Vibration spectrum of a water pipe under the effect of unsteady fluid loading

A simplified method for estimating the vibrations of water pipes under the effect of unsteady fluid flows is proposed. The first natural frequencies of water pipes being about some 10 Hz due to standard design rules, and supports being arranged with spans of the order of 5 m, the fluid flow can reasonably be described as incompressible, so that acoustics do not play a significant role within this framework. Assuming for the sake of simplicity that the fluid velocity field is the gradient of a potential, it generates an inertial pressure field along the pipe. Simple equations are derived for describing the fluid flow associated with a given mode shape of the pipe, and coupled equations are provided which link the unsteady fluid flow to the vibrations. A simple test case is provided, which supports the idea that for water pipes, the vibration velocity of the structure and the unsteady fluid velocity are in the same order of magnitude.