Fluid Flow. The streamlines associated with a certain fluid flow are represented by the family of curves y = x – 1 + ke-x. The velocity potentials of the flow are just the orthogonal trajectories of this family. (a) Use the method described in Problem 32 of Exercises 2.4 to show that the velocity potentials satisfy dx + (x -y) dy = 0.
[Hint: First express the family y = x -1 +ke –x in the form F (x,y) = k.]
(b) Find the velocity potentials by solving the equation obtained in part (a).
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