Researchers at New York University’s Courant Institute of Mathematical Sciences have made a groundbreaking discovery that challenges previously established laws governing fluid dynamics. Through innovative experiments involving drinking straws and metallic pipes, they have derived a universal mathematical formula capable of predicting fluid flow in any pipe or tube. This breakthrough holds immense potential for fields like medicine and engineering, revolutionizing fluid management in various applications.
The scientific community is buzzing with excitement as a team of scientists uncovers novel principles dictating fluid flow dynamics. By harnessing the humble drinking straw, these researchers have unraveled valuable insights that could transform fluid management practices in medical and engineering domains.
Leif Ristroph, an associate professor at New York University’s Courant Institute of Mathematical Sciences and one of the study’s authors, explains the unexpected revelation: “We discovered that the traditional laws governing the resistance and friction of fluid flow through pipes and tubes are defied when sipping through a straw.” This intriguing observation prompted the team to search for a new, all-encompassing law capable of describing fluid movement through pipes of any size, with any type of fluid, and at any flow rate.
The movement of liquids and gases through conduits, such as pipes, tubes, and ducts, is a fundamental occurrence in both natural and industrial settings. This phenomenon is observed in crucial processes like blood circulation and oil transportation through pipelines.
Ristroph, who also serves as the director of NYU’s Applied Mathematics Laboratory, highlights the significance of the pipe-flow problem: “Addressing this problem has been a cornerstone of fluid mechanics since its inception.”
However, in their comprehensive research, Ristroph and his colleagues uncovered a striking realization—existing laws concerning pressure and flow rate hold true only under specific conditions.
To reach this groundbreaking conclusion, the team conducted a series of experiments, meticulously measuring flow rate and pressure in metallic pipes of varying lengths and diameters, using different types of liquids. The aim was to determine how these variables related to the frictional resistance experienced by the flowing fluid.
Ristroph elaborates on their findings: “Our data revealed that the well-known classical laws for flow friction are accurate only for certain combinations of flow speeds and pipe sizes. We identified situations where these laws fail, and an obvious example was right in front of us: drinking through a straw.”
Drinking straws have been utilized for thousands of years, with evidence of their use dating back to the ancient Mesopotamian civilization of Sumeria. Surprisingly, the hydrodynamics of their operation had not been previously studied.
Expanding their investigations, the researchers examined various types of straws, ranging from thin coffee stirrers to regular soda straws and wide bubble tea straws. They conducted experiments to measure friction for flow rates typically observed during drinking.
The data obtained from both straws and pipes of similar sizes defied the established laws named after notable scientists such as Evangelista Torricelli and Jean Léonard Marie Poiseuille. The researchers discovered that each classical law faltered due to assumptions about either extremely short or long pipes, as well as very slow or fast flow rates. The intermediate cases, including straws, involve intricate factors like changes in flow along the pipe’s length and the transition between smooth, laminar flow and rough, turbulent flow.
By accurately modeling these effects, the team derived a single mathematical formula that precisely predicted the experimental measurements for all tested pipes, straws, fluids, and flow speeds.
Ristroph reflects on the potential impact of this universal formula: “Such a versatile formula could prove invaluable in understanding and modeling blood flow in our circulatory system, where veins, arteries, and capillaries resemble pipes with varying diameters, lengths, and flow rates.”
The study, published in the Journal of Fluid Mechanics, was authored by Olivia Pomerenk, a doctoral student at Courant, Simon Carrillo Segura, a doctoral student at NYU’s Tandon School of Engineering, and Fangning Cao and Jiajie Wu, who were NYU undergraduates at the time of the study. The research was generously supported by the National Science Foundation.
