Circular hydraulic jump not caused by gravity

A FLUID mechanics phenomenon commonly seen when tap water hits a sink, and first observed by Leonardo da Vinci, has finally been explained as being caused by surface tension and viscosity, and not gravity as previously thought.

When a fast-flowing liquid is abruptly slowed, the fluid suddenly increases in height. This phenomenon is known as a hydraulic jump and was first documented by Leonardo da Vinci in the 1500s. It can be observed at dams and in river rapids, but is most commonly seen in the kitchen sink when the water from the tap spreads out radially in a thin film before the water height suddenly increases.

Since the 1820s, it was believed that the hydraulic jump could be partially explained using gravity, but researchers at the University of Cambridge have now proven that gravity plays no part in the circular hydraulic jumps of thin liquid films. They fired jets of water downwards, upwards, and sideways onto flat surfaces, and saw that the radius of the hydraulic jump was the same in all cases for the same fluid and flow rate.

“If the hydraulic jump happens due to gravity, then when you change the orientation of the surface, you should see a completely different shape,” said Rajesh Bhagat, a chemical engineering PhD student, and lead author on the paper. “This experiment unequivocally disproves the previous gravity-based theories.”

In order to understand the conditions creating the hydraulic jump, the team varied the surface tension and viscosity of the flow by using different water-alcohol solutions and a surfactant. They found that lowering the surface tension increases the radius of the jump, while increasing the viscosity reduces the radius. These experiments were in excellent agreement with their models, but only when gravity was excluded, showing that surface tension and viscosity are the main factors behind the hydraulic jump.

Paul Linden, director of research at the department of applied mathematics and theoretical physics and an author of the paper, said: “Bhagat’s experiments and theory show that the surface tension of the liquid is the key to the process and has this has never before been recognised even though the problem was discussed by da Vinci and many others since. This work represents a remarkable achievement in our understanding of the dynamics of thin layers of fluid."

As heat transfer and energy loss occur within the radius of the jump, understanding exactly how the process works has the potential to improve efficiency in water use in industry and households. “Knowing how to manipulate the boundary of a hydraulic jump is very important and now with this theory we can easily extend or reduce the boundary,” said Bhagat. “The new theory is already being used in practical work in the chemical engineering department. People can use this theory to find new ways to clean everything from cars to factory equipment.”

Journal of Fluid Mechanics http://doi.org/csvf