A Review of Water Hammer Theory and Practice

Abstract

Hydraulic transients in closed conduits have been a subject of both theoretical study and intense practical interest for more than one hundred years. While straightforward in terms of the one-dimensional nature of pipe networks, the full description of transient fluid flows pose interesting problems in fluid dynamics. For example, the response of the turbulence structure and strength to transient waves in pipes and the loss of flow axisymmetry in pipes due to hydrodynamic instabilities are currently not understood. Yet, such understanding is important for modeling energy dissipation and water quality in transient pipe flows. This paper presents an overview of both historic developments and present day research and practice in the field of hydraulic transients. In particular, the paper discusses mass and momentum equations for one-dimensional Flows, wavespeed, numerical solutions for one-dimensional problems, wall shear stress models; two-dimensional mass and momentum equations, turbulence models, numerical solutions for two-dimensional problems, boundary conditions, transient analysis software, and future practical and research needs in water hammer. The presentation emphasizes the assumptions and restrictions involved in various governing equations so as to illuminate the range of applicability as well as the limitations of these equations. Understanding the limitations of current models is essential for (i) interpreting their results, (ii) judging the reliability of the data obtained from them, (iii) minimizing misuse of water-hammer models in both research and practice, and (iv) delineating the contribution of physical processes from the contribution of numerical artifacts to the results of waterhammer models. There are 134 refrences cited in this review article.

Effect of drop in pipe wall stiffness on water-hammer speed and attenuation

“…The former is estimated using the Darcy-Weisbach or the Hazen-Williams formulae, whereas the latter results from empirically-based models such as in Bergant et al (2001) or from physically-based models such as in Vardy et al (1993). The wave dissipation due to steady or unsteady friction becomes important for high friction factors or long pipes of small internal diameter (Ghidaoui et al 2005).…”

Experimental method for the evaluation of the dynamic transfer matrix using pressure transducers

“…The equations used to obtain the following transfer matrix components are based on the one-dimensional (1D) representation of transient flows, which are described by, among others, Streeter & Wylie (1967) or more recently in a review by Ghidaoui, Zhao, McInnis, & Axworthy (2005). In the present study, the following assumptions are made.…”

Optimizing Intermittent Water Supply in Urban Pipe Distribution Networks

“…Bernoulli's equation applied to flow through an orifice gives 13) where h in = h(A in ), h ext is a height between 0 and D that indicates the valve opening, g is the acceleration due to gravity, and A = A(h ext ) is the area of the outflow orifice.…”

“…Water distribution software abounds, including the free and open source software EPANET [27] produced by the US government, as well as many commercial packages [13]. Yet, to the authors' knowledge, all these fail to account for filling, emptying, and instances…”