In this paper, the conservation laws of classical fluid mechanics are used to derive a quasi-one-dimensional model of fluid flow in an elastic tube of time-varying cross-sectional area, representing the human vocal tract. The global flow equations are then decomposed into aerodynamic and acoustic components, representing respiratory flow and sound propagation during speech. The nature of the coupling between the two systems is investigated, and a new interpretation of the traditional source-filter model of speech production is proposed.