Ae312_spring_2008_midterm_1 - Prof. Daniel J. Bodony AE312,...

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Unformatted text preview: Prof. Daniel J. Bodony AE312, Spring 2008 Midterm #1 In class, February 22, 2008 Instructions: You have 50 minutes to complete this exam. Show all work and use the supplemental material provided. You will be primarily graded on your demonstation of logic in solving the problems. Name: Date: Student code: I agree to abide by the University of Illinois Student Code. I attest that the work on this exam is my own. Sign: Problem 1 Air is flowing in a highly insulated constant-area duct (see sketch below) where, at station 1, the following data apply: M1 = 0.3 T 1 = 60 C p1 = 1.8 105 Pa (abs) If the duct area is A = 0.04 m2 and, at section 2, the Mach number is 0.7, (a) Find the mass flow rate, m. (b) Derive the expression for the drag D on the duct between sections 1 and 2. State all of your assumptions. (c) Evaluate your drag expression from (b) using the data from this problem. 11111111111111111111111111111 00000000000000000000000000000 11111111111111111111111111111 00000000000000000000000000000 11111111111111111111111111111 00000000000000000000000000000 1 0 1 0 1 0 1 0 M1 1 0 1 0 Control volume 1 0 1 0 M T0 1 1 0 1 2 1 0 1 0 p0 1 0 1 1 11111111111111111111111111111 00000000000000000000000000000 1 0 1 0 11111111111111111111111111111 00000000000000000000000000000 1 0 11111111111111111111111111111 00000000000000000000000000000 1 Figure 1: Schematic for Problem 1. 2 Problem 2 A ground-level explosion causes a blast wave to propagate into still air at 14.7 psi (abs) and 70 F. A recording instrument on the ground registers a maximum gage pressure of 100 psi as the wave passes. Considering the wave as a traveling shock, (a) Show that the expression for the speed of the shock, V s , is V s = a1 - 1 p2 + 1 + 2 p1 2 1/2 where p1 is the static pressure ahead of the shock, p2 is the static pressure behind the shock, a1 is the speed of sound ahead of the shock, and is the specific heat ratio. (b) Evaluate (a) for the speed of the shock, in m/s. (c) Determine the wind speed, u, following the shock, in m/s. Blast wave 1111111111111111111111111111111111 0000000000000000000000000000000000 1111111111111111111111111111111111 0000000000000000000000000000000000 Just after explosion Pressure recorder p1 Vs Explosion u 11111111111111111111111111111111111 00000000000000000000000000000000000 11111111111111111111111111111111111 00000000000000000000000000000000000 11111111111111111111111111111111111 00000000000000000000000000000000000 After shock passes recorder Pressure recorder p2 Figure 2: Schematic for Problem 2. ...
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