Unstop your bathtub and the draining water will form a tiny tornado-shaped vortex over the outlet. Four centuries ago Torricelli developed a mathematical equation to describe how long it would take to empty the container, based on the height of the fluid in the tank. Now researchers have made a more generalized version of Torricelli’s law, based on experiments with a rotating tank. They found that measuring the water level above the outlet (i.e., taking into account the surface level dip caused by the vortex) gave better agreement. The stronger the vortex, the lower the surface dips and the slower the container drains. (Image and research credit: A. Caquas et al.)
Tag: bathtub vortex
Black Holes in a Bathtub
Physicist Silke Weinfurtner studies fluids, not for themselves, but for what they can teach us about black holes, cosmic inflation, and quantum gravity. Black holes are notoriously difficult to study directly, but, mathematically speaking, it’s possible to set up a fluid system that behaves in the same way a black hole does. The result is a bathtub-like arrangement with a central vortex, seen above. And within this “bathtub,” Weinfurtner and her colleagues can directly measure sound waves equivalent to Hawking radiation, the theoretical means by which black holes emit heat. Learn more about these analogue gravity experiments in her interview over at Quanta Magazine. (Image credit: P. Ammon; via Quanta Magazine; submitted by clogwog)
Ice Cream Vortex
[original media no longer available]
Here’s a fun demonstration of vorticity: sticking an ice cream cone in a bathtub vortex. Now, before someone points out that this is clearly a sink, not a bathtub, the term “bathtub vortex” actually has a standard scientific usage; it’s used to describe a vortex that forms when water drains out a small hole in a larger container.
Vortices like this have a surprisingly complex flow structure. Although there is some flow dragged into the vortex near the surface, flow visualization shows that most of the flow actually occurs along the bottom of the container. Fluid there gets dragged along the surface, then sucked upward near the center of the vortex, and finally gets pulled down the drain.
So what’s going on here? As long as the ice cream cone stays balanced inside the center of the vortex, it spins with the fluid due to viscous drag. When it’s unbalanced – like when it precesses too far or throws a chunk of cone off – I suspect the bottom of the cone is encountering that area of upwelling, which tips the cone completely. The surface flow then pulls it back into the center of the vortex, allowing it to right itself. (Video credit: Cheesemadoodles; research credit: A. Anderson et al.; submitted by randumblrposts and eclecticca)
Fluid Black Holes
Fluid systems can sometimes serve as analogs for other physical phenomena. For example, bouncing droplets can recreate quantum effects and a hydraulic jump can act like a white hole. In this work, a bathtub vortex serves as an analog for a rotating black hole, a system that’s extremely difficult to study under normal circumstances. In theory, the property of superradiance makes it possible for gravitational waves to extract energy from a rotating black hole, but this has not yet been observed. A recent study has, however, observed superradiance for the first time in this fluid analog.
To do this, the researchers set up a vortex draining in the center of a tank. (Water was added back at the edges to keep the depth constant.) This served as their rotating black hole. Then they generated waves from one side of the tank and observed how those waves scattered off the vortex. The pattern you see on the water surface in the top image is part of a technique used to measure the 3D surface of the water in detail, which allowed the researchers to measure incoming and scattered waves around the vortex. For superradiance to occur, scattered waves had to be more energetic after interacting with the vortex than they were before, which is exactly what the researchers found. Now that they’ve observed superradiance in the laboratory, scientists hope to probe the process in greater detail, which will hopefully help them observe it in nature as well. For more on the experimental set-up, see Sixty Symbols, Tech Insider UK, and the original paper. (Image credit: Sixty Symbols, source; research credit: T. Torres et al., pdf; via Tech Insider UK)
The Bathtub Vortex
If you’ve ever watched a swirling vortex disappear down the drain of your bathtub and wondered what was happening, you’ll appreciate these images. This dye visualization shows a one-celled bathtub vortex, created by rotating a cylindrical tank of water until all points have equal vorticity before opening a drain in the bottom of the tank. A recirculating pump feeds water back in to keep the total fluid mass constant. Once a steady vortex is established, green dye is released from the top plate of the tank and yellow dye from the bottom. The green dye quickly marks the core of the vortex. Ekman layers–similar to the boundary layers of non-rotating flows–form along the top and bottom surfaces, and the yellow dye is drawn upward in a region of upwelling driven by Ekman pumping. (Photo credit: Y. Chen et al.)
Just a reminder for those at Texas A&M University: I will be giving a talk today Wednesday, October 2nd entitled “The Beauty of the Flow” as part of the Applied Mathematics Undergraduate Seminar series at 17:45 in BLOC 164.
