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p1028

p1028 - 1354 CHAPTER 10 VORTICITY VISCOSITY LIFT AND DRAG...

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1354 CHAPTER 10. VORTICITY, VISCOSITY, LIFT AND DRAG 10.28 Chapter 10, Problem 28 Problem: The horizontal speed, u , of a baseball thrown by a professional baseball pitcher is accurately approximated by the equation mdu/dt = π 8 ρ D 2 C D u 2 , where m , D and C D are the ball’s mass, diameter and drag coefficient, respectively. Also, ρ is the density of air. (a) If C D is constant, the distance from the pitcher’s mound to home plate is f and the pitcher releases the ball with a speed u o , verify that the time for a baseball to travel from pitcher to batter is t = 8 m πρ D 2 C D u o ± e πρ D 2 C D f / (8 m ) 1 = (b) Consider two pitchers, one with a 90-mph fastball and the other with a 100-mph fastball. Referring to Figure 10.9, convince yourself that C D 0 . 40 and 0 . 20 for 90-mph and 100-mph fastballs, respectively. D = 3 inches and the kinematic viscosity of air is ν = 1 . 62 · 10 4 ft 2 /sec. NOTE: The rapid drop in C D occurs because of the so-called drag crisis . Assume that, because of the a baseball’s

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