Wave-Action in Gases: The Attenuation and Reflection of Compression Waves Propagated in Pipes

Abstract

The investigation supplements a previous examination (Bannister and Mucklow 1948)‡ of the wave-action following sudden discharge of compressed gas into pipes. The paper consists of two parts, Part I dealing with the relation between the frictional attenuation of compression waves propagated in pipes and the effects of friction under conditions of steady flow. The object of the work covered in Part II was to compare experimentally the pressure amplitude of compression waves before and after closed-end and open-end reflection, with a view to verifying considerations based on theoretical argument. The apparatus consisted of a series of cylinders of 1.5, 2.0, and 4.285 inches bore, from which compressed air was discharged suddenly into pipes of varying length and of the same bore as the cylinder in use. Indicator diagrams were recorded at suitable intervals along the pipes. Theoretical considerations show that, with the same particle velocity, a simple relation exists between the rate of decay of small-amplitude waves and the steady-flow pressure-drop along a pipe. Experiment suggests that this relation applies approximately to finite-amplitude waves and, on this basis, a simple expression is devised to relate wave-head decay with initial amplitude, pipe diameter, and distance propagated, within the range considered. By use of this expression, the mean velocity of propagation may also be determined. The processes of open- and closed-end reflection of compression waves are examined and considerations outlined in an appendix to the previous paper are amplified. The resulting conclusions are supported by experimental evidence. The effects of discharge through a constriction are considered in the Appendix.