1. For the following velocity fields, determine if they are possible for incompressible flows and if they are irrotational: (a) ▼ = î(x+y) + ĵ(x − y+ z) + k(x+y+3) (b) ▼ = î(xy) + ĵ(yz) + k(yz + z²) (c) ▼ = î[x(y + z)] + ĵ[y(x + z)] + Ê[−(x + y)z − z²] (d) V = î(xyzt) + ĵ(−xyzt²) + k[(z²/2)(xt² — yt)]
1. For the following velocity fields, determine if they are possible for incompressible flows and if they are irrotational: (a) ▼ = î(x+y) + ĵ(x − y+ z) + k(x+y+3) (b) ▼ = î(xy) + ĵ(yz) + k(yz + z²) (c) ▼ = î[x(y + z)] + ĵ[y(x + z)] + Ê[−(x + y)z − z²] (d) V = î(xyzt) + ĵ(−xyzt²) + k[(z²/2)(xt² — yt)]
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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![1. For the following velocity fields, determine if they are possible for incompressible flows
and if they are irrotational:
(a) ▼ = î(x + y) + ĵ(x − y + z) + Â(x + y + 3)
(b) ▼ = î(xy) + ĵ(yz) + Â(yz + z²)
(c) V = î[x(y +z)] + ĵ[y(x + z)] + k[−(x + y)z − z²]
(d) V = î(xyzt) + ĵ(−xyzt²) + k[(z²/2)(xt² — yt)]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4ed04b1a-8ef1-487d-ab34-a2261f9ce8a1%2Fb5700f20-683f-474b-a958-a6274a7b63b5%2Ffy22e86_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. For the following velocity fields, determine if they are possible for incompressible flows
and if they are irrotational:
(a) ▼ = î(x + y) + ĵ(x − y + z) + Â(x + y + 3)
(b) ▼ = î(xy) + ĵ(yz) + Â(yz + z²)
(c) V = î[x(y +z)] + ĵ[y(x + z)] + k[−(x + y)z − z²]
(d) V = î(xyzt) + ĵ(−xyzt²) + k[(z²/2)(xt² — yt)]
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