Consider lifting flow over a circular cylinder. a) Starting with the following elementary flows (uniform flow, doublet, and vortex), de- rive an expression for the stream function :(r, ). b) For I' = 0 (clockwise circulation), find the possible #-locations of the stagnation points on the cylinder surface, when r = R, and give the condition required for this to occur. Show your work. c) Derive the pressure coefficient on the cylinder surface, c,(r = R, f). Show your work. d) Using cp(r = R.#), demonstrate that the resulting drag force on the cylinder will be zero. Show your work. e) Demonstrate that the resulting lift coefficient for the same cp(r = R, ) ise = I'/ RUx. Show your work. Explain why the model is able to produce lift but not drag? f)yFor Uy =1, k = 1, and ' = 4, plot the velocity field, streamlines, and pressure coefficient distribution for this flow using the included script as a template. g) The lift on a spinning circular cylinder in a freestream with a velocity of 30 m/s and at standard sea level conditions is 6 N/m of span. Calculate the circulation around the cylinder. Now if V. is doubled while keeping I' the same, does the shape of the streamlines change