# hw_03 - Due: In class, Friday September 21, 2007 Name ME...

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Due: In class, Friday September 21, 2007 Name For instructor or TA use only: Problem Score Points 1 10 2 20 3 15 4 10 5 45 ME 521 Fall Semester, 2007 Homework Set # 3 Professor J. M. Cimbala Total: 100 1 . (10 pts) Text problem 2.2 . Note : First re-write the tensor notation equation into vector notation form. Then make arguments based on the definitions of dot and cross product, and the right-hand rule. Be sure to include sketches to support your arguments. Note : To be more precise, the problem statement should read “Show that a necessary condition…”. In other words, this is a necessary condition, but not a sufficient condition since we can think of situations in which the equation is satisfied even though the three vectors are not coplanar. 2 . (20 pts) Text problem 3.4 . For consistency, use tensor notation for your algebra where possible. Do five parts to the problem as shown: ( a ) Find the linear strain rates. ( b ) Find the rates of shear strain and write out the entire strain rate tensor. Be careful with the factor of 2. ( c ) Find the vorticity. Is this an irrotational flow? ( d ) Find the stream function (There may be a factor of 2 error in the answer given in the text). Sketch a few streamlines.

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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 Penn State.

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hw_03 - Due: In class, Friday September 21, 2007 Name ME...

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