 are indeed correct, including the “extra” terms.
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