Frequency-Dependent Friction in Transient Pipe Flow

Abstract

An equation is derived, which relates the wall shear stress in transient laminar pipe flow to the instantaneous mean velocity and to the weighted past velocity changes. The term is applied to the method of characteristics to calculate water-hammer phenomena in viscous fluids, in which effects of frequency-dependent friction cause distortion of traveling waves. Theoretical results are compared with the experimental pressure fluctuation due to an instantaneous valve closure and show accurate prediction of the response curve.