Steady, Gravity-Driven Water Flow in a Full Pipe of Constant Cross Section

We consider the problem of water flow in a pipe of constant cross sectional area due to an elevation change between the pipe inlet and outlet. The flow is assumed to be steady and the pipe flows full at all cross sections. The application is the design of a single leg of a water distribution network that is fed by one reservoir (the “source”). There are many references for this type of design (The Blue Book). The present work is not intended to be a thorough, comprehensive treatment of the subject matter. It is, however, an attempt to provide a link between the subject of fluid mechanics learned in a typical undergraduate mechanical engineering curriculum, with which the students should already be familiar, and the more-comprehensive coverage of this topic in a book such as The Blue Book.