Scientific progress is not usually straightforward. Researchers pursue and abandon lines of inquiry. Results languish. Theories take decades to cohere. But sometimes the accumulation of scientific ...

The Navier-Stokes equations capture in a few succinct terms one of the most ubiquitous features of the physical world: the flow of fluids. The equations, which date to the 1820s, are today used to ...

The famed Navier-Stokes equations can lead to cases where more than one result is possible, but only in an extremely narrow set of situations. For nearly two centuries, all kinds of researchers ...

In some form or another, they have been invoked to study how bacteria swim and how airplanes fly. The equations have been found to be able to handle fluid flow at the molecular level with as much ...

The Navier-Stokes equations represent a cornerstone of fluid dynamics, providing a mathematical framework to describe the motion of viscous fluids. These nonlinear partial differential equations ...

For centuries, mathematicians have sought to understand and model the motion of fluids. The equations that describe how ripples crease the surface of a pond have also helped researchers to predict the ...

SIAM Journal on Numerical Analysis, Vol. 28, No. 6 (Dec., 1991), pp. 1523-1547 (25 pages) The isentropic Navier-Stokes equations at low Mach numbers describe almost incompressible flow. By a variable ...

Stochastic fluid dynamics extends classical fluid mechanics by incorporating randomness and uncertainty directly into the governing equations. This approach utilises stochastic differential equations ...

Chezy and Manning developed equations that are used to determine the average volumetric flowrate in open channels. This article explains a laboratory method that was developed and tested to further ...

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 ...