Unsteady friction and visco-elasticity in pipe fluid transients

The current waterhammer models coupled with friction models cannot adequately represent the pressure wave attenuation observed in real-world pipe systems, because the pressure wave damping is affected by additional effects not accounted for. One such effect is pipe visco-elasticity from the material behaviour of pipe-wall to be investigated herein. The numerical results indicate that the pressure head attenuation attributable to unsteady friction is comparable to the visco-elastic effect during the initial transient stage, while the visco-elastic effect becomes dominant both in terms of damping and phase shift at later stages. An analytical analysis shows that the visco-elastic effect is more critical if the visco-elastic retardation time is less than the wave travel time along the entire pipeline length. In addition, it is demonstrated that the visco-elastic term in waterhammer models is wrongly referred to in the literature as energy dissipation instead of energy transfer between fluid and pipe-wall by the work done by the pressure force.