p0446 - 4.46. CHAPTER 4, PROBLEM 46 419 4.46 Chapter 4,...

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Unformatted text preview: 4.46. CHAPTER 4, PROBLEM 46 419 4.46 Chapter 4, Problem 46 Since the flow is two dimensional, the equation defining a streamline is dy v −Cy y == =− dx u Cx x Hence, rearranging terms, we have dx dy + =0 x y =⇒ d n(xy ) = 0 Integrating once, we conclude that xy = constant As shown in Figure 4.17, this defines a family of hyperbolas. This flow is known as stagnation-point flow. . . . . . .. . .. . .. .. .. . .. . . .. ... . .. ... . . .. ... ... . .. . . . .. ... .. ... . . . ... .. ... . .. ... ... . .. .. .. ... ... . ... ... ... .. ... . . .. . ... ... ... .. ... .... .. . ... .... .. ... ... ... .... . . .... .. ... ... ...... . .. ... .... ... ...... .. .... . . . .. .... .... .. .. .... .... ... .... ... .... ... . ... ..... ... ... ..... ... ..... .. .. ... .. ..... .. .. ....... ... ... ...... ...... .... .... .... .... .. .. ..... ..... ..... ...... ...... ... ... ....... ........ ........ . .. ... ... ........... ........... . . .. ... ... ..... ..... . y ... ... .. .. .. . . .. .. . .. .. . . .. . .. .. .. . ... . ... . .. . .. . ... ... . . .. . .. ... ... . . .. . ... .. ... . . ... . .. ... .. . . ... .. ... .. .. .. ... ... ... ... .. ... ... .. ... ... ... ... .. ... .... ... .... .. ... .... .... ... .. .. .... .. ... .... .. ... .. ..... ... .... .. ...... ... . .... .... .. .. .... .... .. .. .... .... ... ... .... .... ... ... ..... ..... ... ... ..... ..... . ... ... ....... ....... . .... .... .. ..... ..... .... .... .... ..... ..... ..... ...... ...... ....... ....... ........ ........ ............. ........... .. .. . .. ...... s Figure 4.17: Stagnation-point flow streamlines. ... .. ...... ... ..... x ...
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This note was uploaded on 02/09/2012 for the course AME 309 taught by Professor Phares during the Spring '06 term at USC.

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