Transcription of The Physical Basis of DIMENSIONAL ANALYSIS
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The Physical Basis of DIMENSIONAL ANALYSIS
1 The Physical Basis ofDIMENSIONAL ANALYSISAin A. SoninSecond Edition2 Copyright 2001 by Ain A. SoninDepartment of Mechanical EngineeringMITC ambridge, MA 02139 First Edition published 1997. Versions of this material have been distributed in Fluid Mechanics and other courses at MIT since picture by Pat Keck (Untitled, 1992)3 Contents1. Introduction12. Physical Quantities and quantities and base Unit and numerical Derived quantities, dimension, and dimensionless quantities Physical equations, DIMENSIONAL homogeneity, andphysical constants Derived quantities of the second of units Recapitulation 273.
Step 2: Dimensional considerations 30 Step 3: Dimensional variables 32 Step 4: The end game and Buckingham’s Π -theorem 32 3.2 Example: Deformation of an elastic sphere striking a wall 33 Step 1: The independent variables 33 Step 2: Dimensional considerations 35 Step 3: Dimensionless similarity parameters 36 Step 4: The end game 37
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