p0284 - (a) Since the ball diameter is the same for model...

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282 CHAPTER 2. DIMENSIONAL ANALYSIS 2.84 Chapter 2, Problem 84 Problem: To analyze the dynamics of a golf ball, wind-tunnel tests are proposed for a full-scale ball in a tunnel whose maximum flow speed is U m = 140 ft/sec. The temperature of the tunnel air supply can be adjusted to change the viscosity, μ m . A professional golfer can hit a ball at U p = 210 ft/sec with an angular velocity of ω p =24sec 1 . Dimensional analysis shows that dynamic similitude can be achieved by matching Strouhal and Reynolds numbers, St ω D/U and Re ρ UD/μ ,whe re ρ is fluid density and D = 1.67 in is the diameter of a golf ball. (a) If the air density for model and prototype is the same, what must ω m and μ m be? (b) Assuming μ T 0 . 68 and T p =75 o F, what must the wind-tunnel temperature be? Solution:
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Unformatted text preview: (a) Since the ball diameter is the same for model and prototype, necessarily m D m U m = p D p U p = m = p U m U p m U m D m m = p U p D p p = m = p U m U p We are given U m = 140 ft/sec and U p = 210 ft/sec. Thus, U m U p = 140 ft / sec 210 ft / sec = 2 3 Hence, since p = 24 sec 1 , we conclude that m = 16 sec 1 and m = 2 3 p 2.84. CHAPTER 2, PROBLEM 84 283 (b) If we assume the viscosity follows a power-law, then the viscosity ratio is m p = X T m T p ~ . 68 = T m T p = X m p ~ 1 . 47 Hence, for the conditions of Part (a), we must have T m = w 2 3 W 1 . 47 T p = 0 . 55 T p We are given T p = 75 o F = 534.67 o R. Therefore, T m = 0 . 55(534 . 67 o R) = 294 . 1 o R 166 o F...
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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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p0284 - (a) Since the ball diameter is the same for model...

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