This article describes the reproduction and extended analysis of Reynolds’ color-band experiment. Reynolds found two critical Reynolds numbers (Rc) in pipe flows: Rc1 of 12,830 from laminar to turbulent flow and Rc2 of 2030 from turbulent to laminar flow. Since no clear relationship has been established between them, we studied how the entrance shape affects Rc⁠. Thus, for the first time, a hysteresis graph can be drawn by connecting the two curves of Rc1 and Rc2 such that the two Rc values lie on separate branches of the hysteresis plot.

Issue Section:
Fundamental Issues and Canonical Flows
Keywords:
hysteresis, laminar to turbulent transitions, pipe flow
Topics:
Flow (Dynamics), Pipe flow, Pipes, Reynolds number, Turbulence, Water, Shapes
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 by American Society of Mechanical Engineers
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