Consider a steady, two-dimensional, incompressible flow field for which the u velocity component is u = ax² – bxy, where a = 0.45 (ft·s)^–1, and b = 0.75 (ft·s)^–1. Let v = 0 for all values of x when y = 0 (that is, v = 0 along the x-axis). Generate an expression for the stream function and plot some streamlines of the flow. For consistency, set ψ = 0 along the x-axis, and plot in the range 0 < x < 3 ft and 0 < y < 4 ft.