15_1_11 - x = C 1 sin ( z-C 2 ) intersect the cylinders x 2...

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11. v ( x , y , z ) = y i - x j + k . The streamlines satisfy dx y = - dy x = dz . Thus x dx + y dy = 0, so x 2 + y 2 = C 2 1 . Therefore, dz dx = 1 y = 1 q C 2 1 - x 2 . This implies that z = sin - 1 x C 1 + C 2 . The streamlines are the spirals in which the surfaces
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Unformatted text preview: x = C 1 sin ( z-C 2 ) intersect the cylinders x 2 + y 2 = C 2 1 ....
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This note was uploaded on 03/08/2012 for the course MATH 120 taught by Professor Onurfen during the Spring '12 term at Middle East Technical University.

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