Hysteresis curve in reproduction of Reynolds' color-band experiments

This article describes the reproduction and extended analysis of Reynolds' color-band experiment. Reynolds found two critical Reynolds numbers (R(c)) in pipe flows: R(c1) of 12,830 from laminar to turbulent flow and R(c2) of 2030 from turbulent to laminar flow. Since no clear relationship has been established between them, we studied how the entrance shape affects R(c). Thus, for the first time, a hysteresis graph can be drawn by connecting the two curves of R(c1) and R(c2) such that the two R(c) values lie on separate branches of the hysteresis plot.