Pressure variations of fluid transients in a pressurized pipeline

Abstract

Pressure variations during fluid transients in pipelines are of significant interest to hydraulic engineers and scientists. To clarify the effects of unsteady wall shear stress on the propagation of pressure waves, we re-examine an analytical solution that was recently developed with unsteady wall shear stress included. Physical insights about the effects of unsteady wall shear stress are obtained. Comparisons of the solution with available experimental data and the numerical results of an instantaneous-acceleration-based model are carried out. It is found that unsteady wall shear stress can cause both the amplitude decay and phase shifts of the water hammer pressure. The phase shifts caused by unsteady wall shear stress are indicated by the deformation of pressure variations. Furthermore, we highlight that for initial-laminar and low-Reynolds-number flow conditions, the effect of unsteady wall shear stress is independent of the initial Reynolds number but is related to another dimensionless parameter that has a clear physical significance; that is, the ratio of viscosity diffusion time to the period of water hammer or the ratio of boundary layer thickness to the pipe radius.