Transformation between damped and undamped waterhammer waves

Abstract

This paper derives a mathematical relation between the damped and undamped waves propagating in a fluid-filled pipe. The damping considered is caused by the steady and unsteady friction and the pipe wall visco-elasticity. The derived relation is solved so that the idealized undamped pressure wave signal is obtained from the measured damped pressure signal. Physically, the proposed transformation is an amplification operation that adds back the energy that was lost due to the damping. This means that measurement errors will also be amplified under the transformation, making the problem ill-posed. The truncated singular value decomposition method is used to regularize the transformation. Both numerical and laboratory experiments are conducted to show the validity of this transformation. The results show that the transformation can accurately predict the shape and size of the reflections that were distorted due to the wave dissipation and dispersion.