A Systematic Investigation of the Moody Plot in Transitional Pipe Flow

The transition between smooth laminar and rough turbulent flow dates back over 150 years. Although significant progress has been made on the transitional flow regime from a fundamental perspective, applications in the engineering domain are less well developed. This is exemplified by the famous "Moody diagram", a plot of non-dimensional friction versus Reynolds number within which the transitional regime is usually indeterminate. Here we provide data from a novel method which establishes a systematic dependence for friction within the transitional regime. Specifically, we approach the transitional regime from above by reducing the flow speed from an initially turbulent flow state to try and circumvent the difficulties associated with initial conditions. We find that different gravity-driven pipe flow experiments yield a single curve corresponding to a maximum density of the transitional flow structures. We test the generality of this result using a mass displacement device to drive the flow through the pipe. Our investigation of the flow driven by a syringe produces a different curve, indicating that the method of driving the flow has a significant impact on the final states and the paths leading to them.