## Publication: Generalized water hammer algorithm for piping systems with unsteady friction

##### Authors
Suárez-Acuña, Jaime
Silva-Araya, Walter F.
##### College
College of Engineering
##### Department
Department of Mechanical Engineering
M.S.
2005
##### Abstract
Unsteady flow in pipe networks is usually analyzed by means of one-dimensional models, in which the energy dissipation is computed assuming the friction factor dependent on the local and instantaneous Reynolds Number (quasi-steady model). This model underestimates the friction forces and overestimates the persistence of oscillations following the first one. Unsteady friction has great importance in pipe networks because the maximum oscillation may occur after the first one. Silva-Araya and Chaudhry developed (1993) a model to simulate unsteady friction in transient flow which was tested in simple pipe – valve systems only. The model approximates the velocity profiles during the transient flow and computes the actual energy dissipation. The ratio of the energy dissipation at any instant and the energy dissipation obtained by the quasi-steady approximation is defined as the Energy Dissipation Factor. This is a time-varying, non-dimensional parameter that is incorporated in the friction term of the transient flow governing equations. The objective of this study is to extend Silva-Araya and Chaudhry’s unsteady friction model for water hammer analysis to series and branching pipe systems. The conduits at these systems may have different diameters, wall thickness, wall material, and/or friction factors. For the computation of the initial steady state conditions a subroutine that solves the network flow equations using the Hardy Cross linear analysis is used. The subroutine allows for the input of minor losses, use of either the Darcy-Weisbach or Hazen-Willians pipe frictional loss. Either SI or English units are permissible. To create a “user friendly” Windows interface, the extended application was developed using VBA (Visual Basic for Applications) in Excel for general program applications. The model was tested for three cases: single, series and branching piping systems. The computed pressures are compared with the experimental data obtained for Silva Araya (1993) for a single piping system case. For a series and a branching piping system the computed results obtained by using unsteady friction are compared with the data obtained by using steady friction model.