Given the planar velocity field vr = −A sin(Ωt) sin θ r 2 vθ = A sin(Ωt) cos θ r 2 , where A and Ω are known constants,
1. Determine the vorticity. 2. Compute the dilatation rate ∇ · v¯. 3. Comment on the existence of velocity potential and stream function and, if they do exist, compute them. 4. Find the acceleration for points along the line θ = 0 5. Obtain the trajectories and the streamlines. 6. Determine the fluid line that at t = 0 is given by θ = 0 and 0 < r < ∞.
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