HW 8 - 11/20/09 Professor Philip S. Marcus ME106 Problem...

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11/20/09 Professor Philip S. Marcus ME106 Problem Set 8 Due in class November 30, 2009 Read Munson Chapter 7 Dimensional Analysis, Similitude and Modeling . Be sure to read about “Reynolds number similarity”, and do problems 7.34, 7.37, 7.61, 7.63, 7.69 and 7.72. Students who do problem number 7.7 on page 235 will automatically fail the course. Do the following “O” problems. I have included one review problem about Archimedes to remind ourselves that Final Exams are on December 12. O1) Blowing with velocity v across the top of an empty Coke TM bottle (that holds 8 ±uid ounces when ²lled), I can produce sound – a musical note with frequency f = 440 cycles/second. Note that the Mach number m ≡ | v | /c 1, where c is the speed of sound. Experimentation shows that | v | has little or no e³ect upon the frequency of the the note that is produced (although, when it is too large or too small, no sound is produced). I now blow across the top of a new, larger Coke bottle with the same geometric proportions as the ²rst. This bottle holds 64 ±uid ounces. A note with a new frequency is produced. What is the frequency? Use dimensional analysis. Show your work. 1
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l l 2 H O U ± ² z zD ³ 0 z L A atm P Figure 1: The balance is balanced. O2) Archimedes’ brother-in-law suspended two pieces of gold from the balance shown in the ±gure. Both pieces of gold had the same density, mass and volume. The gold
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HW 8 - 11/20/09 Professor Philip S. Marcus ME106 Problem...

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