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HW21solution - Supplements’ folder on the BlackBoard site...

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AAE 334 Fall 2011, Homework 21 SOLUTIONS Due Wednesday, November 2 at the beginning of class. We wish to find the value of upstream Mach number for which the downstream Mach number is one half of the upstream Mach number. Perform this work numerically: 1. Use the fzero function in Matlab and the NS_M2.m or NS_M1.m functions supplied last week. fzero is useful for many iterative solutions and is handy to know how to use. Hand in hard copy of your use of fzero and list the value of upstream Mach number that you found. 2. Check your work using the nearest value to your answer to part 1 in the Normal Shock Table. This is appendix B in your text or can be downloaded from the `Educational
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Unformatted text preview: Supplements’ folder on the BlackBoard site. Is your work in part 1 correct? The numerical answer can be found with one line of Matlab instruction: Mone = fzero( @(x) 0.5*x-NS_M2(x), 2) which gives the value 444 . 1 1 M This use of fzero seeks to zero the difference between half of the upstream Mach number, which is represented by 0.5*x , and the downstream Mach number, NS_M2(x) , near x = 2 . To verify, check the tables that you can download from the Blackboard site. The column for upstream Mach number has nearest value of 1.44 which gives downstream Mach number of 0.724, which checks pretty well....
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