Search results
Results from the WOW.Com Content Network
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 (/ n æ v ˈ j eɪ s t oʊ k s / nav-YAY STOHKS) are partial differential equations which describe the motion of viscous fluid substances. They were named after French engineer and physicist Claude-Louis Navier and the Irish physicist and mathematician George Gabriel Stokes. They were developed over several decades ...
The basic tool required for the derivation of the RANS equations from the instantaneous Navier–Stokes equations is the Reynolds decomposition.Reynolds decomposition refers to separation of the flow variable (like velocity ) into the mean (time-averaged) component (¯) and the fluctuating component (′).
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]
From the Womersley number it can be shown that the transient inertia force is represented by , and from the last term in the non-modified Navier-Stokes equation that viscous force is represented by (subscript one indicates that the boundary layer thickness is that of the transient boundary layer).
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]
Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasmas) and the forces on them. [1]: 3 It has applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical, and biomedical engineering, as well as geophysics, oceanography, meteorology, astrophysics, and biology.
The full problem of viscous flow, described by the non-linear Navier–Stokes equations, is in general not mathematically solvable. However, using his hypothesis (and backed up by experiments) Prandtl was able to derive an approximate model for the flow inside the boundary layer, called boundary-layer theory ; while the flow outside the ...