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hw_07 - Due In class Friday Name ME 521 Fall Semester 2007...

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Due: In class, Friday October 26, 2007 Name For instructor or TA use only: Problem Score Points 1 15 2 15 3 20 4 50 ME 521 Fall Semester, 2007 Homework Set # 7 Professor J. M. Cimbala Total: 100 1 . (15 pts) Text problem 3.7 . Do two parts, i.e. split the stream function into an inner and outer part, and match the two at r = R . For consistency, assume ψ = 0 at the origin. ( a ) Calculate ψ for r R . ( b ) Calculate ψ for r R . 2 . (15 pts) Text problem 4.7 . Note: Stay in variables until the end. Please start with the control volume form of the linear momentum equation, as given in class. 3 . (20 pts) Text problem 5.4 . Do two parts to this problem: ( a ) Find the vortex path, as asked for in the text. ( b ) Sketch the path of a vortex which passes through location ( x = 1, y = 1), and has positive circulation Γ . Indicate the direction of movement along the path. 4 . (50 pts) Consider a viscous, incompressible, Newtonian fluid, initially at rest. An infinitely long solid cylinder of radius R (infinitely long in the z -direction out of the page) starts rotating at constant angular
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