The results of the derived analytical expression for the volumetric flow rate (i.e. Eq. 19 with n = 1, a = b = R, k = µ, and ∂p/∂z = ∇P ) were compared to the results of this formula (i.e. Eq. 26) and they were identical. A sample of these comparisons is given in Figure . 2. Elliptic Newtonian: the volumetric flow rate for the flow of Newtonian fluids through a tube of elliptical cross section with semi-axes a and b is given by (see ):