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Let v = (x²z, 2 –— 2xyz − 3y + x²y, 3z − x²z) be the velocity field of a fluid. Compute the flux of across the surface x² + y² + z² = 9 where y> 0 and the surface is oriented away from the origin.

Let v = (x²z, 2 –— 2xyz − 3y + x²y, 3z − x²z) be the velocity field of a fluid. Compute the flux of across the surface x² + y² + z² = 9 where y> 0 and the surface is oriented away from the origin.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let **\(\vec{v} = \langle x^2 z, 2 - 2xyz - 3y + x^2 y, 3z - x^2 z \rangle\)** be the velocity field of a fluid. Compute the flux of **\(\vec{v}\)** across the surface **\(x^2 + y^2 + z^2 = 9\)** where **\(y > 0\)** and the surface is oriented away from the origin. Hint: Use the Divergence Theorem.
Transcribed Image Text:Let **\(\vec{v} = \langle x^2 z, 2 - 2xyz - 3y + x^2 y, 3z - x^2 z \rangle\)** be the velocity field of a fluid. Compute the flux of **\(\vec{v}\)** across the surface **\(x^2 + y^2 + z^2 = 9\)** where **\(y > 0\)** and the surface is oriented away from the origin. Hint: Use the Divergence Theorem.
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