Consider potential flow in a 2-D channel with a butterfly valve shown in the figure below. Poo Ppo I/N H H L 00 For this configuration, you are given the following: Poo = 1 kg/m, U = 50 m/s, Poo = 100,000 Pa, H = 0.2 m, L = 1.0 m, = 45. You can also try other numbers. (1) Develop a computer program to solve the equation governing potential flow in this configuration; namely, 20 with appropriate boundary conditions on all walls. (2) Generate solutions and plot the streamlines, velocities, and pressure contours. (3) What did you do to ensure that you have accurate solutions? In your solution procedure, clearly describe - the problem being solved the governing equations with the boundary conditions the derivation of the finite-difference equations (FDES) for the governing equations the numerical method used to obtain solutions to the FDES (e.g., Gauss-Seidel with SOR) what steps were taken to ensure that you obtained accurate solutions. Plot solutions obtained by using different number of grid points.