The results of the derived analytical expressions for the flow velocity profile (i.e. Eqs. 17 and 18 with n = 1, a = b = R, k = µ and ∂p/∂z = ∇P ) were compared to the results of this formula (i.e. Eq. 23) and they were identical. A sample of these comparisons is given in Figure . 2. Elliptic Newtonian: the velocity profile for the flow of Newtonian fluids through a tube of elliptical cross section with semi-axes a and b is given by (see ):