The equations of motion of curved pipes conveying fluid

Abstract The non-linear differential equations of motion of a fluid conveying pipe, the no-flow configuration of which is in the shape of a one-dimensional line arbitrarily curved and twisted in space, are derived by making use of the Newtonian approach. The extensible dynamics of the beam is based on the Timoshenko beam theory. Some significant differences with the equations available in the open literature are discussed. The stressed-by-flow configuration is found to be the only equilibrium state adequate for the study of the linear stability of such pipe-fluid systems.