Physicists Solve A Problem They've Been Working On For 130 Years

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We love flowing water. Putting our feet in a slow-moving stream or standing under a pouring hot shower makes us feel great, but working out how the liquid is actually flowing is not an equally calming experience. Over 130 years ago, British physicist Osborne Reynolds produced equations to describe both slow-moving liquids, like streams, and fast-moving liquids, like showers. The issue was trying to describe the transition of one fluid type to the other.

Researchers at the Okinawa Institute for Science and Technology (OIST) in Japan have finally solved this problem, and it turns out that we had the right tools all along. Reynolds' equations can be used to work out the friction between the fluid and the pipes for example, and they work differently for the calm laminar flow and the fast turbulent flow.

What the researchers discovered is that when a fluid is in the transitional state between laminar and turbulent, it can still be described by the same set of equations. The transitional state is made of patches of laminar and turbulent, and it turns out that to measure the property on the whole, you just have to measure the properties of the parts. The results are published in Physical Review Letters.

“We have shown that, although the transitional state appears to be a menagerie of flow states, these can all be characterized by laws we already know,” Professor Pinaki Chakraborty, leader of OIST's Fluid Mechanics Unit, said in a statement. “This simplifies a fundamental problem.”

The discovery might seem obvious now but it was not trivial beforehand. During transitional flow, friction varies with no apparent pattern, which is usually an indication that whatever physics we are using is wrong. The team ran water through a 20-meter (65-foot) glass pipe and placed particles in it so that they could use a laser beam to work out the alternating patches of laminar and chaotic flow. They also placed pressure sensors in the pipe so they could measure the friction.

Different types of pipe flow. From top to bottom: laminar, transitional, and turbulent. Pinaki Chakraborty/OIST

“We repeated a textbook experiment that is routinely done by thousands of engineering undergraduates every year all around the world,” lead author Dr Rory Cerbus explained. “We used essentially the same tools, but with the crucial distinction of analyzing the patches separately.”

This discovery could be useful in many industries as it could minimize energy waste.

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