Consider the streamfunction:

(a) [5] Determine the velocity field, u = (ur, ue). (b) [5] Is the flow divergence free? Calculate to show or explain why. (c) [5] Is the flow irrotational? Calculate to show or explain why. (d) [5] If possible, from u derive the expression for the potential function, (r, 0). (e) [5] Find the location of the stagnation point (s) in the flow field, if any exist. (f) [Bonus+2.5] Sketch the streamlines for r > 1. (g) [Bonus+2.5] Determine the area flux, [L²/T], between the streamlines that pass through the coordinates Pt₁ = (r,0) = (2, π/4) and Pt₂ = (4,π/4). Assume the dimensions of = [L²/T] and u= [L/T]