Question 4. Consider the speed field i = æzî – yj + a²yk and the surface s given by the paraboloid of revolution given by the equation z = 1 – x² – y² in the first octant. (a) Draw the surface described above. (b) directly calculate the circulation of i along the path C defined by the intersection of the paraboloid and the planes x = 0, y = 0 and z = 0, traveled counterclockwise to an observer on the first octant. (c) Use Stokes' theorem to calculate the circulation of item (b) through the flow of the rotational ở through the surface S.

Question 4. Consider the speed field i = æzî – yj + a²yk and the surface s given by the paraboloid of revolution given by the equation z = 1 – x² – y² in the first octant. (a) Draw the surface described above. (b) directly calculate the circulation of i along the path C defined by the intersection of the paraboloid and the planes x = 0, y = 0 and z = 0, traveled counterclockwise to an observer on the first octant. (c) Use Stokes' theorem to calculate the circulation of item (b) through the flow of the rotational ở through the surface S.

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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