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p0318

# p0318 - according to T = T − α z = ⇒ T = T α z So...

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3.18. CHAPTER 3, PROBLEM 18 267 3.18 Chapter 3, Problem 18 Yeager flew at an altitude of z = 43000 ft = 8.14 mi, which lies in the stratosphere. We have sufficient information to determine the temperature at this altitude, T 1 , on the day of his flight. That is, using the definition of the Mach number and the fact that the speed of sound, a ,isg ivenby a = γ RT ,wehave U = Ma = M ± γ RT 1 = T 1 = U 2 γ RM 2 The stratosphere temperature is constant in the U. S. Standard atmosphere, which extends downward to z 1 = 6.84 mi where it interfaces with the troposphere. In the troposphere,
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Unformatted text preview: according to T = T − α z = ⇒ T = T + α z So, since T = T 1 = U 2 / ( γ RM 2 ) at z = z 1 , the ground temperature is T = U 2 γ RM 2 + α z 1 We are given U = 700 mph = 1026.9 ft/sec, γ = 1.4, R = 1716 ft 2 /(sec 2 · o R), z = 6.84 mi. Also, α = 18.85 o R. Thus, T = (1026 . 9 ft / sec) 2 1 . 4 ² 1716 ft 2 / (sec 2 · R) = (1 . 06) 2 + (18 . 85 o R / mi) (6 . 84 mi) = 390 . 66 o R + 128 . 93 o R = 519 . 59 o R = 59 . 9 o F...
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