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EGN 5456 Homework 5 Fall 1996

1. Solve 5.25 of the book.
2. Solve 5.27b of the book.
3. Solve 5.29 of the book.
4. Solve 5.23 of the book.
5. Solve 5.34 of the book. (In fluid mechanics terms, both solutions have a shock coming from x=1. The first solution has an 'expansion shock' coming from the origin and the second an expansion fan.)
6. Solve 5.31a in the book.
7. (5.22 generalized.) The Euler equations of 2D steady compressible, inviscid, nonconducting flow are:

   

   

   

   

   Classify this system after rewriting the last equation as

   

   where . Give the directions of the characteristic lines. Show that one family of characteristics corresponds to the streamlines of the flow. Write the two compatibility conditions corresponding to the streamlines and show that one expresses conservation of entropy along the streamlines while the other gives the compressible Bernoulli law.