p0284

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

This preview shows pages 1–2. Sign up to view the full content.

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:

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

This note was uploaded on 02/09/2012 for the course AME 309 taught by Professor Phares during the Spring '06 term at USC.

Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online