Skalakʹs extended theory of water hammer

Half a century ago Richard Skalak [see T.C. Skalak, A dedication in memoriam of Dr. Richard Skalak, Annual Review of Biomedical Engineering 1 (1999) 1–18] published a paper with the title “An extension of the theory of water hammer” [R. Skalak, An Extension of the Theory of Water Hammer, PhD Thesis, Faculty of Pure Science, Columbia University, New York, USA, 1954; R. Skalak, An extension of the theory of water hammer, Water Power 7/8 (1955/1956) 458–462/17–22; R. Skalak, An extension of the theory of water hammer, Transactions of the ASME 78 (1956) 105–116], which has been the basis of much subsequent work on hydraulic transients with fluid–structure interaction (FSI). The paper considers the propagation of pressure waves in liquid-filled pipes and the coupled radial/axial response of the pipe walls. In a tribute to Skalakʹs work, his paper is revisited and some of his less-known results are used to assess the dispersion of pressure waves in long-distance pipelines. Skalakʹs theory predicts that the spreading of wave fronts due to FSI is small, at most of the order of 10 pipe diameters.