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, ...

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.

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 ...