x cos z - xe cos y, y cos z, e² cos y) be the velocity field of a fluid. Compute the flux of v across the surface x² + y² + z² = 4 where x > 0 and the surface is oriented away from the origin. 2 Let v = (4

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
Let v = (4
xe cos y, y cos z, e² cos y) be
the velocity field of a fluid. Compute the flux of v across
the surface x² + y² + z²
surface is oriented away from the origin.
[₂₁
S
X COS Z
HINT: Call the surface in this problem S₁. S₁ is "open"
and does not enclose a 3D region, so Divergence
Theorem cannot be used directly to calculate the flux
across S₁.
-
Instead, try "capping" the S₁ with a disk S₂. Then the
surface formed by combining S₁ and S₂ is a "closed"
surfce S which does enclose a 3D region. Use the fact
that
F.dS=
= 4 where x > 0 and the
S₂
= [F-ds + [₁
S₂
F.dS
and calculate FdS by instead calculating
S₁
F. dS (using Divergence Theorem) and calculating
S
FdS (using the original formula).
Transcribed Image Text:Let v = (4 xe cos y, y cos z, e² cos y) be the velocity field of a fluid. Compute the flux of v across the surface x² + y² + z² surface is oriented away from the origin. [₂₁ S X COS Z HINT: Call the surface in this problem S₁. S₁ is "open" and does not enclose a 3D region, so Divergence Theorem cannot be used directly to calculate the flux across S₁. - Instead, try "capping" the S₁ with a disk S₂. Then the surface formed by combining S₁ and S₂ is a "closed" surfce S which does enclose a 3D region. Use the fact that F.dS= = 4 where x > 0 and the S₂ = [F-ds + [₁ S₂ F.dS and calculate FdS by instead calculating S₁ F. dS (using Divergence Theorem) and calculating S FdS (using the original formula).
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 13 images

Blurred answer
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,