Behavior of Short Lateral Dead Ends on Pipeline Transients: A Lumped Parameter Model and an Analytical Solution

By integrating the continuity equation over a short lateral dead end, the effects of a short lateral dead end side branch on pipeline fluid transients can be lumped into a node. The analytical solution to a linearized equation shows that a pipeline transient can be expressed as a Fourier series and presence of a lateral dead end reduces the frequencies of the harmonic components. The impact of the lateral dead end on the observed transients depends on a parameter $Sd$⁠, which is related to the location of the lateral dead end, the relative volume, and the wave speed of the lateral dead end with respect to the pipeline. A lumped parameter approach that can be incorporated into the method of characteristics has also been developed in this paper. It has been found that it is possible to take account of the effects of a short lateral dead end in an accurate and computational efficient manner.