p1008 - 1080 CHAPTER 10. VORTICITY AND VISCOSITY 10.8...

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1080 CHAPTER 10. VORTICITY AND VISCOSITY 10.8 Chapter 10, Problem 8 x = x o x = x o + x y x h ............................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........................................ .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........................... . . . . . .............................................. . . . . . . ......................................................... . . . . . . ............................................................. . . . . . . ................................................................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Figure 10.1: Viscous flow near a solid boundary—velocity profile shown is for K = 1 2 . By definition, the circulation is Γ = - C u · d s where we use the standard mathematical convention that integration is positive in the counterclockwise direction. x o x o + x x 0 h y Contour C d s = i dx d s = i dx d s = j dy d s = j dy ............... . . . . . . . . . . . . . . . . . . . . . . . . . . ...... ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................................................................ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... Figure 10.2: Rectangular contour with differential direction vectors. 10.8(a): In general, to evaluate a line integral, we treat the integral as the sum of
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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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p1008 - 1080 CHAPTER 10. VORTICITY AND VISCOSITY 10.8...

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