hw_11 - Due: In class, Friday December 7, 2007 Name ME 521...

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Due: In class, Friday December 7, 2007 Name For instructor or TA use only: Problem Score Points 1 10 2 15 3 10 4 30 5 35 ME 521 Fall Semester, 2007 Homework Set # 11 Professor J. M. Cimbala Total: 100 1 . (10 pts) Consider creeping flow (Stokes flow) at freestream speed U over a body of characteristic length L . As discussed in class, we define nondimensional variables */ ii x xL = , uu U = , tt U L = , and p pL U μ = . ( a ) Show that the momentum equation (ignoring gravity) reduces to () 2 ** * * Re * * * i k ki k u p u tx x x ⎡⎤ ∂∂ += + ⎢⎥ ⎣⎦ * k x where Re UL ρ = . Show all your algebra for full credit. ( b ) Consider a small particle of characteristic length L = 10 μ m (microns) in air at 20 o C. How fast can the particle move such that the left-hand side of the above equation can be considered negligible? For consistency as an upper limit, assume that any term smaller than one order of magnitude less than the other terms is negligible. 2 . (15 pts) Text problem 6.6 . Do three parts: ( a ) Generate the expressions for u r and u θ .
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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.

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