p0862

p0862 - 8.62. CHAPTER 8, PROBLEM 62 975 8.62 Chapter 8,...

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975 8.62 Chapter 8, Problem 62 Figure 8.14: Supersonic flow through a nozzle. Because γ W =1 . 4 , we cannot use the isentropic-flow and normal-shock tables. Rather, we must use the appropriate algebraic relations as needed. 8.62(a): We are given the pressure ahead of the shock and the Mach number behind the shock. First, we note that the Mach numbers are related by M 2 2 = 1+ γ 1 2 M 2 1 γ M 2 1 γ 1 2 However, a straightforward algebraic exercise shows that this equation is valid with the subscripts interchanged, wherefore M 2 1 = 1+ γ 1 2 M 2 2 γ M 2 2 γ 1 2 This is more convenient as we can solve directly for M 1 . Using the given value of M 2 = 0.7, there follows M 2 1 = 1+ p 1 . 28 1 2 Q (0 . 7) 2 1 . 28(0 . 7) 2 p 1 . 28 1 2 Q =2 . 1933 = M 1 =1 . 4810 Turning to the pressure, the appropriate normal-shock relation is p 2 p 1 =1+ 2 γ γ +1 p M 2 1 1 Q =1+ 2(1 . 28) 1 . 28 + 1 ± (1 . 4810) 2

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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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p0862 - 8.62. CHAPTER 8, PROBLEM 62 975 8.62 Chapter 8,...

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