An approximate solution for the stream function inside the duct can be obtained solving numerically Laplace$$s equation, $2=0,$ with the appropriate boundary conditions. First, define a grid as the one shown below, using $==0\mathrm{.}2$ m$.$ Next, you will have to prescribe the value of the stream function $$ along the boundary points $($i$.$e$.,$ the blue points in the picture below$).$