Consider a steady, laminar flow through a straight horizontal tube having the constant e...

Consider a steady, laminar flow through a straight horizontal tube having the constant elliptical cross section given by the equation

The streamlines are all straight and parallel. Investigate the possibility of using an equation for the z component of velocity of the form

as an exact solution to this problem. With this velocity distribution, what is the relationship between the pressure gradient along the tube and the volume flowrate through the tube?