Navier-Stokes equations

Navier-Stokes equations : "Navier-Stokes equations
The Navier-Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, are a set of equations that describe the motion of fluid substances like liquids and gases. These equations establish that changes in momentum (acceleration) of the particles of a fluid are simply the product of changes in pressure and dissipative viscous forces (similar to friction) acting inside the fluid. These viscous forces originate in molecular interactions and dictate how sticky (viscous) a fluid is. Thus, the Navier-Stokes equations are a dynamical statement of the balance of forces acting at any given region of the fluid.
They are one of the most useful sets of equations because they describe the physics of a large number of phenomena of academic and economic interest. They are useful to model weather, ocean currents, water flow in a pipe, motion of stars inside a galaxy, flow around an airfoil (wing). They are also used in the design of aircraft and cars, the study of blood flow, the design of power stations, the analysis of the effects of pollution, etc.
The Navier-Stokes equations are differential equations which describe the motion of a fluid. These equations, unlike algebraic equations, do not seek to establish a relation among the variables of interest (e.g. velocity and pressure), rather they establish relations among the rates of change or fluxes of these quantities. In mathematical terms "
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