Maximum pressure head rises, which result from total closure of the valve from an initially fully open position, are calculated and plotted for the valve end and for the midpoint of a simple pipeline. Uniform, equal-percentage, optimum, and parabolic closure arrangements are analysed. Basic parameters such as pipeline constant, relative closure time, and pipe wall friction are considered with closures from full valve opening only. The results of this paper can be used to draw the maximum hydraulic grade line along the pipe with good accuracy for the closure arrangements considered. It is found that the equal-percentage closure arrangement yields consistently less pressure head rise than does the parabolic closure arrangement. Further, the optimum closure arrangement yields consistently less head rise than the equal-percentage one. Uniform closure produces pressure head rise that usually lies between those produced by the parabolic and the equal-percentage closure arrangements, except for the range of low pressure head rise combined with low or zero friction, where the rise due to uniform closure approaches that produced by optimum closure.
Interpolation schemes for valve closure modelling
