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University of Alabama, Huntsville *

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755

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Mechanical Engineering

Date

Nov 24, 2024

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1

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Example 4b: F-35 Speed Calculation * Consider the F-35 flying at sea level, p = 1 atm. The pitot tube measures 4.0 atm. Determine the Mach number. * We are given p = 1 atm and p, = 4.0 atm P ?/ftm pressure is the * First, is the flow subsonic or supersonic? iR i b * Use 1sentropic ratio for M = 1: Do —1 7-1 'ConsidermeFJS.flying at sea evel, =114+ M2 = 0.528 =1 atm. The piot tube measures p 2 40 atm. Determin the Mach number * For a pressure ratio greater than this, flow is supersonic * For our problem, p,/p = 4.0, so we must solve the Rayleigh Pitot Tube Formula, iteratively P.s _( (v + 1)?M} )W X (1 —y+ 2yM%) 1 \4yM{-2(y—1) y+1 Bisection Method # a b |(b-a2| p fa) fip) f{a)*f(p) 1 | 1.0000 | 6.0000 [2.50000| 3.5000| 2.1071 | -42.8152 | -90.2147 2 | 1.0000 | 3.5000 [ 1.25000| 2.2500 | 2.1071 | -12.2420 | -25.7948 3 | 1.0000 | 2.2500 [ 0.62500| 1.6250 | 2.1071 -3.0018 | -6.3251 4 [1.0000(1.6250(0.31250| 1.3125| 2.1071 0.0928 0.1956 5 | 1.3125|1.6250 [ 0.15625| 1.4688 | 1.2460 0.0928 0.1157 6 |1.4688(1.6250(0.07813|1.5469| 0.7035 0.0928 0.0653 Secant Method # po pl q0 ql p p-pl 1 1.4688 1.6250 0.7035 0.0928 1.6488 | 2.38E-02 2 1.6250 1.6488 0.0928 -0.0058 | 1.6474 |-1.40E-03 3 1.6488 1.6474 -0.0058 0.0000 1.6474 | 1.01E-05 * [teratively, we find that M = 1.6474 * You are encouraged to modify the Python version of your Nonlinear solver code to solve this problem ....
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