Determine the stream function for the steady incompressible flow between parallel plates. The velocity profile is parabolic and given by \(u=u_{c}+a y^{2}\), where \(u_{c}\) is the centerline velocity and \(y\) is the distance measured from the centerline. The plate spacing is \(2 b\) and the velocity is zero at each plate. Explain why the stream function is not a function of \(x\).