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p0444

# p0444 - 4.44 CHAPTER 4 4.44 Chapter 4 Problem 44 Since the...

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Unformatted text preview: 4.44. CHAPTER 4, PROBLEM 44 417 4.44 Chapter 4, Problem 44 Since the flow is two dimensional, the equation defining a streamline is dy v -Cx/ (x2 + y 2 ) x = = =- 2 + y2) dx u Cy/ (x y Hence, rearranging terms, we have x dx + y dy = 0 Integrating once, we conclude that x2 + y 2 = constant As shown in Figure 4.15, this defines a family of concentric circles centered at the origin. This is a potential vortex. y ............... . . . . . . . . ...................... . ...................... .. .. . .... . .... .... . .... . . . ... ... . ... . ... . ... ... . . ... . ... .. .. . .. .. ............. .. .............. . .. . . .. . ... .. ... .... .. . .. .... .. . . ... ... . . ... . . .. . ... . .. . ... . .. ... . . .. . . .. .. . . . . . . . . .. . . .. . .... . . .. . ... . ... ... . . . . . . . . ... . ... . . ... . ... . . . . . .. . . . . .. . . ....................................... . . .. ........................................................ . . . . . .. .. . . . ................. . . . . . .. .. . . . . .. . .. . . . . .. . . . . . . . . .......... . . ... . ......... . . . . . . . . . .. . .. . . .. .. . . . . .. . .. .. .. . .. .. . . ... .. .. .. ... .. ... .. . .... ... .... .. ... . .. .. ................ ............... .. .. .. .. . ... . ... .. ... ... ... ... ... ... ... ... .... .... ... .... ....... ........ ........... ....... ....... .... = 1 d x2 + y 2 = 0 2 x Figure 4.15: Potential-vortex streamlines. ...
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