Consider the velocity field F(x, y, z) = (x+ 5VÝ,y – 10x³, z). Let S be the portion of 2x – y – 5z = 0 bounded by x = 4 in the first octant. (a) Find the flux of a fluid with velocity F as it flows through S with a positive orientation. (b) Let C be the boundary of S. Set-up a surface integral equal to F- dR.
Consider the velocity field F(x, y, z) = (x+ 5VÝ,y – 10x³, z). Let S be the portion of 2x – y – 5z = 0 bounded by x = 4 in the first octant. (a) Find the flux of a fluid with velocity F as it flows through S with a positive orientation. (b) Let C be the boundary of S. Set-up a surface integral equal to F- dR.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter8: Further Techniques And Applications Of Integration
Section8.3: Volume And Average Value
Problem 12E
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Transcribed Image Text:Consider the velocity field F(x, y, z) = (r + 5/ỹ, y – 10r³, 2). Let S be the portion
of 2x – y – 5z = 0 bounded by x = 4 in the first octant.
(a) Find the flux of a fluid with velocity F as it flows through S with a positive
orientation.
(b) Let C be the boundary of S. Set-up a surface integral equal to
F. dR.
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