Frequency-dependent friction in oscillatory laminar pipe flow

Abstract

Based on the Iberall model of fluid transients, a frequency-dependent friction coefficient is derived for laminar pipe flow of compressible fluids. The analysis, employing Laplace transformation, is of particular utility in the description of fluid motions which are naturally periodic and, hence, where the dependency of skin friction on frequency of excitation can be accounted for by expressing the coefficient in terms of the dominant frequency of the system. The analytical result is applied to the classical example of oscillations of an incompressible fluid in an open-ended U-tube. In distinct contrast to predictions based on the very common, quasi-steady engineering approximation of skin friction effects, the theory is found to be in excellent agreement with actual observations of successive peaks of the column motion over the whole range of frequencies investigated.