Redefining Fluid Dynamics: Ancient Invention Unleashes Modern Breakthrough

Physics of fluids

A team of researchers from New York University’s Courant Institute of Mathematical Sciences has discovered new laws that regulate the flow of fluids, contradicting previously known laws. Their discovery, based on experiments with metal straws and pipes, led to the derivation of a universal mathematical formula that can predict fluid flow in any pipe or tube, which could have significant implications for fields such as medicine and engineering. .

The recent breakthrough has great potential for both medical and industrial applications.

A group of scientists has discovered new laws that regulate the flow of fluids by conducting experiments on an ancient technology: the straw. This new understanding has the potential to improve fluid management in medical and engineering settings.

We found that sipping through a straw defies all previously known laws for the resistance or friction of flow through a tube or pipe, explains Leif Ristroph, an associate professor at New York University’s Courant Institute of Mathematical Sciences and an author of the study. appearing in the Journal of Fluid Mechanics. This motivated us to look for a new law that could work for any type of fluid moving at any speed through any size pipe.

The movement of liquids and gases through conduits such as pipes, tubes and ducts is a common phenomenon in both natural and industrial settings, including scenarios such as the circulation of blood or the transport of oil through pipelines.

The pipe flow problem has always been one of the most basic and important in the study of fluid mechanics, and in many ways, the field has developed to address this problem, explains Ristroph, director of NYU’s Applied Mathematics Laboratory, where research was conducted.

However, in their work, Ristroph and his colleagues found that all known laws relating to pressure and flow were only accurate under certain conditions.

To reach this conclusion, they conducted a series of flow and pressure measurement experiments for metal pipes of different lengths and diameters using different types of liquid. The goal was to determine how these factors relate to the frictional resistance of the flow through the pipe.

Our data showed that the well-known and classical laws for flow friction are only accurate for certain combinations of flow velocity and pipe size, Ristroph explains. We’ve mapped out the conditions where existing laws don’t work well, and we’ve found a good example right under our noses: drinking through a straw.

Straws are thought to have been used as early as 5,500 years ago in the early Mesopotamian civilization of Sumeria. But the hydrodynamics of their operation has not been studied before.

The researchers expanded their study to include different types of straws, a narrow coffee stirrer type, a regular soda type, and a loose bubble tea type, and ran experiments to determine friction for typical flow rates during consumption.

The data on straws and pipes of similar size did not match any of the known laws, named after their discoverers, scientists Evangelista Torricelli and Jean Lonard Marie Poiseuille, among others.

The researchers found that every classical law fails because it assumes that the pipe is very short or very long and that the flow is very slow or very fast. Intermediate cases, including straws, involve complicated factors such as how the flow changes along the length of the pipe and whether it becomes smooth and laminar or rough and turbulent.

Modeling those effects allowed the team to derive a single mathematical formula, and its predictions matched the experimental measurements for all the pipes and straws and for all the fluids and flow rates they tested.

A universal formula could be very useful, for example, for understanding and modeling blood flow in the circulatory system, Ristroph notes. Our veins, arteries and capillaries are basically tubes with different diameters, lengths and flow rates.

Reference: Hydrodynamics of Finite Length Pipes at Intermediate Reynolds Numbers by Olivia Pomerenk, Simon Carrillo Segura, Fangning Cao, Jiajie Wu, and Leif Ristroph, Journal of Fluid Mechanics.
DOI: 10.1017/jfm.2023.99

The paper’s other authors included Olivia Pomerenk, a doctoral student at Courant, Simon Carrillo Segura, a doctoral student at NYU’s Tandon School of Engineering, and undergraduate students Fangning Cao and Jiajie WuNYU at the time of the study.

The study was funded by the National Science Foundation.

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