For more than 250 years, mathematicians have wondered if the Euler equations might sometimes fail to describe a fluid’s flow. A new computer-assisted proof marks a major breakthrough in that quest.

points 1 and 2 lie on a streamline, the fluid has constant density, the flow is steady, and there is no friction. Although these restrictions sound severe, the Bernoulli equation is very useful, ...

Nearly 200 years ago, the physicists Claude-Louis Navier and George Gabriel Stokes put the finishing touches on a set of equations that describe how fluids swirl. And for nearly 200 years, the ...

Tests of a proposed friction-factor equation have shown it to be accurate for calculating pressure loss in turbulent flow for a pipeline transporting a non-Newtonian fluid, such as most crude oils and ...