As indicated already, the proposal of the use of stress function is fully explained and justified in and hence we do not repeat. So, all we need to do here is to continue from the final stage that we reached in where we identified the components of the stress function (i.e. the Newtonian stress function which we assume here to be universal) for a number of geometries including the elliptical geometry which is the subject of interest in the present investigation. For a tube with an elliptical cross section (centered on the origin of coordinates) of semi-major axis a along the x axis and semi-minor axis b along the y axis (refer to Figure ) and whose central axis in oriented along the z axis, the components of the stress function are given by: pressure at the inlet and outlet of the tube (or at any cross section). In other words, the fluid and flow properties (as well as the tube properties) are independent of the magnitude of the applied pressure at the inlet and outlet (or at any cross section).