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p0444

# p0444 - x y s

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4.44. CHAPTER 4, PROBLEM 44 533 4.44 Chapter 4, Problem 44 Problem: Consider the flowfield whose velocity is given by u = Cx i Cy j ,whe re C is a constant of dimensions 1 /T . Derive an equation defining the streamlines for this flow. Sketch a few streamlines for the upper half plane, i.e., for y> 0 . Indicate f lowd irec t iononthes tream l inesfo r C> 0 . Solution: Since the flow is two dimensional, the equation defining a streamline is dy dx = v u = Cy Cx = y x Hence, rearranging terms, we have dx x + dy y =0 = d f n ( xy )=0 Integrating once, we conclude that xy = constant . . . . . . . . . . . . . . . . . . ....... . . . . . . . . . . . . . . . . . . ....... ....... ....... . . . . . . . . . . . . ....... . . . . . . . . . . . . ....... . . . . . . . . . . . . . . . . ...... ....... . . . . . . ..... . ....... . . . . . . ... . . ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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