Acoustical analysis of pipes with flow using invariant field functions

An analysis of the pressure field within a pipe is carried out using simplified formulations of pipe acoustics. The fluid contained within the pipe is considered non-viscous, while the flow velocity of the fluid is assumed to be smaller than the speed of sound.The analysis is limited to frequencies which are well below the pipe ring frequency, i.e., at which only simple waves can propagate. Expressions and diagrams are given which specify the applicable frequency range in each particular case.Three invariant functions of the internal pressure field are evaluated. These functions allow for the determination of the following quantities: base pressure spectrum (spatial mean r.m.s. value), lower and upper bounds of the pressure spectrum for the entire pipe, pressure spectrum at an arbitrary position, speed of sound in the contained fluid and fluid flow velocity.Experimental identification of these quantities requires simultaneous measurement at three points. A few measurements carried out on one air-filled and one water-filled pipe have demonstrated the potential of pipe invariant functions for acoustical analysis.