Skin Friction in Unsteady Laminar Pipe Flow

The routine approach toward solving problems of unsteady pipe flow utilizes either the concept of a constant friction coefficient, or the model of quasi-steady flow. These two hypotheses are tested using exact analytical solutions and corroborating experimental evidence for two cases of time-dependent laminar pipe flow: (1) The establishment of Poiseuille flow: and (2) U-tube oscillations. It is shown that neither of the simplifying assumptions corresponds to reality, and that both tend to severely underestimate the frictional resistance. It is suggested that similar conclusions may also pertain to unsteady turbulent pipe flow.