Differential Equations and Urine
looorg writes:
Urinals have had the same or a similar design since its invention or introduction. Sometimes it leaves things to be desired, that or the aim of the people using them. New designs promises to lower water consumption and collect more, or lead to less spillage. By changing the geometry. Lets hope it's not piss-poor-math.
"Splash-free urinals for global sustainability and accessibility: Design through physics and differential equations "
We theoretically predict and experimentally validate that when the impinging angle is below an invariant critical value of ~30, the flow rate of splashback under human urination conditions can be significantly suppressed. We propose novel urinal designs that were generated by solving differential equations derived from the isogonal curve problem to ensure the urine stream impacts at or below this critical angle. Experiments validate that these designs can substantially reduce splashback to only 1.4% of the splash of a common contemporary commercial urinal.
https://academic.oup.com/pnasnexus/article/4/4/pgaf087/8098745?login=false
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