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# hw_08 - Due In class Friday November 2 2007 Name ME 521...

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Due: In class, Friday November 2, 2007 Name For instructor or TA use only: Problem Score Points 1 15 2 15 3 10 4 15 5 10 6 35 ME 521 Fall Semester, 2007 Homework Set # 8 Professor J. M. Cimbala Total: 100 1 . (15 pts) Consider the following velocity potential function for a steady, incompressible, irrotational, two-dimensional flow field in cylindrical ( r , θ ) coordinates: () 2 ,c a rU r r o s φ ⎛⎞ =+ ⎜⎟ ⎝⎠ , where a is a constant. ( a ) Write the Cauchy-Riemann conditions in r - coordinates, and then use them to generate an expression for stream function ψ ( r , ). ( b ) Sketch some streamlines and equipotential lines for this flow field. For consistency, use solid lines for the streamlines and dashed lines for the equipotential lines. [A neat hand-drawn sketch is acceptable, but some of you may prefer to generate the sketch electronically – also acceptable.] What kind of classical flow field does this model? Hint : There is something special about radius r = a ; calculate the value of stream function along r = a to help you interpret what kind of flow this represents. Note : Be sure to sketch streamlines and equipotential lines for both r < a and r > a . ( c ) Calculate velocity components u r and u for any arbitrary location ( r , ) in the flow field. Calculate velocity components u r and u along r = a , and calculate the minimum and maximum speed (magnitude of velocity) along r = a .

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hw_08 - Due In class Friday November 2 2007 Name ME 521...

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