What is the significance of Navier-Stokes equation?
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The Navier–Stokes equations are useful because they describe the physics of many phenomena of scientific and engineering interest. They may be used to model the weather, ocean currents, water flow in a pipe and air flow around a wing.
What is Stokes law and factor involved in Stokes law?
In Stokes’s law, the drag force F acting upward in resistance to the fall is equal to 6πrηv, in which r is the radius of the sphere, η is the viscosity of the liquid, and v is the velocity of fall. …
There are three kinds of forces important to fluid mechanics: gravity (body force), pressure forces, and viscous forces (due to friction). Gravity force, Body forces act on the entire element, rather than merely at its surfaces.
What is Navier-Stokes equation derive it?
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.
What is Stokes law for settling velocity?
According to Stokes’ law, the particle sedimentation velocity is proportional to the density difference between the solid phase and the liquid phase, inversely proportional to the viscosity of the liquid, and proportional to the square of particle diameter.
What is Stokes law derive the relation by the method of dimension?
Answer: Stokes law defines the force required to move a sphere through a given viscous fluid at a low uniform velocity is directly proportional to the velocity and radius of the sphere. We can calculate the viscous F on the sphere by dimensional analysis.
The strain rate is related to the constant viscosity tensor that does not depend upon the stress and velocity of the flow. Thus, the relationship is linear and isotropic. 9. What is the incompressibility condition in Navier-Stokes equation? a) ∇.u=0.
What is Navier Stokes equation derive it?
Partial results The Navier–Stokes problem in two dimensions was solved by the 1960s: there exist smooth and globally defined solutions. is sufficiently small then the statement is true: there are smooth and globally defined solutions to the Navier–Stokes equations.