p0216 - U 2 A = 8 F U 2 D 2 where we use the fact that A =...

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2.16. CHAPTER 2, PROBLEM 16 125 2.16 Chapter 2, Problem 16 2.16(a): The dimensions of F , μ , ρ , D and U are [ F ]= ML T 2 , [ μ ]= M LT , [ ρ ]= M L 3 , [ D ]= L, [ U ]= L T Thus, the two terms in the Stokes-Oseen formula have the following dimensions. [ μUD ]= M LT L T L = ML T 2 ± ρ U 2 D 2 = = M L 3 L 2 T 2 L 2 = ML T 2 Since both terms have dimensions of force, the equation is dimensionally homogeneous. 2.16(b): By definition, the drag coefficient is C D = F 1 2 ρ U
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Unformatted text preview: U 2 A = 8 F U 2 D 2 where we use the fact that A = 4 D 2 . Hence, from the Stokes-Oseen equation, C D = 8 3 UD + 9 16 U 2 D 2 U 2 D 2 = 24 UD + 9 2 Finally, introducing the Reynolds number, Re = UD/ , and rearranging terms a bit, we arrive at C D = 24 Re } 1 + 3 16 Re ]...
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This note was uploaded on 10/12/2009 for the course AME 309 at USC.

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