Epic
Navier–Stokes equations
Equations of motion for viscous fluids
Navier–Stokes equations
The Navier–Stokes equations ( nav-YAY STOHKS) describe the motion of viscous fluids. This system of partial differential equations was named after Claude-Louis Navier and George Gabriel Stokes, who developed them over a few decades of progressive work, from 1822 (Navier) to 1842–1850 (Stokes). Siméon Denis Poisson independently achieved the same results. The Navier–Stokes equations mathematically express momentum balance for Newtonian fluids and make use of the conservation of mass. They are sometimes accompanied by an equation of state relating pressure, temperature and density. They arise from applying Newton's second law to fluid motion, together with the assumption that the stress in the fluid is the sum of a diffusing viscous term (proportional to the gradient of velocity) and a pressure term—hence describing viscous flow. The Navier–Stokes equations generalize the Euler equations which only consider inviscid flow. The Navier–Stokes equations are of great scientific and engineering...
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