Potential flow problem with Matlab part. Consider the flow of a spinning circular cylinder located at the origin (x = 0, y = 0), with a circulation Γ, radius R, and a reestream velocity Pa (ie a uniform flow + a doublet + a vortex, pg. 3-19 of the Chapter 3 notes) a) Express the stream function, ψ, for this flow as a function of x andy, leave「and R as symbols b) Find the polar velocity components, vr and vo, also as functions of x and y; leave Г and R as symbols c) If T-7 m2/s, R-0.5 m, V 2 m/s, and the density is that of sea-level air for the standard atmosphere, what is the lift per unit span, L', i. e. the lift per unit depth into the page? Also, what is the 2-D lift coefficient, ce? d) You will make three plots here, each will have two layers, similar to the plots in Homework 2. For each plot, the "bottom" layer will be color contours (using the "countourf" command) of the pressure coefficient, Cp, and the "top" layer will be black streamlines (black contour lines of ψ using the "contour" command). Make sure one of those contour lines is v -0. Use a spatial domain size of 8 m x 8 m, centered on the origin. Assume that the pressure is that of sea-level air for the standard atmosphere. The required plots: Plot #1, set Г 6.6 m2/s, with R and Ve having the values given above. Plot #2, set 1-4tRV0. Plot #3, set : 18.6 m2/s. . NOTE: in converting from polar to Cartesian in your Matlab formulas, for the θ conversion use "atan2," otherwise the values will be wrong in some plot quadrants. · e) Discussion question. Which of the three plots is the case with the greatest lift, L'"? Do its pressure distributions just above and just below the cylinder indicate this, compared to the other plots?