Consider non-lifting flow over a circular eylinder. a) Starting with the following elementary flows (uniform flow and doublet), derive an expression for the stream function (r,#). Show your work. b) Derive an expression for the pressure coefficient at an arbitrary point (r,#) in this flow, and show that it reduces to , = 14sin # on the surface of the eylinder. Show your work. ) Demonstrate that the resulting lift and drag forces on the eylinder will both be zero. Show your work and describe why you get this result. d) For Uy, = 1 and k = 1, plot the velocity field, streamlines, and pressure coefficient distribution for this flow using the included script as a template. e) Consider the case where V, = 5 m/s, and another case where V, = 10 m/s. Will the shape of the streamlines change by doubling V.7