p0444 - . . . . . . . . . . . . . . . . . . . . . . . . . ....

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
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 . . . . . . . . . . . . . . . . . . ....... . . . . . . . . . . . . . . . . . . ....... ....... ....... . . . . . . . . . . . . ....... . . . . . . . . . . . . ....... . . . . . . . . . . . . . . . . ...... ....... . . . . . . ..... . ....... . . . . . . ... . . ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................... . . . . . . . . . . . . . . . . . . . .. ............................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x y s...
View Full Document

Ask a homework question - tutors are online