One of the objectives of this study was to reduce the undesirable dynamic pressure oscillation that occurs in a simple pipeline due to valve closure and to prevent the occurrence of column separation. This is accomplished by maximizing the minimum pressure in the pipeline. The second objective was to minimize the maximum dynamic pressure, and the third objective was to estimate the best (minimum) time of closure, T*c, that results in a pipe stress equal to the maximum allowable stress. The method of characteristics with the time-line interpolation technique was used to solve the transient stresses and pressures in a liquid-filled piping system. Frequency-dependent friction was used in the equation of motion for the fluid and the pipe wall. A nonlinear optimization technique was utilized to generate the optimum valve closure policy. Maximum and minimum pressure heads resulting from the optimal policy were calculated and compared with those resulting from a uniform valve closure. Plots of pressure variation at the valve for these two valve closure policies were also generated. Examples are presented to demonstrate the advantage of the optimum valve closure policy over the uniform valve closure policy. The reduction in the maximum dynamic pressure and stress at the valve for different Tc is also presented.

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