Given the planar velocity field vr = -A sin(?t) sin θ r 2 vθ = A sin(?t) cos θ r 2 , where A and ? 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 < ∞.