For a flow in the \(x y\) plane, the \(x\) component of velocity is given by \(u=A x^{2} y^{2}\), where \(A=0.3 \mathrm{~m}^{-3} \cdot \mathrm{s}^{-1}\), and \(x\) and \(y\) are measured in meters. Find a possible \(y\) component for steady, incompressible flow.

Is it also valid for unsteady, incompressible flow? Why? How many possible \(y\) components are there? Determine the equation of the streamline for the simplest \(y\) component of velocity. Plot the streamlines through points \((1,4)\) and \((2,4)\).