Piping systems are commonly designed to withstand the first transient pressure peak, which is unaffected by dissipation. However, for multiple operations of control equipment, for example, pump start-up following pump shutdown, and load acceptance following load rejection on hydraulic turbines, an accurate prediction of the dissipation of pressure oscillations is needed to select a suitable time for the second operation. For this purpose, following a simple procedure used for computing the dissipation of vibrations of bridges and other structures with time, a method is presented to compute the dissipation of pressure oscillations in piping systems. Similar to structural engineering, this method is simple to apply, does not require simulation of the entire system, is not computationally intensive, and gives reasonable results for practical applications for a complex phenomenon whose mechanics is not well understood at present. An empirical equation for the damping ratio is developed using dimensional analysis and by nonlinear regression. Comparisons of the computed and experimental results for 17 tests conducted in laboratories all over the globe show good agreement. It is found that the damping ratio increases with increases in the Reynolds number or Mach number and decreases with the diameter-to-length ratio of the pipeline. Uncertainty, quantified using a Bayesian inference approach, shows that the model predicts the value of the damping ratio successfully