## Fluid mechanics, water hammer, dynamic stresses, and piping design

As noted, the text consists of three topics: water hammer and piping design which are related through a third topic of dynamic stresses. Although new developments continue in the field of fluid transients, the basic theory with respect to water hammer is well established. This text provides a review of requisite fluid mechanics in Chapter 2 and static piping design in Chapter 3. Significant piping damages may occur both during initial system startup and shutdown due to a one-time material overload, but failures may also occur due to material fatigue after long hours of operation. In other words, a lack of failure at system startup does not guarantee failure free operation in the future. To consider the differences between overload and fatigue failure mechanisms, Chapter 4 reviews available failure theories. Chapters 5 and 6 provide a description of water hammer mechanisms, case studies of water hammer accidents, and recommended techniques to address water hammer concerns for liquid filled systems and steam condensate systems.

For piping design, pipe stresses are greater than those calculated by assuming that a static stress exists due to a slowly applied pressure in a steady state system. The pipe stresses are greater since the pipe vibrates in response to water hammer. This heightened response is described by vibration equations and dynamic magnification factors, which are described in Chapter 7. The pipe response is comparable to a spring which is suddenly loaded with a force. The spring overshoots its equilibrium, or static position, but gradually returns to equilibrium. The dynamic magnification factor expresses.

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the value of maximum overshoot above the equilibrium position. Chapters 8 and 9 apply these vibration equations to pipes and equipment, since many cracked pipes and leaking valves in industrial and municipal facilities are the direct result of fluid transients. In short, Chapters 1 through 9 describe water hammer and pipe failures in systems that initially exist at steady state conditions. Specifically, the initial flow rate prior to a fluid transient is typically a constant value or zero. Another type of water hammer analysis concerns some types of positive displacement pumps, where the initial condition prior to the transient is provided by an oscillating, nearly harmonic flow, which is, in itself, a transient condition. Each chapter builds on the material presented in previous chapters, and although research continues, these chapters provide the first comprehensive overview and status of a multidisciplinary technique developed to answer the question, Is the fluid transient in a particular system acceptable, and, if not, how may the transient be corrected? The text has two primary applications.

One is the evaluation of accidents and piping failures. The other is the prevention of these events. For example, recently developed theory contained in this text identified numerous water hammer problems and prevented further multi-million-dollar damages at Savannah River Site (SRS). A series of more than two hundred pipe failures which occurred over forty years abruptly came to a halt, but an outstanding milestone to recognize success was nonexistent. The lack of pipe failures over several years was the measure of success. To understand water hammer induced failures, explanations of many other pipe failure mechanisms are discussed to ensure that failure causes can be differentiated by the investigator. Application of this text is hoped to prevent injuries, fatalities, and pipe system damages.

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