summary2 - Best invariants are not unique, some try and...

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Lecture 2 - summary R e v i e w : Galileo problem Pi-theorem (allows one to systematically approach the problem of expressing a physical situation in nondimensional variables) By means of dimensional analysis reduce the complexity of a problem from N+1 parameters to N+1-k parameters Procedure: Define physical problem (critical!) – define N+1 parameters that characterize the problem Set up exponent matrix – linear system; determine rank k Choose
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Unformatted text preview: Best invariants are not unique, some try and error you can always recombine invariants as power functions of others. If N = k , jackpot you have the solution (close to a multiplying constant) Application : Atomic bomb explosion pp. 8-15 in manuscript known known unknown D-analysis 10.5 9.5 8.5-3.0-2.0-1.0 log t 5 2 log r 5 2 1 2 E log r = log ( )+ log t ~8-4 Figure by MIT OpenCourseWare, adapted from Taylor, G. I. "Formation of a Blast Wave by a Very Intense Explosion. II. The Atomic Explosion of 1945." Proceedings of the Royal Society A 201 (1950): 175-186....
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