Physics of peeingDesigning better toilet bowls

Although we do not often think about it, fluid dynamics touches almost every aspect of our lives, from a billowing breeze that buffets a flag, to swirling river currents that shape canyons to the surging blood that sustains our lives. One of the basest of bodily functions – urination — is governed primarily by the equations of fluid motion.

An APS release reports that later this month, at the 66th Annual Meeting of the American Physical Society [APS] Division of Fluid Dynamics in Pittsburgh, Pennsylvania, two teams of researchers reveal new insight into the physics of peeing.

In the laboratory of Georgia Tech’s David Hu, scientists and engineers look to nature for engineering ideas. In work that could help in the design of scalable hydrodynamic systems, researchers from the Hu lab recently filmed the urination habits of sixteen animals of varying sizes — five mice, five rats, one dog, two goats, two cows, and one elephant.

The results? Size matters. Small animals such as mice and rats take about two seconds to pee, but urination “events” in animals larger than about five kilograms consistently clocked in at an average of twenty-one seconds.

“An elephant has a large bladder and a urethra with dimensions comparable to a household pipe,” says graduate student and study leader Patricia Yang. As gravity pulls fluid down to the bottom of the urethra, Yang explains, the flow speed increases, causing urine to be eliminated more quickly than in a medium-sized animal, like a dog, which has a shorter urethra and gets less of a boost from gravity. The dog, however, has a smaller bladder, and “this is why an elephant and a dog empty their bladder in the same time,” she says.

When it comes to urination accuracy, however, speed and size are less important than angle, says fluid dynamicist Randy Hurd of Brigham Young University, who will present a study of the dynamics of urinal use. Hurd and his graduate advisor, Tadd Truscott, got the idea for the work during a caffeine- and sugar-fueled midnight road trip from San Diego following last year’s APS Division of Fluid Dynamics (DFD) meeting. The two were brainstorming about new and creative projects for Truscott’s Splash Lab, which uses high-speed imaging techniques to study fluid behavior.

At the Splash Lab, Hurd and his colleagues created an artificial male urethra on a 3D printer.

The urethra — a cylinder with a 8 mm x 3 mm elliptical channel running down the center — was attached with tubing to a pressurized container, allowing it to deliver a steady stream of dyed water at twenty-one milliliters per second, the expected flow rate for a healthy, middle-aged male. High-speed cameras were used to visualize the flow as it struck both a solid surface (representing the porcelain back wall of most urinals) and a “free” surface (representing standing water); white paper was placed below the surfaces to track where splash droplets ended up.

Perhaps not surprisingly, the researchers found that it is indeed possible to use a urinal without splashing onto yourself or your own clothing. The key? Angle.

“For typical male urination, the stream breaks up into droplets before impacting the urinal wall or the water surface,” he says. Significant splash-back occurs if that stream is angled perpendicular to the urinal wall, down to angles of about 45 degrees. When this impact angle becomes very small, however, “it is much easier for the droplets to only slightly change direction, and slide along the porcelain surface without generating large splashes,” says Hurd, who hopes eventually to create an optimization function to find the ideal approach for urinal usage.

“Although reducing the impact angle would also work in traditional toilets, these angles tend to only present themselves around the rim of the bowl, simultaneously increasing the chances of missing the bowl entirely,” says Hurd. “I wouldn’t recommend this approach to anyone but military snipers.”

— Read more in in Jonathan Pham et al., “The Hydrodynamics of Urination: to drip or jet”; and Randy Hurd et al., “Urinal Dynamics” (papers to be presented at the 66th Annual Meeting of the American Physical Society [APS] Division of Fluid Dynamics, David L. Lawrence Convention Center, Pittsburgh, Pennsylvania, Sunday, 24 November 2013, Room 333); “BYU engineers study male urine ‘splashback’,” Salt Lake Tribune, 7 November 2013; and “Physicists probe urination ‘splashback’ problem,” BBC, 6 November 2013