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The derivation of the Navier–Stokes equations as well as their application and formulation for different families of fluids, is an important exercise in fluid dynamics with applications in mechanical engineering, physics, chemistry, heat transfer, and electrical engineering.
The Navier–Stokes equations, even when written explicitly for specific fluids, are rather generic in nature and their proper application to specific problems can be very diverse. This is partly because there is an enormous variety of problems that may be modeled, ranging from as simple as the distribution of static pressure to as complicated ...
The Navier–Stokes existence and smoothness problem concerns the mathematical properties of solutions to the Navier–Stokes equations, a system of partial differential equations that describe the motion of a fluid in space. Solutions to the Navier–Stokes equations are used in many practical applications.
The equation of motion for Stokes flow can be obtained by linearizing the steady state Navier–Stokes equations.The inertial forces are assumed to be negligible in comparison to the viscous forces, and eliminating the inertial terms of the momentum balance in the Navier–Stokes equations reduces it to the momentum balance in the Stokes equations: [1]
Navier–Stokes equation and the continuity equation [ edit ] In order to analytically find the stability of fluid flows, it is useful to note that hydrodynamic stability has a lot in common with stability in other fields, such as magnetohydrodynamics , plasma physics and elasticity ; although the physics is different in each case, the ...
In fluid dynamics, Stokes' law gives the frictional force – also called drag force – exerted on spherical objects moving at very small Reynolds numbers in a viscous fluid. [1] It was derived by George Gabriel Stokes in 1851 by solving the Stokes flow limit for small Reynolds numbers of the Navier–Stokes equations. [2]
This solution will not depend upon the function . If this is used for the above equation consisting of Navier stokes equation and continuity equations with time derivative of pressure, then the solution will be same as the stationary solution of the original Navier Stoke problem. This process also introduce the new term artificial time as t→∞.
The Navier–Stokes equations (named after Claude-Louis Navier and George Gabriel Stokes) are differential equations that describe the force balance at a given point within a fluid. For an incompressible fluid with vector velocity field , the Navier–Stokes equations are [13] [14] [15] [16]