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Unformatted text preview: 650:460 Aerodynamics Homework Assignment No. 1 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 Problem 1.6 Nitrogen is often used in wind tunnels as the test gas substitute for air. Compare the value of the kinematic viscosity ν = μ/ρ for nitrogen at a temperature of 350 deg F and 150 psia with that for air at the same conditions. Solution Converting to consistent English units, p = 2 . 16 · 10 4 lbf/ft 2 and T = 809 . 67 deg R. The gas constant for air is R = 1716 ft 2 /s 2 · deg R. The density of air is obtained from the ideal gas equation ρ = p RT = 2 . 16 · 10 4 1716 · 809 . 67 = 1 . 5546 · 10 2 slug/ft 3 Note that lbf = slug · ft/s 2 2 Problem 1.6 The dynamic molecular viscosity for air is μ = 2 . 27 · 10 8 T 1 . 5 T + 198 . 6 = 2 . 27 · 10 8 (809 . 67) 1 . 5 (809 . 67 + 198 . 6) = 5 . 187 · 10 7 lbf · s/ft 2 Thus, the kinematic viscosity for air is ν = 5 . 187 · 10 7 1 . 5546 · 10 2 = 3 . 337 · 10 5 ft 2 /s 3 Problem 1.6 The gas constant for nitrogen is R = 1774 ft 2 /s 2 · deg R. The density of nitrogen is obtained from the ideal gas equation ρ = p RT = 2 . 16 · 10 4 1774 · 809 . 67 = 1 . 504 · 10 2 slug/ft 3 The dynamic molecular viscosity for nitrogen is μ = 2 . 16 · 10 8 T 1 . 5 T + 183 . 6 = 2 . 16 · 10 8 (809 . 67) 1 . 5 (809 . 67 + 183 . 6) = 5 . 010 · 10 7 lbf · s/ft 2 Thus, the kinematic viscosity for nitrogen is ν = 5 . 010 · 10 7 1 . 504 · 10 2 = 3 . 331 · 10 5 ft 2 /s 4 Problem 1.8 A perfect gas undergoes a process whereby the pressure is doubled and its density is decreased to threequarters of its original value. If the initial temperature is 200 deg F, what is the final temperature in deg F ? in deg C ? Solution Converting the temperature to absolute units, the initial temperature is T 1 = 659 . 67 deg R. From the perfect gas equation p 1 = ρ 1 RT 1 and p 2 = ρ 2 RT 2 Thus, p 2 p 1 = ρ 2 T 2 ρ 1 T 1 and T 2 T 1 = p 2 p 1 ρ 1 ρ 2 = 2 . 75 = 2 . 667 Thus, T 2 = (2 . 667)(659 . 67) = 1759 deg R and T 2 = 1299 deg F=704.1 deg C 5 Problem 1.24 A Utube manometer is used to measure the pressure at the...
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 Spring '09
 Knight
 Fluid Dynamics, dy dx dx

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