Moving tubes: the role of walls in a modified Bernoulli equation

Abstract

Abstract In this paper, standard and introductory examples of fluid dynamics are analyzed from an unusual perspective, choosing reference frames in which the tube carrying the fluid is also moving. In such frames, Bernoulli’s equation is not valid, and to analyze the energy balance one must account for the work exerted by the tube’s wall. This example provides a useful pedagogical bridge between fluid dynamics and mechanics courses, allowing both instructors and curious students to (i) reinforce tools such as the work–energy theorem and (ii) appreciate the special nature of the tube’s rest frame, a point rarely emphasized in textbooks. In addition, it is shown how elementary arguments may be used to construct, for a class of representative examples, a frame invariant expression for the pressure difference.