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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

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 ρ 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....
View Full Document

This note was uploaded on 11/29/2011 for the course CIVIL 1.018j taught by Professor Markusbuehler during the Fall '08 term at MIT.

Ask a homework question - tutors are online