12 and therefore represent a second order tensor 6

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Unformatted text preview: 2), and therefore represent a second-order tensor. 6 presents transformation of one set of ortogonal axes into another. ow that for a second-order tensor A, the following thee quantities 5. Sh Ch 2: Problem 5 arant under the rotation of axes: II = A¡¡ I A. A33 A3Ai Al31 A12 /z = I Aii1 A2I2+ A322 A23/ + I 1 iA33 A2 13 = det(A¡j). 7 Ch. 2 Question 10 8 Ch. 2 Question 10 9 Ch. 2 Question 10 10 Ch. 2 Question 11 11 Ch. 2 Question 11 12 Ch. 2 Question 11 13 Kinematics of Fluid Flow (Ch. 3) 1. Streamlines, pathlines, and convective (material) derivative 2. Translations, Deformation, and Rotation of a fluid element (Cauchy-Stokes Decomposition) 14 Kinematics of Fluid Flow (Ch. 3) 15 Eulerian Description (Field Variables) 16 Time Derivatives “advective” + “unsteady” 17 Streamlines and Pathlines 18 Streamlines and Pathlines (cont.) y Streamlines 8 Blue, t 4 and Pathlines Red, 0 t 4 7 6 5 4 3 2 1 2 4 6 8 10 12 14 x 19 l-Ù 'v ~ - .J ~ ~ lU ~ V' Streaklines or “Smoke Lines” .. i. .~ ~ ~ '- :j il '\...
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This document was uploaded on 02/28/2014 for the course PHYS 4200 at Columbia.

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