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Question 2. (i) In a particular fluid, the Eulerian velocity is given by U2 = (2xz, 2xyz, −z²)e¯*. Show that this velocity u2 represents an incompressible flow. (ii) Show also that, in this flow u2, p is constant for a material particle (that is DP = 0), for a density field p of the form p = f(s) where s = x², for any function f(s). [Hint: You will need to use the Chain Rule; for instance θρ dp მs - dx ds Ox

Question 2. (i) In a particular fluid, the Eulerian velocity is given by U2 = (2xz, 2xyz, −z²)e¯*. Show that this velocity u2 represents an incompressible flow. (ii) Show also that, in this flow u2, p is constant for a material particle (that is DP = 0), for a density field p of the form p = f(s) where s = x², for any function f(s). [Hint: You will need to use the Chain Rule; for instance θρ dp მs - dx ds Ox

Elements Of Electromagnetics
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.

and and Very very grateful!

Question 2. (i) In a particular fluid, the Eulerian velocity is given by U2 = (2xz, 2xyz, −z²)e¯x Show that this velocity u₂ represents an incompressible flow. (ii) Show also that, in this flow u2, p is constant for a material particle (that is field p of the form p = f(s) where s = xz², for any function f(s). [Hint: You will need to use the Chain Rule; for instance др dp ds = dx ds Ox Dt = = 0), for a density
Transcribed Image Text:Question 2. (i) In a particular fluid, the Eulerian velocity is given by U2 = (2xz, 2xyz, −z²)e¯x Show that this velocity u₂ represents an incompressible flow. (ii) Show also that, in this flow u2, p is constant for a material particle (that is field p of the form p = f(s) where s = xz², for any function f(s). [Hint: You will need to use the Chain Rule; for instance др dp ds = dx ds Ox Dt = = 0), for a density
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