When a fluid is in motion, it must move in such a way that mass is conserved. To see how mass conservation places restrictions on the velocity field, consider the steady flow of fluid through a duct ...

Drew, an oceanography graduate student, writes: “This, on my leg, is the incompressible form of the conservation of mass equation in a fluid, also known as the continuity equation. When people ask ...

Editor’s note: The Basics department this month is an excerpt from the ISA book Flow of Industrial Fluids – Theory and Equations by Raymond Mulley. Some material in this section may seem self-evident ...

The study of free boundary problems in the Navier-Stokes equations addresses the subtle interplay between the dynamics of viscous, incompressible fluids and the evolution of interfaces whose locations ...

An in-depth understanding of the flow physics and the skills of mathematically analysing the fluid flow problems are important attributes of mechanical engineers and future scientific leaders. These ...

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.

For centuries, mathematicians have tried to prove that Euler’s fluid equations can produce nonsensical answers. A new approach to machine learning has researchers betting that “blowup” is near. For ...