Question

Define Navier-Stokes equation with derivation

Answer 1

Answer:

Navier-Stokes equation, in fluid mechanics, a partial differential equation that describes the flow of incompressible fluids. The equation is a generalization of the equation devised by Swiss mathematician Leonhard Euler in the 18th century to describe the flow of incompressible and frictionless fluids.

Answer 2

Answer:

The Navier-Stokes equations, developed by Claude-Louis Navier and George Gabriel Stokes in 1822, are equa- tions which can be used to determine the velocity vector field that applies to a fluid, given some initial conditions.

The derivation of the Navier–Stokes equation involves the consideration of forces acting on fluid elements, so that a quantity called the stress tensor appears naturally in the Cauchy momentum equation.

General Form of the Navier-Stokes Equation

Denoting the stress deviator tensor as T, we can make the substitution σ=−pI+T. Substituting this into the previous equation, we arrive at the most general form of the Navier-Stokes equation: ρD→vDt=−∇p+∇⋅T+→f.