Estimation and examination of linepack pressures in long liquid pipelines

Abstract

In the past, many researchers have carried out water-hammer pressure analysis using Joukowsky equation. However, it has been observed that the computed pressure surge is no longer applicable based on the equation. The Joukowsky equation cannot be used even within the reflection time of the long pipeline. In such cases, the actual pressure rise due to the sudden closure of a quick acting valve will be several times more than that of the sudden increase in pressure as calculated by the Joukowsky equation. The phenomenon of rising pressure at the upstream of an instantaneously closed valve with the passage of time caused by the pipe friction is commonly called as linepacking. In this paper, various parameters affecting the linepack pressure have been thoroughly investigated. As the relative roughness increases, the resulting non-dimensional linepack pressure P LP =P o ð Þsignificantly increases and the proportionality constant was equal to 1.5. The linepack pressure was determined to be decreasing with increasing valve closure time. The dominant parameter that influences the linepack pressure is found to be the Reynolds number as compared to the Mach number, and the relative roughness. Furthermore, the linepack pressure is found to be proportional to frictional head loss h L =D ð Þ, and inversely proportional to inlet pressure P o = cL o ð Þ ð Þ. Finally, a linear regression equation was developed in terms of non-dimensional variables to estimate the linepack pressure using hand calculations without undergoing numerical modeling procedures. The proposed equation was validated for sudden valve closure pressure histories available in the literature. The proposed method is applicable to long distance water supply pipelines where the linepack pressures are significant.