Pulse Propagation in Fluid-Filled Tubes

Abstract

A new theory for the propagation of pressure pulses in an inviscid compressible fluid contained in a thin-walled elastic tube is presented. This theory represents an improvement over the classical waterhammer theory because the restriction that the speed of sound in the tube material must be much greater than that in the fluid has been removed and because the restriction that the pulse length must be much greater than the tube diameter has been somewhat relaxed. The new theory is applied to a water-filled copper tube with an axial impulsive force of very short duration applied either to a piston inserted in the anchored end of the tube or to a cap on the free end of the tube. Numerical solutions using the method of characteristics are presented, and comparison is made with the predictions of classical waterhammer theory. A check on the numerical solution is provided by the analytical solution for the capped tube and for the special case when the speeds of sound in the tube material and in the fluid are equal.