Exact computation of the axial vibration of two coupled liquid-filled pipes

A simple recursion is presented that finds exact solutions to the problem of two coupled axially-vibrating liquid-filled pipes.Fluid-structure interaction at pipe ends and junction, and along the pipe because of axial-radial Poisson contraction, is taken into account. The solutions obtained for a waterhammer problem show unprecedented details that resemble noise. Keywords waterhammer, pipe vibration, fluid-structure interaction, travelling wave, method of characteristic

A precursor in waterhammer analysis : rediscovering Johannes von Kries

In 1883 Johannes von Kries published the theory of waterhammer in a study of blood flow in arteries. He derived the “Joukowsky formula ” before Joukowsky (1898) and Frizell (1898) did. He considered skin friction in unsteady laminar flow and thus derived formulas for wave attenuation and line pack. The theory was confirmed by experimental results obtained in rubber hoses. In 1892 he published the first textbook describing “classical ” waterhammer. It presents formulas for phase-velocity and damping that are frequency-dependent because of skin friction, and in this sense it is the first contribution to the – these days popular – subject of unsteady friction

A. Isebree Moens and D.J. Korteweg: on the speed of propagation of waves in elastic tubes

The Moens-Korteweg formula for the speed of propagation of pressure waves dates back to 1878 and was used by Kries in haemodynamics and Frizell, Joukowsky, Allievi and others in waterhammer to calculate the pressure variations in unsteady pipe flows. This paper describes the life and work of Dutchmen Isebree Moens and Korteweg. Their doctoral dissertations (in Dutch) are partly translated, reviewed and compared with their key publications (in German). Korteweg gave Moens’ semi-empirical wavespeed a mathematical basis and he made the first contributions toward the study of fluid-structure interaction and unsteady friction. Their work is placed in historical context, in terms of both their predecessors and contemporaries, and also how it was subsequently built on by their successors in different disciplines

Thomas Young's research on fluid transients : 200 years on

Thomas Young published in 1808 his famous paper (1) in which he derived the pressure wave speed in an incompressible liquid contained in an elastic tube. Unfortunately, Young's analysis was obscure and the wave speed was not explicitly formulated, so his achievement passed unnoticed until it was rediscovered nearly half a century later by the German brothers Weber. This paper briefly reviews Young's life and work, and concentrates on his achievements in the area of hydraulics and waterhammer. Young's 1808 paper is "translated" into modern terminology. Young's discoveries, though difficult for modern readers to identify, appear to include most if not all of the key elements which would subsequently be combined into the pressure rise equation of Joukowsky