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Question: steady flow in a pipe of circular crosssection and radius...

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Steady flow in a pipe of circular cross-section and radius a can be described by the vector field where r-Va2+y is the distance from the centreline of the pipe (z-axis). a) Calculate the flux of u through the circular cross-section of the pipe b) Calculate the circulation of the vector field 1 a2+ 4a2 around the circumference of the pipe, ie. the circle C = {x2 + y2-a2. z = const). c) Show that ▽ x v = u and hence verify Stokes theorem in this case.
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