Consider a two-dimensional square with boundaries x = 0 and d and y = 0 and d. Within this square, we define a stream function, (x, y): (x, y) = Asin(x/d) sin(ny/d), (1) where A is a constant. (a) (2 points) If this flow is divergence free, what is the velocity filed (i.e., the expressions for u and u, the x and y components of velocity)? (b) (4 points) Draw a box and draw two contours of (e.g., = A/3 and = 2A/3). (c) (4 points) Draw a few "arrows" on the streamlines to indicate the sense of flow. Make sure to indicate where the origin is and what the positive x and y directions are. Do everything by hand!.