Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.Very very grateful!Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrowideas from gpt, but please do not believe its answer.Very very grateful! Four prototypical flow fields are expressed below in terms of Cartesian coordinates. In theseexpressions, y is a constant.i) Planar elongation:ii) Uniaxial extension:iii) Biaxial extension:iv) Pure rotation:For each of these flows, determine:v = ixe - jye, +0e₂v=2jxex - y e, - ize₂v = jxe + jy e, - 2jze.v = vyex - Ÿxẹ, +0e₂a) the rate of strain tensor € = / [Vy + Vy¹] andb) the deviatoric stress tensor + ² = 1 { [ Dy - D₂²].Based only on your answers to parts (a) and (b), determine:c) whether the flow is incompressible (i.e., is V · y = 0?)d) whether the flow is irrotational. (i.e., is V × v =v = 0 ?)

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Answered: Four prototypical flow fields are…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.Very very grateful!Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.Very very grateful!

Four prototypical flow fields are expressed below in terms of Cartesian coordinates. In these
expressions, y is a constant.
i) Planar elongation:
ii) Uniaxial extension:
iii) Biaxial extension:
iv) Pure rotation:
For each of these flows, determine:
v = ixe - jye, +0e₂
v=2jxex - y e, - ize₂
v = jxe + jy e, - 2jze.
v = vyex - Ÿxẹ, +0e₂
a) the rate of strain tensor € = / [Vy + Vy¹] and
b) the deviatoric stress tensor + ² = 1 { [ Dy - D₂²].
Based only on your answers to parts (a) and (b), determine:
c) whether the flow is incompressible (i.e., is V · y = 0?)
d) whether the flow is irrotational. (i.e., is V × v =
v = 0 ?)

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