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solution7 - 650:460 Aerodynamics Homework Assignment No 7...

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650:460 Aerodynamics Homework Assignment No. 7 Prof. Doyle Knight Tel: 732 445 4464, Email: [email protected] Office hours: Tues and Thur, 4:30 pm - 6:00 pm and by appointment Fall 2009 1

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Problem 8.1 The test section of the wind tunnel of Example 8.6 has a square cross section that is 1.22 m x 1.22 m. a) What is the mass flow rate of air through the test section for the flow conditions of the example ( i.e. , M = 3 . 5, p = 7 . 231 · 10 3 Pa, and T = 90 . 18 K) ? b) What is the volume flow rate of air through the test section ? Solution The mass flow rate is ˙ m = ρ U A . The cross sectional area A = (1 . 22) 2 m 2 = 1.4884 m 2 . The density is obtained from the ideal gas equation ρ = p RT = 7 . 231 · 10 3 (287)(90 . 18) = 0 . 2794 kg/m 3 2
Problem 8.1 The velocity is obtained from U = M a = M radicalbig γ RT = (3 . 5) radicalbig (1 . 4)(287)(90 . 18) = 666 . 24 m/s The mass flow rate is ˙ m = ρ U A = (0 . 2794)(666 . 24)(1 . 4884) = 277 . 1 kg/s The volume flow rate is ˙ V = U A = (666 . 24)(1 . 4884) = 991 . 6 m 3 /s 3

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Problem 8.2 A practical limit for the stagnation temperature of a continuously operating superosnic wind tunnel is 1000 K. With this value for the
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