Formulas for compression wave and oscillating flow in circular pipe

Abstract

This paper shows analytical solutions for compression wave and for steady-state oscillating flow in a pipe with a circular cross section. We considered the compression wave to be one of fluid phenomena, and paid our attention to the equation of fluid motion and of continuity. Pressure and flow velocity are directly treated in analytical solutions. Not only either of them but also flow rate may be chosen as an input and outputs by easy rearrangement of the formulas. This paper enables us to express various behavior of the compression wave by using analytical solutions with the phase velocity and the spatial absorption coefficient. Those analytical solutions enable us to reduce computation time and analysis cost on not only duct acoustics but also water hammer and combustion instabilities. Of course, our formulas may contribute to designing of microdevices such as MEMS strongly influenced by wall-viscosity.