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Fundamentals of Aerodynamics Book 2.4 is a document available to read on EtoBox.
The streamlines for the given 2D steady velocity field are circles centered at the origin with radii dependent on an arbitrary constant k. To obtain this result, the stream function equations are used to relate the x and y components of velocity to the derivatives of the stream function with respect to x and y. This yields a separable differential equation that can be integrated to get the equation of the streamlines as circles.
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