Our plan in this paper (following this introduction) is to prepare the scene for this investigation by stating the assumptions and conditions that apply to the fluid, flow and tube (see § 2). We then present the stress-function-based mathematical formulations which lead to the derivation of the aforementioned analytical expressions (see § 3). An outline of the tests and checks that were conducted to partially validate the derived formulae and rule out gross errors is then presented (see § 4). The paper is ended with a list of the main achievements and conclusions of this investigation (see § 5).