Based on the experimental data, John has obtained an empirical relation for the velocity profile of steady flow around a 60^o corner as a function of the positions (x and y):  
     
      V = 3(x² - y²) i - 6xy j
    
where the flow field lies in the positive x-y plane, as shown in the figure. He is now searching for an effective way of presenting the predicted flow field to his colleagues.

Obtain an expression for the stream function, and plot the streamlines.

• First verify if the obtained velocity profile is for incompressible flow.