Engineering with simple math: From urinals in restrooms to diagnostics in fluid mechanics labs
University of Waterloo
Abstract
We present distinct research projects that demonstrate how simple mathematics can provide solutions to engineering problems. In the first part, we solve isogonal curve problem to design splashless urinals, which are a staple of public spaces yet their designs have remained essentially stagnant for over a century. Our experiments confirm that the new designs reduce splashback to 1.4% of that produced by a “standard” commercial urinal. Broad adoption of these designs could significantly conserve human resources and water, delivering large-scale benefits for sustainability, hygiene, and accessibility. In the second part, we turn to the well-posedness analysis of elliptic equations and least squares to resolve a longstanding misconception in flow diagnostics: that the omnidirectional integration method (ODI) invented by Liu and Katz (2006) for pressure field reconstruction from image velocimetry is fundamentally different and superior to the pressure Poisson equation (PPE) based methods. We show that ODI and PPE are equivalent, clarifying two decades of misunderstanding in the field, while unveiling their shared limitations and inspiring potential improvement.
About the speaker
Dr. Zhao Pan is an Associate Professor of Mechanical and Mechatronics Engineering at the University of Waterloo, Canada. He earned his Ph.D. from Brigham Young University in 2016 and was a postdoctoral fellow at the Florida Center for Advanced Aero-Propulsion and Utah State University before joining Waterloo in 2019. His interdisciplinary research spans flow diagnostics, data assimilation, and the physics of droplets, bubbles, and granular flows.
