Equations describing the hoop stresses in a pipe due to water hammer have been presented in the literature in a series of papers, and this paper discusses the complete derivation of the pertinent equations. The derivation considers the pipe wall response to a water hammer induced shock wave moving along the inner wall of the pipe. Factors such as fluid properties, pipe wall materials, pipe dimensions, and damping are considered. These factors are combined to present a single, albeit rather complicated, equation to describe the pipe wall vibrations and hoop stresses as a function of time. This equation is also compared to another theoretical prediction for hoop stresses, which is also derived herein. Specifically, the two theories predict different maximum stresses, and the differences between these predictions are graphically displayed.

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