Flow Pattern and Frictional Losses in Pulsating Pipe Flow : Part 4, General Representation of Turbulent Frictional Losses

Abstract

Friction factors in a pulsating turbulent pipe flow are estimated from the flow pattern diagrams shown in a previous paper and the effect of frequency and time-averaged Reynolds number Re+a on the frictional losses is verified with experimental data. The instantaneous friction factor λ_u, ta may be generally expressed as functions of ω'/Re³/4_ta, where ω' is a dimensionless frequency. Here, λ/u(t) is almost equal to the quasi-steady friction factor λ_g in the quasi-steady region, but in the intermediate and the inertia dominant regions, λ_u, ta increases with an increase in both ω'/Re³/4_ta and velocity amplitude ratio A₁. In addition, more adequate values indicating the limits between the above mentioned three regions are proposed.