p0438 - 4.38. CHAPTER 4, PROBLEM 38 411 4.38 Chapter 4,...

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4.38. CHAPTER 4, PROBLEM 38 411 4.38 Chapter 4, Problem 38 0 Lx 0 H y Contour C d s = i dx d s = i dx d s = j dy d s = j dy ............... . . . . . . . . . . . . . . . . . . . . . . . . . . ...... ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................................................................ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .... Figure 4.10: Rectangular contour with differential direction vectors. In general, to evaluate a line integral, we treat the integral as the sum of conventional integrals on each segment of the contour, with the sign determined by the differential distance vector, d s . Hence, referring to Figure 4.10, we see that Γ = 8 L 0 u ( x, 0) · ( i dx )+ 8 H 0 u ( L,y ) · ( j dy ) + 8 L 0 u ( x,H ) · ( i dx 8 H 0 u (0 ,y ) · ( j dy ) = 8 L 0 [ u ( x, 0) u ( )] dx + 8 H 0 [ v ( ) v (0 )] dy Thus, for the given velocity vector,
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